TSTP Solution File: ITP386_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP386_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.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 : Sun May 5 07:15:12 EDT 2024
% Result : Theorem 5.09s 1.08s
% Output : Refutation 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2899
% Syntax : Number of formulae : 6913 (1744 unt; 736 typ; 0 def)
% Number of atoms : 15973 (6133 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 15686 (5890 ~;5877 |;1803 &)
% (1668 <=>; 439 =>; 0 <=; 9 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 92 ( 91 usr)
% Number of type conns : 1167 ( 578 >; 589 *; 0 +; 0 <<)
% Number of predicates : 1419 (1416 usr;1335 prp; 0-4 aty)
% Number of functors : 562 ( 562 usr; 67 con; 0-4 aty)
% Number of variables : 12579 (11838 !; 741 ?;12579 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'B_b_option_fun_b_b_option_fun_fun$': $tType ).
tff(type_def_6,type,
'B_b_option_fun_b_option_fun$': $tType ).
tff(type_def_7,type,
'A_option_c_option_fun$': $tType ).
tff(type_def_8,type,
'A_a_option_fun_c_c_option_fun_fun$': $tType ).
tff(type_def_9,type,
'A_c_fun$': $tType ).
tff(type_def_10,type,
'C_c_option_fun$': $tType ).
tff(type_def_11,type,
'C_option$': $tType ).
tff(type_def_12,type,
'C_c_option_fun_a_a_option_fun_fun$': $tType ).
tff(type_def_13,type,
'B_option$': $tType ).
tff(type_def_14,type,
'B_option_c_option_bool_fun_fun$': $tType ).
tff(type_def_15,type,
'B_b_fun$': $tType ).
tff(type_def_16,type,
'B_c_c_option_fun_fun$': $tType ).
tff(type_def_17,type,
'C_c_c_fun_fun$': $tType ).
tff(type_def_18,type,
'C_c_fun$': $tType ).
tff(type_def_19,type,
'B_option_b_option_fun$': $tType ).
tff(type_def_20,type,
'B_c_option_fun$': $tType ).
tff(type_def_21,type,
'C_a_option_fun$': $tType ).
tff(type_def_22,type,
'C_option_set$': $tType ).
tff(type_def_23,type,
'C_a_fun$': $tType ).
tff(type_def_24,type,
'C_option_c_option_bool_fun_fun$': $tType ).
tff(type_def_25,type,
'A_option_bool_fun$': $tType ).
tff(type_def_26,type,
'B_option_b_fun$': $tType ).
tff(type_def_27,type,
'C_option_c_fun$': $tType ).
tff(type_def_28,type,
'C_option_a_option_bool_fun_fun$': $tType ).
tff(type_def_29,type,
'B_b_b_option_fun_fun$': $tType ).
tff(type_def_30,type,
'C_b_option_fun$': $tType ).
tff(type_def_31,type,
'B$': $tType ).
tff(type_def_32,type,
'C_c_option_fun_b_b_option_fun_fun$': $tType ).
tff(type_def_33,type,
'C_option_b_option_bool_fun_fun$': $tType ).
tff(type_def_34,type,
'A_a_option_fun_b_b_option_fun_fun$': $tType ).
tff(type_def_35,type,
'A_a_sum_a_fun$': $tType ).
tff(type_def_36,type,
'C$': $tType ).
tff(type_def_37,type,
'A_option_b_option_fun$': $tType ).
tff(type_def_38,type,
'B_option_c_option_fun$': $tType ).
tff(type_def_39,type,
'C_b_b_fun_fun$': $tType ).
tff(type_def_40,type,
'C_c_c_option_fun_fun$': $tType ).
tff(type_def_41,type,
'C_b_fun$': $tType ).
tff(type_def_42,type,
'B_b_sum_c_option_fun$': $tType ).
tff(type_def_43,type,
'A_option$': $tType ).
tff(type_def_44,type,
'A_a_option_fun_a_a_option_fun_fun$': $tType ).
tff(type_def_45,type,
'A_option_c_option_bool_fun_fun$': $tType ).
tff(type_def_46,type,
'B_a_fun$': $tType ).
tff(type_def_47,type,
'C_option_b_option_fun$': $tType ).
