TSTP Solution File: ITP386_1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP386_1 : TPTP v8.2.0. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 : Mon May 20 22:26:51 EDT 2024
% Result : Theorem 11.21s 4.28s
% Output : Refutation 11.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 156
% Syntax : Number of formulae : 196 ( 34 unt; 118 typ; 0 def)
% Number of atoms : 175 ( 147 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 667 ( 22 ~; 0 |; 35 &; 548 @)
% ( 14 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 92 ( 91 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 8 con; 0-2 aty)
% Number of variables : 204 ( 0 ^ 180 !; 24 ?; 204 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'B_b_option_fun_b_b_option_fun_fun$\'_type',type,
'\'B_b_option_fun_b_b_option_fun_fun$\'': $tType ).
thf('\'B_b_option_fun_b_option_fun$\'_type',type,
'\'B_b_option_fun_b_option_fun$\'': $tType ).
thf('\'A_option_c_option_fun$\'_type',type,
'\'A_option_c_option_fun$\'': $tType ).
thf('\'A_a_option_fun_c_c_option_fun_fun$\'_type',type,
'\'A_a_option_fun_c_c_option_fun_fun$\'': $tType ).
thf('\'A_c_fun$\'_type',type,
'\'A_c_fun$\'': $tType ).
thf('\'C_c_option_fun$\'_type',type,
'\'C_c_option_fun$\'': $tType ).
thf('\'C_option$\'_type',type,
'\'C_option$\'': $tType ).
thf('\'C_c_option_fun_a_a_option_fun_fun$\'_type',type,
'\'C_c_option_fun_a_a_option_fun_fun$\'': $tType ).
thf('\'B_option$\'_type',type,
'\'B_option$\'': $tType ).
thf('\'B_option_c_option_bool_fun_fun$\'_type',type,
'\'B_option_c_option_bool_fun_fun$\'': $tType ).
thf('\'B_b_fun$\'_type',type,
'\'B_b_fun$\'': $tType ).
thf('\'B_c_c_option_fun_fun$\'_type',type,
'\'B_c_c_option_fun_fun$\'': $tType ).
thf('\'C_c_c_fun_fun$\'_type',type,
'\'C_c_c_fun_fun$\'': $tType ).
thf('\'C_c_fun$\'_type',type,
'\'C_c_fun$\'': $tType ).
thf('\'B_option_b_option_fun$\'_type',type,
'\'B_option_b_option_fun$\'': $tType ).
thf('\'B_c_option_fun$\'_type',type,
'\'B_c_option_fun$\'': $tType ).
thf('\'C_a_option_fun$\'_type',type,
'\'C_a_option_fun$\'': $tType ).
thf('\'C_option_set$\'_type',type,
'\'C_option_set$\'': $tType ).
thf('\'C_a_fun$\'_type',type,
'\'C_a_fun$\'': $tType ).
thf('\'C_option_c_option_bool_fun_fun$\'_type',type,
'\'C_option_c_option_bool_fun_fun$\'': $tType ).
thf('\'A_option_bool_fun$\'_type',type,
'\'A_option_bool_fun$\'': $tType ).
thf('\'B_option_b_fun$\'_type',type,
'\'B_option_b_fun$\'': $tType ).
thf('\'C_option_c_fun$\'_type',type,
'\'C_option_c_fun$\'': $tType ).
thf('\'C_option_a_option_bool_fun_fun$\'_type',type,
'\'C_option_a_option_bool_fun_fun$\'': $tType ).
thf('\'B_b_b_option_fun_fun$\'_type',type,
'\'B_b_b_option_fun_fun$\'': $tType ).
thf('\'C_b_option_fun$\'_type',type,
'\'C_b_option_fun$\'': $tType ).
thf('\'B$\'_type',type,
'\'B$\'': $tType ).
thf('\'C_c_option_fun_b_b_option_fun_fun$\'_type',type,
'\'C_c_option_fun_b_b_option_fun_fun$\'': $tType ).
thf('\'C_option_b_option_bool_fun_fun$\'_type',type,
'\'C_option_b_option_bool_fun_fun$\'': $tType ).
thf('\'A_a_option_fun_b_b_option_fun_fun$\'_type',type,
'\'A_a_option_fun_b_b_option_fun_fun$\'': $tType ).
thf('\'A_a_sum_a_fun$\'_type',type,
'\'A_a_sum_a_fun$\'': $tType ).
thf('\'C$\'_type',type,
'\'C$\'': $tType ).
thf('\'A_option_b_option_fun$\'_type',type,
'\'A_option_b_option_fun$\'': $tType ).
thf('\'B_option_c_option_fun$\'_type',type,
'\'B_option_c_option_fun$\'': $tType ).
thf('\'C_b_b_fun_fun$\'_type',type,
'\'C_b_b_fun_fun$\'': $tType ).