tff(type_def_48,type,
tlbool: $tType ).
tff(type_def_49,type,
'A_option_a_fun$': $tType ).
tff(type_def_50,type,
'A_a_option_fun$': $tType ).
tff(type_def_51,type,
'A_option_a_option_fun$': $tType ).
tff(type_def_52,type,
'A_bool_fun$': $tType ).
tff(type_def_53,type,
'C_option_a_option_fun$': $tType ).
tff(type_def_54,type,
'A_set$': $tType ).
tff(type_def_55,type,
'B_b_option_fun_c_c_option_fun_fun$': $tType ).
tff(type_def_56,type,
'C_bool_fun$': $tType ).
tff(type_def_57,type,
'A_b_fun$': $tType ).
tff(type_def_58,type,
'B_c_c_fun_fun$': $tType ).
tff(type_def_59,type,
'B_set$': $tType ).
tff(type_def_60,type,
'B_option_a_option_bool_fun_fun$': $tType ).
tff(type_def_61,type,
'Bool_c_option_fun$': $tType ).
tff(type_def_62,type,
'A$': $tType ).
tff(type_def_63,type,
'B_option_option$': $tType ).
tff(type_def_64,type,
'Bool_b_option_fun$': $tType ).
tff(type_def_65,type,
'A_b_b_option_fun_fun$': $tType ).
tff(type_def_66,type,
'A_b_option_fun$': $tType ).
tff(type_def_67,type,
'C_c_sum_c_option_fun$': $tType ).
tff(type_def_68,type,
'Bool_bool_fun$': $tType ).
tff(type_def_69,type,
'B_a_option_fun$': $tType ).
tff(type_def_70,type,
'A_a_a_fun_fun$': $tType ).
tff(type_def_71,type,
'B_b_option_fun_a_a_option_fun_fun$': $tType ).
tff(type_def_72,type,
'C_option_c_option_fun$': $tType ).
tff(type_def_73,type,
'A_a_fun$': $tType ).
tff(type_def_74,type,
'B_b_sum_b_option_fun$': $tType ).
tff(type_def_75,type,
'B_b_b_fun_fun$': $tType ).
tff(type_def_76,type,
'B_b_option_fun$': $tType ).
tff(type_def_77,type,
'C_option_option$': $tType ).
tff(type_def_78,type,
'A_option_b_option_bool_fun_fun$': $tType ).
tff(type_def_79,type,
'C_c_sum_c_fun$': $tType ).
tff(type_def_80,type,
'A_a_sum_b_option_fun$': $tType ).
tff(type_def_81,type,
'A_a_option_fun_a_option_fun$': $tType ).
tff(type_def_82,type,
'C_option_bool_fun$': $tType ).
tff(type_def_83,type,
'A_option_a_option_bool_fun_fun$': $tType ).
tff(type_def_84,type,
'C_c_option_fun_c_option_fun$': $tType ).
tff(type_def_85,type,
'A_b_b_fun_fun$': $tType ).
tff(type_def_86,type,
'C_c_option_fun_c_c_option_fun_fun$': $tType ).
tff(type_def_87,type,
'B_option_bool_fun$': $tType ).
tff(type_def_88,type,
'B_option_a_option_fun$': $tType ).
tff(type_def_89,type,
'B_c_fun$': $tType ).
tff(type_def_90,type,
'C_set$': $tType ).
tff(type_def_91,type,
'B_option_b_option_bool_fun_fun$': $tType ).
tff(type_def_92,type,
'B_bool_fun$': $tType ).
tff(type_def_93,type,
'A_c_option_fun$': $tType ).
tff(type_def_94,type,
'B_option_set$': $tType ).
tff(type_def_95,type,
'B_b_sum_b_fun$': $tType ).
tff(func_def_0,type,
'register_from_getter_setter$d': ( 'C_c_fun$' * 'C_c_c_fun_fun$' ) > 'C_c_option_fun_c_c_option_fun_fun$' ).
tff(func_def_1,type,
'map_option$c': 'C_c_fun$' > 'C_option_c_option_fun$' ).
tff(func_def_2,type,
'fun_app$ab': ( 'C_c_option_fun_c_option_fun$' * 'C_c_option_fun$' ) > 'C_option$' ).
tff(func_def_3,type,
'comp$aw': ( 'B_option_c_option_fun$' * 'C_b_option_fun$' ) > 'C_c_option_fun$' ).
tff(func_def_4,type,
'uuq$': ( 'C_option_bool_fun$' * 'C_c_option_fun$' ) > 'C_bool_fun$' ).
tff(func_def_5,type,
'comp$ax': 'B_option_b_option_fun$' > 'B_b_option_fun_b_b_option_fun_fun$' ).
tff(func_def_6,type,
'fun_app$ao': ( 'B_a_fun$' * 'B$' ) > 'A$' ).
tff(func_def_7,type,
'combine_options$': ( 'A_a_a_fun_fun$' * 'A_option$' ) > 'A_option_a_option_fun$' ).
tff(func_def_8,type,
'comp$ag': ( 'B_b_fun$' * 'C_b_fun$' ) > 'C_b_fun$' ).
tff(func_def_9,type,
'none$a': 'B_option$' ).
tff(func_def_10,type,
'the$': 'B_option_b_fun$' ).
tff(func_def_11,type,
'collect$c': 'C_option_bool_fun$' > 'C_option_set$' ).
tff(func_def_12,type,
'the$c': 'A_bool_fun$' > 'A$' ).
tff(func_def_13,type,
'comp$an': ( 'C_c_option_fun_c_c_option_fun_fun$' * 'B_b_option_fun_c_c_option_fun_fun$' ) > 'B_b_option_fun_c_c_option_fun_fun$' ).
tff(func_def_14,type,
'some$a': 'C_c_option_fun$' ).
tff(func_def_15,type,
'update1$': ( 'A$' * 'A$' ) > 'A_a_option_fun$' ).
tff(func_def_16,type,
'uuv$': ( 'A_b_b_option_fun_fun$' * 'B$' ) > 'A_b_option_fun$' ).
tff(func_def_17,type,
'uvm$': 'B_b_fun$' ).
tff(func_def_18,type,
'comp$s': ( 'B_a_fun$' * 'A_b_fun$' ) > 'A_a_fun$' ).
tff(func_def_19,type,
'bot$e': 'B_bool_fun$' ).
tff(func_def_20,type,
'comp$z': ( 'B_option_c_option_fun$' * 'C_option_b_option_fun$' ) > 'C_option_c_option_fun$' ).
tff(func_def_21,type,
'fun_app$t': ( 'B_b_b_option_fun_fun$' * 'B$' ) > 'B_b_option_fun$' ).
tff(func_def_22,type,
def_1: ( 'C_bool_fun$' * 'C$' ) > tlbool ).
tff(func_def_23,type,
'case_option$l': ( 'B$' * 'B_option_b_fun$' * 'B_option_option$' ) > 'B$' ).
tff(func_def_24,type,
def_7: ( 'Bool_bool_fun$' * tlbool ) > tlbool ).
tff(func_def_25,type,
'bind$b': ( 'B_option$' * 'B_c_option_fun$' ) > 'C_option$' ).
tff(func_def_26,type,
'map_option$e': 'A_b_fun$' > 'A_option_b_option_fun$' ).
tff(func_def_27,type,
'case_option$d': ( 'B_option$' * 'A_b_option_fun$' ) > 'A_option_b_option_fun$' ).
tff(func_def_28,type,
def_4: ( 'C_bool_fun$' * 'C$' ) > tlbool ).
tff(func_def_29,type,
'register_apply$a': ( 'B_b_option_fun_c_c_option_fun_fun$' * 'B_b_fun$' ) > 'C_c_fun$' ).
tff(func_def_30,type,
'fun_app$ba': ( 'A_option_b_option_bool_fun_fun$' * 'A_option$' ) > 'B_option_bool_fun$' ).
tff(func_def_31,type,
'uur$': 'B$' > 'A_b_option_fun$' ).
tff(func_def_32,type,
def_2: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_33,type,
'uux$': ( 'A_a_a_fun_fun$' * 'A_option$' ) > 'A_a_option_fun$' ).
tff(func_def_34,type,
'comp$t': ( 'C_option_b_option_fun$' * 'C_option_c_option_fun$' ) > 'C_option_b_option_fun$' ).