thf('\'C_c_c_option_fun_fun$\'_type',type,
'\'C_c_c_option_fun_fun$\'': $tType ).
thf('\'C_b_fun$\'_type',type,
'\'C_b_fun$\'': $tType ).
thf('\'B_b_sum_c_option_fun$\'_type',type,
'\'B_b_sum_c_option_fun$\'': $tType ).
thf('\'A_option$\'_type',type,
'\'A_option$\'': $tType ).
thf('\'A_a_option_fun_a_a_option_fun_fun$\'_type',type,
'\'A_a_option_fun_a_a_option_fun_fun$\'': $tType ).
thf('\'A_option_c_option_bool_fun_fun$\'_type',type,
'\'A_option_c_option_bool_fun_fun$\'': $tType ).
thf('\'B_a_fun$\'_type',type,
'\'B_a_fun$\'': $tType ).
thf('\'C_option_b_option_fun$\'_type',type,
'\'C_option_b_option_fun$\'': $tType ).
thf(tlbool_type,type,
tlbool: $tType ).
thf('\'A_option_a_fun$\'_type',type,
'\'A_option_a_fun$\'': $tType ).
thf('\'A_a_option_fun$\'_type',type,
'\'A_a_option_fun$\'': $tType ).
thf('\'A_option_a_option_fun$\'_type',type,
'\'A_option_a_option_fun$\'': $tType ).
thf('\'A_bool_fun$\'_type',type,
'\'A_bool_fun$\'': $tType ).
thf('\'C_option_a_option_fun$\'_type',type,
'\'C_option_a_option_fun$\'': $tType ).
thf('\'A_set$\'_type',type,
'\'A_set$\'': $tType ).
thf('\'B_b_option_fun_c_c_option_fun_fun$\'_type',type,
'\'B_b_option_fun_c_c_option_fun_fun$\'': $tType ).
thf('\'C_bool_fun$\'_type',type,
'\'C_bool_fun$\'': $tType ).
thf('\'A_b_fun$\'_type',type,
'\'A_b_fun$\'': $tType ).
thf('\'B_c_c_fun_fun$\'_type',type,
'\'B_c_c_fun_fun$\'': $tType ).
thf('\'B_set$\'_type',type,
'\'B_set$\'': $tType ).
thf('\'B_option_a_option_bool_fun_fun$\'_type',type,
'\'B_option_a_option_bool_fun_fun$\'': $tType ).
thf('\'Bool_c_option_fun$\'_type',type,
'\'Bool_c_option_fun$\'': $tType ).
thf('\'A$\'_type',type,
'\'A$\'': $tType ).
thf('\'B_option_option$\'_type',type,
'\'B_option_option$\'': $tType ).
thf('\'Bool_b_option_fun$\'_type',type,
'\'Bool_b_option_fun$\'': $tType ).
thf('\'A_b_b_option_fun_fun$\'_type',type,
'\'A_b_b_option_fun_fun$\'': $tType ).
thf('\'A_b_option_fun$\'_type',type,
'\'A_b_option_fun$\'': $tType ).
thf('\'C_c_sum_c_option_fun$\'_type',type,
'\'C_c_sum_c_option_fun$\'': $tType ).
thf('\'Bool_bool_fun$\'_type',type,
'\'Bool_bool_fun$\'': $tType ).
thf('\'B_a_option_fun$\'_type',type,
'\'B_a_option_fun$\'': $tType ).
thf('\'A_a_a_fun_fun$\'_type',type,
'\'A_a_a_fun_fun$\'': $tType ).
thf('\'B_b_option_fun_a_a_option_fun_fun$\'_type',type,
'\'B_b_option_fun_a_a_option_fun_fun$\'': $tType ).
thf('\'C_option_c_option_fun$\'_type',type,
'\'C_option_c_option_fun$\'': $tType ).
thf('\'A_a_fun$\'_type',type,
'\'A_a_fun$\'': $tType ).
thf('\'B_b_sum_b_option_fun$\'_type',type,
'\'B_b_sum_b_option_fun$\'': $tType ).
thf('\'B_b_b_fun_fun$\'_type',type,
'\'B_b_b_fun_fun$\'': $tType ).
thf('\'B_b_option_fun$\'_type',type,
'\'B_b_option_fun$\'': $tType ).
thf('\'C_option_option$\'_type',type,
'\'C_option_option$\'': $tType ).
thf('\'A_option_b_option_bool_fun_fun$\'_type',type,
'\'A_option_b_option_bool_fun_fun$\'': $tType ).
thf('\'C_c_sum_c_fun$\'_type',type,
'\'C_c_sum_c_fun$\'': $tType ).
thf('\'A_a_sum_b_option_fun$\'_type',type,
'\'A_a_sum_b_option_fun$\'': $tType ).
thf('\'A_a_option_fun_a_option_fun$\'_type',type,
'\'A_a_option_fun_a_option_fun$\'': $tType ).
thf('\'C_option_bool_fun$\'_type',type,
'\'C_option_bool_fun$\'': $tType ).
thf('\'A_option_a_option_bool_fun_fun$\'_type',type,
'\'A_option_a_option_bool_fun_fun$\'': $tType ).
thf('\'C_c_option_fun_c_option_fun$\'_type',type,
'\'C_c_option_fun_c_option_fun$\'': $tType ).
thf('\'A_b_b_fun_fun$\'_type',type,
'\'A_b_b_fun_fun$\'': $tType ).
thf('\'C_c_option_fun_c_c_option_fun_fun$\'_type',type,
'\'C_c_option_fun_c_c_option_fun_fun$\'': $tType ).
thf('\'B_option_bool_fun$\'_type',type,
'\'B_option_bool_fun$\'': $tType ).
thf('\'B_option_a_option_fun$\'_type',type,
'\'B_option_a_option_fun$\'': $tType ).
thf('\'B_c_fun$\'_type',type,
'\'B_c_fun$\'': $tType ).
thf('\'C_set$\'_type',type,
'\'C_set$\'': $tType ).
thf('\'B_option_b_option_bool_fun_fun$\'_type',type,
'\'B_option_b_option_bool_fun_fun$\'': $tType ).
thf('\'B_bool_fun$\'_type',type,
'\'B_bool_fun$\'': $tType ).
thf('\'A_c_option_fun$\'_type',type,
'\'A_c_option_fun$\'': $tType ).
thf('\'B_option_set$\'_type',type,
'\'B_option_set$\'': $tType ).
thf('\'B_b_sum_b_fun$\'_type',type,
'\'B_b_sum_b_fun$\'': $tType ).
thf('\'none$a\'_type',type,
'\'none$a\'': '\'B_option$\'' ).
thf('\'some$a\'_type',type,
'\'some$a\'': '\'C_c_option_fun$\'' ).
thf('\'bind$b\'_type',type,
'\'bind$b\'': '\'B_option$\'' > '\'B_c_option_fun$\'' > '\'C_option$\'' ).
thf('\'g$\'_type',type,
'\'g$\'': '\'B_b_option_fun_c_c_option_fun_fun$\'' ).
thf('\'none$\'_type',type,
'\'none$\'': '\'C_option$\'' ).
thf('\'map_option$d\'_type',type,
'\'map_option$d\'': '\'B_c_fun$\'' > '\'B_option_c_option_fun$\'' ).
thf('\'fun_app$an\'_type',type,
'\'fun_app$an\'': '\'B_option_c_option_fun$\'' > '\'B_option$\'' > '\'C_option$\'' ).
thf('\'some$\'_type',type,
'\'some$\'': '\'B_b_option_fun$\'' ).
thf('\'uvg$\'_type',type,
'\'uvg$\'': '\'B_c_fun$\'' > '\'B_c_option_fun$\'' ).
thf('\'thesis$\'_type',type,
'\'thesis$\'': $o ).
thf('\'uwc$\'_type',type,
'\'uwc$\'': '\'C_c_option_fun$\'' ).
thf('\'preregister$b\'_type',type,
'\'preregister$b\'': '\'B_b_option_fun_c_c_option_fun_fun$\'' > $o ).
thf('\'fun_app$k\'_type',type,
'\'fun_app$k\'': '\'C_c_fun$\'' > '\'C$\'' > '\'C$\'' ).
thf('\'fun_app$n\'_type',type,
'\'fun_app$n\'': '\'B_c_option_fun$\'' > '\'B$\'' > '\'C_option$\'' ).
thf('\'fun_app$am\'_type',type,
'\'fun_app$am\'': '\'B_b_option_fun_c_c_option_fun_fun$\'' > '\'B_b_option_fun$\'' > '\'C_c_option_fun$\'' ).
thf('\'valid_getter_setter$\'_type',type,
'\'valid_getter_setter$\'': '\'C_b_fun$\'' > '\'B_c_c_fun_fun$\'' > $o ).
thf('\'case_option$c\'_type',type,
'\'case_option$c\'': '\'C_option$\'' > '\'B_c_option_fun$\'' > '\'B_option_c_option_fun$\'' ).
thf('\'register_from_getter_setter$a\'_type',type,
'\'register_from_getter_setter$a\'': '\'C_b_fun$\'' > '\'B_c_c_fun_fun$\'' > '\'B_b_option_fun_c_c_option_fun_fun$\'' ).
thf('\'register$a\'_type',type,
'\'register$a\'': '\'B_b_option_fun_c_c_option_fun_fun$\'' > $o ).
thf('\'fun_app$y\'_type',type,
'\'fun_app$y\'': '\'B_c_c_fun_fun$\'' > '\'B$\'' > '\'C_c_fun$\'' ).