tff(func_def_35,type,
'map_option$j': ( 'C_option_c_option_fun$' * 'C_option_option$' ) > 'C_option_option$' ).
tff(func_def_36,type,
'fun_app$r': ( 'A_a_fun$' * 'A$' ) > 'A$' ).
tff(func_def_37,type,
'fun_app$bp': ( 'A_a_option_fun_a_option_fun$' * 'A_a_option_fun$' ) > 'A_option$' ).
tff(func_def_38,type,
'fun_upd$b': ( 'B_b_fun$' * 'B$' ) > 'B_b_b_fun_fun$' ).
tff(func_def_39,type,
'comp$be': ( 'A_a_fun$' * 'A_a_fun$' ) > 'A_a_fun$' ).
tff(func_def_40,type,
'uug$': 'B_bool_fun$' ).
tff(func_def_41,type,
'map_option$f': 'A_c_fun$' > 'A_option_c_option_fun$' ).
tff(func_def_42,type,
'comp$aa': ( 'B_c_fun$' * 'C_b_fun$' ) > 'C_c_fun$' ).
tff(func_def_43,type,
'case_option$k': ( 'C$' * 'C_c_fun$' ) > 'C_option_c_fun$' ).
tff(func_def_44,type,
'comp$x': ( 'C_option_b_option_fun$' * 'B_option_c_option_fun$' ) > 'B_option_b_option_fun$' ).
tff(func_def_45,type,
'image$': ( 'C_c_option_fun$' * 'C_set$' ) > 'C_option_set$' ).
tff(func_def_46,type,
'fun_app$ac': ( 'B_b_option_fun_b_option_fun$' * 'B_b_option_fun$' ) > 'B_option$' ).
tff(func_def_47,type,
'register_apply$': ( 'A_a_option_fun_b_b_option_fun_fun$' * 'A_a_fun$' ) > 'B_b_fun$' ).
tff(func_def_48,type,
'bind$d': ( 'A_option$' * 'A_c_option_fun$' ) > 'C_option$' ).
tff(func_def_49,type,
'these$a': 'B_option_set$' > 'B_set$' ).
tff(func_def_50,type,
'g$': 'B_b_option_fun_c_c_option_fun_fun$' ).
tff(func_def_51,type,
'case_sum$': ( 'A_a_fun$' * 'A_a_fun$' ) > 'A_a_sum_a_fun$' ).
tff(func_def_52,type,
'uui$': ( 'B_option_b_option_fun$' * 'A_b_option_fun$' ) > 'A_b_option_fun$' ).
tff(func_def_53,type,
'case_option$i': ( 'A$' * 'A_a_fun$' * 'A_option$' ) > 'A$' ).
tff(func_def_54,type,
'fun_app$d': ( 'C_option_c_option_bool_fun_fun$' * 'C_option$' ) > 'C_option_bool_fun$' ).
tff(func_def_55,type,
'collect$a': 'C_bool_fun$' > 'C_set$' ).
tff(func_def_56,type,
'insert$': ( 'B$' * 'B_set$' ) > 'B_set$' ).
tff(func_def_57,type,
'fun_app$e': ( 'B_option_b_option_bool_fun_fun$' * 'B_option$' ) > 'B_option_bool_fun$' ).
tff(func_def_58,type,
'bind$h': 'A_option$' > 'A_a_option_fun_a_option_fun$' ).
tff(func_def_59,type,
'none$': 'C_option$' ).
tff(func_def_60,type,
'comp$e': ( 'A_a_option_fun$' * 'A_a_fun$' ) > 'A_a_option_fun$' ).
tff(func_def_61,type,
def_12: ( tlbool * 'B_bool_fun$' * 'B_option$' ) > tlbool ).
tff(func_def_62,type,
'fun_app$bn': ( 'C_a_option_fun$' * 'C$' ) > 'A_option$' ).
tff(func_def_63,type,
def_17: ( 'B_bool_fun$' * 'B_option$' ) > tlbool ).
tff(func_def_64,type,
'fun_app$bi': ( 'C_option_a_option_fun$' * 'C_option$' ) > 'A_option$' ).