thf('\'fun_app$m\'_type',type,
'\'fun_app$m\'': '\'C_b_fun$\'' > '\'C$\'' > '\'B$\'' ).
thf('\'uuu$\'_type',type,
'\'uuu$\'': '\'B_c_c_option_fun_fun$\'' > '\'C$\'' > '\'B_c_option_fun$\'' ).
thf('\'uu$\'_type',type,
'\'uu$\'': '\'B_c_c_fun_fun$\'' > '\'C$\'' > '\'B_c_option_fun$\'' ).
thf('\'fun_app$w\'_type',type,
'\'fun_app$w\'': '\'B_c_c_option_fun_fun$\'' > '\'B$\'' > '\'C_c_option_fun$\'' ).
thf('\'fun_app$j\'_type',type,
'\'fun_app$j\'': '\'C_c_option_fun$\'' > '\'C$\'' > '\'C_option$\'' ).
thf('\'fun_app$g\'_type',type,
'\'fun_app$g\'': '\'B_b_option_fun$\'' > '\'B$\'' > '\'B_option$\'' ).
thf('\'fun_app$o\'_type',type,
'\'fun_app$o\'': '\'B_c_fun$\'' > '\'B$\'' > '\'C$\'' ).
thf(28,axiom,
! [A: '\'C$\''] :
( ( '\'fun_app$j\'' @ '\'uwc$\'' @ A )
= '\'none$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom60) ).
thf(174,plain,
! [A: '\'C$\''] :
( ( '\'fun_app$j\'' @ '\'uwc$\'' @ A )
= '\'none$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10,axiom,
! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
( ( '\'register$a\'' @ A )
<=> ? [B: '\'C_b_fun$\'',C: '\'B_c_c_fun_fun$\''] :
( ( A
= ( '\'register_from_getter_setter$a\'' @ B @ C ) )
& ( '\'valid_getter_setter$\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom136) ).
thf(78,plain,
! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
( ( ( '\'register$a\'' @ A )
=> ? [B: '\'C_b_fun$\'',C: '\'B_c_c_fun_fun$\''] :
( ( A
= ( '\'register_from_getter_setter$a\'' @ B @ C ) )
& ( '\'valid_getter_setter$\'' @ B @ C ) ) )
& ( ? [B: '\'C_b_fun$\'',C: '\'B_c_c_fun_fun$\''] :
( ( A
= ( '\'register_from_getter_setter$a\'' @ B @ C ) )
& ( '\'valid_getter_setter$\'' @ B @ C ) )
=> ( '\'register$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [A: '\'B_option$\''] :
( ! [B: '\'B$\''] :
( A
!= ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
<=> ( A = '\'none$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom83) ).
thf(121,plain,
! [A: '\'B_option$\''] :
( ( ! [B: '\'B$\''] :
( A
!= ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
=> ( A = '\'none$a\'' ) )
& ( ( A = '\'none$a\'' )
=> ! [B: '\'B$\''] :
( A
!= ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(24,axiom,
! [A: '\'B_c_fun$\'',B: '\'B$\''] :
( ( '\'fun_app$n\'' @ ( '\'uvg$\'' @ A ) @ B )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ ( '\'fun_app$o\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom15) ).
thf(160,plain,
! [A: '\'B_c_fun$\'',B: '\'B$\''] :
( ( '\'fun_app$n\'' @ ( '\'uvg$\'' @ A ) @ B )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ ( '\'fun_app$o\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(39,axiom,
! [A: '\'B_c_c_fun_fun$\'',B: '\'C_b_fun$\''] :
( ( ! [C: '\'B_b_option_fun$\'',D: '\'C$\''] :
( ( '\'fun_app$j\'' @ ( '\'fun_app$am\'' @ '\'g$\'' @ C ) @ D )
= ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uu$\'' @ A @ D ) ) @ ( '\'fun_app$g\'' @ C @ ( '\'fun_app$m\'' @ B @ D ) ) ) )
& ( '\'valid_getter_setter$\'' @ B @ A ) )
=> '\'thesis$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis73) ).
thf(229,plain,
! [A: '\'B_c_c_fun_fun$\'',B: '\'C_b_fun$\''] :
( ( ! [C: '\'B_b_option_fun$\'',D: '\'C$\''] :
( ( '\'fun_app$j\'' @ ( '\'fun_app$am\'' @ '\'g$\'' @ C ) @ D )
= ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uu$\'' @ A @ D ) ) @ ( '\'fun_app$g\'' @ C @ ( '\'fun_app$m\'' @ B @ D ) ) ) )
& ( '\'valid_getter_setter$\'' @ B @ A ) )
=> '\'thesis$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(20,axiom,
! [A: '\'B_option$\''] :
( ( A != '\'none$a\'' )
<=> ? [B: '\'B$\''] :
( A
= ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom80) ).
thf(141,plain,
! [A: '\'B_option$\''] :
( ( ( A != '\'none$a\'' )
=> ? [B: '\'B$\''] :
( A
= ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) )
& ( ? [B: '\'B$\''] :
( A
= ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
=> ( A != '\'none$a\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(3,axiom,
! [A: '\'B_option$\'',B: '\'B_option$\'',C: '\'B_c_option_fun$\'',D: '\'B_c_option_fun$\''] :
( ( ( A = B )
& ! [E: '\'B$\''] :
( ( B
= ( '\'fun_app$g\'' @ '\'some$\'' @ E ) )
=> ( ( '\'fun_app$n\'' @ C @ E )
= ( '\'fun_app$n\'' @ D @ E ) ) ) )
=> ( ( '\'bind$b\'' @ A @ C )
= ( '\'bind$b\'' @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom420) ).
thf(41,plain,
! [A: '\'B_option$\'',B: '\'B_option$\'',C: '\'B_c_option_fun$\'',D: '\'B_c_option_fun$\''] :
( ( ( A = B )
& ! [E: '\'B$\''] :
( ( B
= ( '\'fun_app$g\'' @ '\'some$\'' @ E ) )
=> ( ( '\'fun_app$n\'' @ C @ E )
= ( '\'fun_app$n\'' @ D @ E ) ) ) )
=> ( ( '\'bind$b\'' @ A @ C )
= ( '\'bind$b\'' @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
( ( '\'none$\''
= ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B ) )
<=> ( B = '\'none$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom223) ).
thf(59,plain,
! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
( ( ( '\'none$\''
= ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B ) )
=> ( B = '\'none$a\'' ) )
& ( ( B = '\'none$a\'' )
=> ( '\'none$\''
= ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,axiom,
! [A: '\'C_option$\'',B: '\'B_c_option_fun$\''] :
( ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ A @ B ) @ '\'none$a\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom108) ).
thf(187,plain,
! [A: '\'C_option$\'',B: '\'B_c_option_fun$\''] :
( ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ A @ B ) @ '\'none$a\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(29,axiom,
! [A: '\'C_option$\'',B: '\'B_c_option_fun$\'',C: '\'B$\''] :
( ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ A @ B ) @ ( '\'fun_app$g\'' @ '\'some$\'' @ C ) )
= ( '\'fun_app$n\'' @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom102) ).
thf(177,plain,
! [A: '\'C_option$\'',B: '\'B_c_option_fun$\'',C: '\'B$\''] :
( ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ A @ B ) @ ( '\'fun_app$g\'' @ '\'some$\'' @ C ) )
= ( '\'fun_app$n\'' @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(38,axiom,
! [A: '\'C_option$\''] :
( ( A != '\'none$\'' )
<=> ? [B: '\'C$\''] :
( A
= ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom79) ).
thf(222,plain,
! [A: '\'C_option$\''] :
( ( ( A != '\'none$\'' )
=> ? [B: '\'C$\''] :
( A
= ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) ) )
& ( ? [B: '\'C$\''] :
( A
= ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) )
=> ( A != '\'none$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(27,axiom,
! [A: '\'C$\''] :
( '\'none$\''
!= ( '\'fun_app$j\'' @ '\'some$a\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom111) ).
thf(170,plain,
! [A: '\'C$\''] :
( '\'none$\''
!= ( '\'fun_app$j\'' @ '\'some$a\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(36,axiom,
! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
( ( '\'preregister$b\'' @ A )
<=> ? [B: '\'C_b_fun$\'',C: '\'B_c_c_option_fun_fun$\''] :
! [D: '\'B_b_option_fun$\'',E: '\'C$\''] :
( ( '\'fun_app$j\'' @ ( '\'fun_app$am\'' @ A @ D ) @ E )
= ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uuu$\'' @ C @ E ) ) @ ( '\'fun_app$g\'' @ D @ ( '\'fun_app$m\'' @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom173) ).
thf(202,plain,
! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
( ( ( '\'preregister$b\'' @ A )
=> ? [B: '\'C_b_fun$\'',C: '\'B_c_c_option_fun_fun$\''] :
! [D: '\'B_b_option_fun$\'',E: '\'C$\''] :
( ( '\'fun_app$j\'' @ ( '\'fun_app$am\'' @ A @ D ) @ E )
= ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uuu$\'' @ C @ E ) ) @ ( '\'fun_app$g\'' @ D @ ( '\'fun_app$m\'' @ B @ E ) ) ) ) )
& ( ? [B: '\'C_b_fun$\'',C: '\'B_c_c_option_fun_fun$\''] :
! [D: '\'B_b_option_fun$\'',E: '\'C$\''] :
( ( '\'fun_app$j\'' @ ( '\'fun_app$am\'' @ A @ D ) @ E )
= ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uuu$\'' @ C @ E ) ) @ ( '\'fun_app$g\'' @ D @ ( '\'fun_app$m\'' @ B @ E ) ) ) )
=> ( '\'preregister$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(35,axiom,
'\'register$a\'' @ '\'g$\'',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom75) ).