tff(func_def_65,type,
'uwg$': 'C_option_bool_fun$' ).
tff(func_def_66,type,
'uvs$': 'C_c_fun$' ).
tff(func_def_67,type,
'fun_app$al': ( 'B_option_b_fun$' * 'B_option$' ) > 'B$' ).
tff(func_def_68,type,
'top$a': 'C_set$' ).
tff(func_def_69,type,
'uvh$': 'A_b_fun$' > 'A_b_option_fun$' ).
tff(func_def_70,type,
'bot$a': 'B_option_set$' ).
tff(func_def_71,type,
'comp$al': ( 'B_b_option_fun_b_b_option_fun_fun$' * 'A_a_option_fun_b_b_option_fun_fun$' ) > 'A_a_option_fun_b_b_option_fun_fun$' ).
tff(func_def_72,type,
'comp$bl': ( 'B_option_b_fun$' * 'B_b_sum_b_option_fun$' ) > 'B_b_sum_b_fun$' ).
tff(func_def_73,type,
'set_option$a': 'C_option_option$' > 'C_option_set$' ).
tff(func_def_74,type,
'uvy$': ( 'C_b_option_fun$' * 'B_c_option_fun$' ) > 'C_c_option_fun$' ).
tff(func_def_75,type,
'case_option$m': ( 'C$' * 'C_option_c_fun$' * 'C_option_option$' ) > 'C$' ).
tff(func_def_76,type,
'fun_app$f': ( 'A_b_option_fun$' * 'A$' ) > 'B_option$' ).
tff(func_def_77,type,
'map_option$': 'C_b_fun$' > 'C_option_b_option_fun$' ).
tff(func_def_78,type,
'comp$h': ( 'B_bool_fun$' * 'A_b_fun$' ) > 'A_bool_fun$' ).
tff(func_def_79,type,
'fun_app$bj': ( 'B_option_a_option_fun$' * 'B_option$' ) > 'A_option$' ).
tff(func_def_80,type,
'case_sum$e': ( 'C_c_option_fun$' * 'C_c_option_fun$' ) > 'C_c_sum_c_option_fun$' ).
tff(func_def_81,type,
def_14: ( 'B_option_bool_fun$' * 'B_option$' ) > tlbool ).
tff(func_def_82,type,
'fun_app$ar': ( 'A_a_option_fun_c_c_option_fun_fun$' * 'A_a_option_fun$' ) > 'C_c_option_fun$' ).
tff(func_def_83,type,
def_19: ( 'C_bool_fun$' * 'C_option$' ) > tlbool ).
tff(func_def_84,type,
'fun_app$v': ( 'C_c_c_option_fun_fun$' * 'C$' ) > 'C_c_option_fun$' ).
tff(func_def_85,type,
def_10: ( 'C_option_bool_fun$' * 'C_option$' ) > tlbool ).
tff(func_def_86,type,
'comp$ba': ( 'A_option_b_option_fun$' * 'C_a_option_fun$' ) > 'C_b_option_fun$' ).
tff(func_def_87,type,
'id$b': 'B_b_fun$' ).
tff(func_def_88,type,
'id$g': 'C_c_option_fun_c_c_option_fun_fun$' ).
tff(func_def_89,type,
'map_option$d': 'B_c_fun$' > 'B_option_c_option_fun$' ).
tff(func_def_90,type,
'comp$p': ( 'C_option_c_option_fun$' * 'B_option_c_option_fun$' ) > 'B_option_c_option_fun$' ).
tff(func_def_91,type,
'fun_app$bo': ( 'B_a_option_fun$' * 'B$' ) > 'A_option$' ).
tff(func_def_92,type,
def_8: ( tlbool * 'C_bool_fun$' * 'C_option$' ) > tlbool ).
tff(func_def_93,type,
'fun_app$an': ( 'B_option_c_option_fun$' * 'B_option$' ) > 'C_option$' ).
tff(func_def_94,type,
'uua$': ( 'A_b_b_fun_fun$' * 'B$' ) > 'A_b_option_fun$' ).
tff(func_def_95,type,
'comp$bh': ( 'B_option_b_fun$' * 'B_option_b_option_fun$' ) > 'B_option_b_fun$' ).