thf(201,plain,
'\'register$a\'' @ '\'g$\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(13,axiom,
! [A: '\'B$\'',B: '\'B$\''] :
( ( ( '\'fun_app$g\'' @ '\'some$\'' @ A )
= ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom97) ).
thf(102,plain,
! [A: '\'B$\'',B: '\'B$\''] :
( ( ( ( '\'fun_app$g\'' @ '\'some$\'' @ A )
= ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( '\'fun_app$g\'' @ '\'some$\'' @ A )
= ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,axiom,
! [A: '\'B_c_fun$\''] :
( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ '\'none$a\'' )
= '\'none$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom278) ).
thf(109,plain,
! [A: '\'B_c_fun$\''] :
( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ '\'none$a\'' )
= '\'none$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(33,axiom,
! [A: '\'C_option$\'',B: '\'C$\''] :
( ( A
= ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) )
=> ( A != '\'none$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom114) ).
thf(193,plain,
! [A: '\'C_option$\'',B: '\'C$\''] :
( ( A
= ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) )
=> ( A != '\'none$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(19,axiom,
! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
( ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
= '\'none$\'' )
<=> ( B = '\'none$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom214) ).
thf(134,plain,
! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
( ( ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
= '\'none$\'' )
=> ( B = '\'none$a\'' ) )
& ( ( B = '\'none$a\'' )
=> ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
= '\'none$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,axiom,
! [A: '\'B_c_c_fun_fun$\'',B: '\'C$\'',C: '\'B$\''] :
( ( '\'fun_app$n\'' @ ( '\'uu$\'' @ A @ B ) @ C )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom49) ).
thf(128,plain,
! [A: '\'B_c_c_fun_fun$\'',B: '\'C$\'',C: '\'B$\''] :
( ( '\'fun_app$n\'' @ ( '\'uu$\'' @ A @ B ) @ C )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(26,axiom,
! [A: '\'B$\''] :
( '\'none$a\''
!= ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom112) ).
thf(166,plain,
! [A: '\'B$\''] :
( '\'none$a\''
!= ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(21,axiom,
! [A: '\'B_option$\'',B: '\'B_option$\'',C: '\'B_c_fun$\'',D: '\'B_c_fun$\''] :
( ( ( A = B )
& ! [E: '\'B$\''] :
( ( B
= ( '\'fun_app$g\'' @ '\'some$\'' @ E ) )
=> ( ( '\'fun_app$o\'' @ C @ E )
= ( '\'fun_app$o\'' @ D @ E ) ) ) )
=> ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ C ) @ A )
= ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom290) ).
thf(148,plain,
! [A: '\'B_option$\'',B: '\'B_option$\'',C: '\'B_c_fun$\'',D: '\'B_c_fun$\''] :
( ( ( A = B )
& ! [E: '\'B$\''] :
( ( B
= ( '\'fun_app$g\'' @ '\'some$\'' @ E ) )
=> ( ( '\'fun_app$o\'' @ C @ E )
= ( '\'fun_app$o\'' @ D @ E ) ) ) )
=> ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ C ) @ A )
= ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(30,axiom,
! [A: '\'C_option$\''] :
( ! [B: '\'C$\''] :
( A
!= ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) )
<=> ( A = '\'none$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom82) ).
thf(180,plain,
! [A: '\'C_option$\''] :
( ( ! [B: '\'C$\''] :
( A
!= ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) )
=> ( A = '\'none$\'' ) )
& ( ( A = '\'none$\'' )
=> ! [B: '\'C$\''] :
( A
!= ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
( ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
= '\'none$\'' )
<=> ( B = '\'none$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom205) ).
thf(71,plain,
! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
( ( ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
= '\'none$\'' )
=> ( B = '\'none$a\'' ) )
& ( ( B = '\'none$a\'' )
=> ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
= '\'none$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: '\'B_option$\'',B: '\'B_option$\'',C: '\'B_c_option_fun$\''] :
( ( A = B )
=> ( ( '\'bind$b\'' @ A @ C )
= ( '\'bind$b\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom387) ).
thf(54,plain,
! [A: '\'B_option$\'',B: '\'B_option$\'',C: '\'B_c_option_fun$\''] :
( ( A = B )
=> ( ( '\'bind$b\'' @ A @ C )
= ( '\'bind$b\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [A: '\'B_option$\'',B: '\'B_c_option_fun$\'',C: '\'C$\''] :
( ( ( '\'bind$b\'' @ A @ B )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) )
<=> ? [D: '\'B$\''] :
( ( A
= ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
& ( ( '\'fun_app$n\'' @ B @ D )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom414) ).
thf(86,plain,
! [A: '\'B_option$\'',B: '\'B_c_option_fun$\'',C: '\'C$\''] :
( ( ( ( '\'bind$b\'' @ A @ B )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) )
=> ? [D: '\'B$\''] :
( ( A
= ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
& ( ( '\'fun_app$n\'' @ B @ D )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) ) ) )
& ( ? [D: '\'B$\''] :
( ( A
= ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
& ( ( '\'fun_app$n\'' @ B @ D )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) ) )
=> ( ( '\'bind$b\'' @ A @ B )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [A: '\'B_option$\'',B: '\'B$\''] :
( ( A
= ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
=> ( A != '\'none$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom115) ).
thf(66,plain,
! [A: '\'B_option$\'',B: '\'B$\''] :
( ( A
= ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
=> ( A != '\'none$a\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(22,axiom,
! [A: '\'B_c_c_option_fun_fun$\'',B: '\'C$\'',C: '\'B$\''] :
( ( '\'fun_app$n\'' @ ( '\'uuu$\'' @ A @ B ) @ C )
= ( '\'fun_app$j\'' @ ( '\'fun_app$w\'' @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom23) ).
thf(155,plain,
! [A: '\'B_c_c_option_fun_fun$\'',B: '\'C$\'',C: '\'B$\''] :
( ( '\'fun_app$n\'' @ ( '\'uuu$\'' @ A @ B ) @ C )
= ( '\'fun_app$j\'' @ ( '\'fun_app$w\'' @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(34,axiom,
! [A: '\'C_b_fun$\'',B: '\'B_c_c_fun_fun$\'',C: '\'B_b_option_fun$\'',D: '\'C$\''] :
( ( '\'fun_app$j\'' @ ( '\'fun_app$am\'' @ ( '\'register_from_getter_setter$a\'' @ A @ B ) @ C ) @ D )
= ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uu$\'' @ B @ D ) ) @ ( '\'fun_app$g\'' @ C @ ( '\'fun_app$m\'' @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom94) ).
thf(198,plain,
! [A: '\'C_b_fun$\'',B: '\'B_c_c_fun_fun$\'',C: '\'B_b_option_fun$\'',D: '\'C$\''] :
( ( '\'fun_app$j\'' @ ( '\'fun_app$am\'' @ ( '\'register_from_getter_setter$a\'' @ A @ B ) @ C ) @ D )
= ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uu$\'' @ B @ D ) ) @ ( '\'fun_app$g\'' @ C @ ( '\'fun_app$m\'' @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(37,axiom,
! [A: '\'C_b_fun$\'',B: '\'B_c_c_fun_fun$\''] :
( ( '\'valid_getter_setter$\'' @ A @ B )
<=> ( ! [C: '\'C$\''] :
( C
= ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ ( '\'fun_app$m\'' @ A @ C ) ) @ C ) )
& ! [C: '\'B$\'',D: '\'C$\''] :
( ( '\'fun_app$m\'' @ A @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ D ) )
= C )
& ! [C: '\'B$\'',D: '\'B$\'',E: '\'C$\''] :
( ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ D ) @ E ) )
= ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom76) ).
thf(209,plain,
! [A: '\'C_b_fun$\'',B: '\'B_c_c_fun_fun$\''] :
( ( ( '\'valid_getter_setter$\'' @ A @ B )
=> ( ! [C: '\'C$\''] :
( C
= ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ ( '\'fun_app$m\'' @ A @ C ) ) @ C ) )
& ! [C: '\'B$\'',D: '\'C$\''] :
( ( '\'fun_app$m\'' @ A @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ D ) )
= C )
& ! [C: '\'B$\'',D: '\'B$\'',E: '\'C$\''] :
( ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ D ) @ E ) )
= ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ E ) ) ) )
& ( ( ! [C: '\'C$\''] :
( C
= ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ ( '\'fun_app$m\'' @ A @ C ) ) @ C ) )
& ! [C: '\'B$\'',D: '\'C$\''] :
( ( '\'fun_app$m\'' @ A @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ D ) )
= C )
& ! [C: '\'B$\'',D: '\'B$\'',E: '\'C$\''] :
( ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ D ) @ E ) )
= ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ E ) ) )
=> ( '\'valid_getter_setter$\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(15,axiom,
! [A: '\'B_c_fun$\'',B: '\'B_option$\'',C: '\'C$\''] :
( ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) )
<=> ? [D: '\'B$\''] :
( ( B
= ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
& ( ( '\'fun_app$o\'' @ A @ D )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom232) ).
thf(112,plain,
! [A: '\'B_c_fun$\'',B: '\'B_option$\'',C: '\'C$\''] :
( ( ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) )
=> ? [D: '\'B$\''] :
( ( B
= ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
& ( ( '\'fun_app$o\'' @ A @ D )
= C ) ) )
& ( ? [D: '\'B$\''] :
( ( B
= ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
& ( ( '\'fun_app$o\'' @ A @ D )
= C ) )
=> ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [A: '\'B_c_option_fun$\''] :
( ( '\'bind$b\'' @ '\'none$a\'' @ A )
= '\'none$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom406) ).
thf(48,plain,
! [A: '\'B_c_option_fun$\''] :
( ( '\'bind$b\'' @ '\'none$a\'' @ A )
= '\'none$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: '\'C$\'',B: '\'C$\''] :
( ( ( '\'fun_app$j\'' @ '\'some$a\'' @ A )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom96) ).
thf(95,plain,
! [A: '\'C$\'',B: '\'C$\''] :
( ( ( ( '\'fun_app$j\'' @ '\'some$a\'' @ A )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( '\'fun_app$j\'' @ '\'some$a\'' @ A )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
'\'thesis$\'',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture72) ).
thf(2,negated_conjecture,
~ '\'thesis$\'',
inference(neg_conjecture,[status(cth)],[1]) ).
thf(40,plain,
~ '\'thesis$\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,axiom,
! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
( ( '\'register$a\'' @ A )
=> ( '\'preregister$b\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom313) ).
thf(158,plain,
! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
( ( '\'register$a\'' @ A )
=> ( '\'preregister$b\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(5,axiom,
! [A: '\'B$\'',B: '\'B_c_option_fun$\''] :
( ( '\'bind$b\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) @ B )
= ( '\'fun_app$n\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom424) ).
thf(51,plain,
! [A: '\'B$\'',B: '\'B_c_option_fun$\''] :
( ( '\'bind$b\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) @ B )
= ( '\'fun_app$n\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,axiom,
! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
= ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uvg$\'' @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom194) ).
thf(190,plain,
! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
= ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uvg$\'' @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(18,axiom,
! [A: '\'B_c_fun$\'',B: '\'B$\''] :
( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ ( '\'fun_app$o\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom287) ).
thf(131,plain,
! [A: '\'B_c_fun$\'',B: '\'B$\''] :
( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
= ( '\'fun_app$j\'' @ '\'some$a\'' @ ( '\'fun_app$o\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(25,axiom,
! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
( ( '\'register$a\'' @ A )
=> ( ( '\'fun_app$am\'' @ A @ '\'some$\'' )
= '\'some$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom92) ).
thf(163,plain,
! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
( ( '\'register$a\'' @ A )
=> ( ( '\'fun_app$am\'' @ A @ '\'some$\'' )
= '\'some$a\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(233,plain,
$false,
inference(cvc4,[status(thm)],[174,78,121,160,229,141,41,59,187,177,222,170,202,201,102,109,193,134,128,166,148,180,71,54,86,66,155,198,209,112,48,95,40,158,51,190,131,163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP386_1 : TPTP v8.2.0. Released v8.0.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n018.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sat May 18 15:50:23 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.29/1.19 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.68/1.87 % [INFO] Parsing done (675ms).
% 3.68/1.89 % [INFO] Running in sequential loop mode.
% 4.82/2.36 % [INFO] eprover registered as external prover.
% 4.82/2.37 % [INFO] cvc4 registered as external prover.
% 4.82/2.37 % [INFO] Scanning for conjecture ...
% 5.48/2.66 % [INFO] Found a conjecture (or negated_conjecture) and 734 axioms. Running axiom selection ...
% 6.26/2.84 % [INFO] Axiom selection finished. Selected 37 axioms (removed 697 axioms).
% 6.87/2.94 % [INFO] Problem is typed first-order (TPTP TFF).
% 6.87/2.95 % [INFO] Type checking passed.
% 6.87/2.96 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 11.21/4.27 % External prover 'cvc4' found a proof!
% 11.21/4.27 % [INFO] Killing All external provers ...
% 11.21/4.28 % Time passed: 3715ms (effective reasoning time: 2381ms)
% 11.21/4.28 % 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)>
% 11.21/4.28 % Axioms used in derivation (37): axiom76, axiom214, axiom173, axiom112, axiom82, axiom232, axiom111, axiom223, hypothesis73, axiom49, axiom92, axiom424, axiom406, axiom115, axiom278, axiom94, axiom83, axiom60, axiom290, axiom108, axiom387, axiom75, axiom80, axiom97, axiom205, axiom79, axiom96, axiom23, axiom313, axiom102, axiom15, axiom114, axiom287, axiom136, axiom414, axiom420, axiom194
% 11.21/4.28 % No. of inferences in proof: 78
% 11.21/4.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3715 ms resp. 2381 ms w/o parsing
% 11.61/4.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.61/4.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------