tff(func_def_96,type,
'id$c': 'C_option_c_option_fun$' ).
tff(func_def_97,type,
'comp$r': ( 'B_option_a_option_fun$' * 'A_option_b_option_fun$' ) > 'A_option_a_option_fun$' ).
tff(func_def_98,type,
'fun_app$bk': ( 'A_c_fun$' * 'A$' ) > 'C$' ).
tff(func_def_99,type,
'uub$': 'A_bool_fun$' ).
tff(func_def_100,type,
'some$c': 'B_option$' > 'B_option_option$' ).
tff(func_def_101,type,
'bind$e': ( 'A_option$' * 'A_b_option_fun$' ) > 'B_option$' ).
tff(func_def_102,type,
'bot$d': 'B_set$' ).
tff(func_def_103,type,
'fun_app$aj': ( 'A_a_a_fun_fun$' * 'A$' ) > 'A_a_fun$' ).
tff(func_def_104,type,
'comp$a': ( 'B_b_option_fun$' * 'C_b_fun$' ) > 'C_b_option_fun$' ).
tff(func_def_105,type,
'uwq$': 'C$' > 'C_bool_fun$' ).
tff(func_def_106,type,
'uud$': 'B_bool_fun$' ).
tff(func_def_107,type,
'fun_app$bc': ( 'C_option_b_option_bool_fun_fun$' * 'C_option$' ) > 'B_option_bool_fun$' ).
tff(func_def_108,type,
'comp$bd': ( 'C_c_fun$' * 'C_option_c_fun$' ) > 'C_option_c_fun$' ).
tff(func_def_109,type,
'uwd$': 'B_b_option_fun$' ).
tff(func_def_110,type,
'uvk$': 'B_option_set$' > 'B_option_bool_fun$' ).
tff(func_def_111,type,
'uwj$': 'B$' > 'B_option_b_fun$' ).
tff(func_def_112,type,
'uvr$': ( 'B_b_option_fun_c_c_option_fun_fun$' * 'C$' ) > 'B_bool_fun$' ).
tff(func_def_113,type,
'fun_app$i': ( 'A_b_b_fun_fun$' * 'A$' ) > 'B_b_fun$' ).
tff(func_def_114,type,
'fun_upd$d': ( 'B_b_option_fun$' * 'B$' * 'B_option$' ) > 'B_b_option_fun$' ).
tff(func_def_115,type,
'uus$': 'B_b_b_option_fun_fun$' > 'B_b_b_option_fun_fun$' ).
tff(func_def_116,type,
'fun_app$p': ( 'A_b_fun$' * 'A$' ) > 'B$' ).
tff(func_def_117,type,
'comp$bc': ( 'C_c_fun$' * 'C_c_fun$' ) > 'C_c_fun$' ).
tff(func_def_118,type,
'top$': 'C_option_set$' ).
tff(func_def_119,type,
'comp$l': ( 'C_bool_fun$' * 'C_c_fun$' ) > 'C_bool_fun$' ).
tff(func_def_120,type,
'case_option$h': ( 'B_option$' * 'C_b_option_fun$' * 'C_option$' ) > 'B_option$' ).
tff(func_def_121,type,
'set_option$c': 'C_option$' > 'C_set$' ).
tff(func_def_122,type,
'some$': 'B_b_option_fun$' ).
tff(func_def_123,type,
'fun_app$bd': ( 'B_option_c_option_bool_fun_fun$' * 'B_option$' ) > 'C_option_bool_fun$' ).
tff(func_def_124,type,
'uvg$': 'B_c_fun$' > 'B_c_option_fun$' ).
tff(func_def_125,type,
'uvt$': 'B_b_option_fun$' > 'B_b_option_fun_b_b_option_fun_fun$' ).
tff(func_def_126,type,
'collect$': 'B_bool_fun$' > 'B_set$' ).
tff(func_def_127,type,
'these$': 'C_option_set$' > 'C_set$' ).
tff(func_def_128,type,
'comp$n': ( 'C_option_c_fun$' * 'C_c_option_fun$' ) > 'C_c_fun$' ).
tff(func_def_129,type,
def_23: ( 'C_bool_fun$' * 'C_option$' ) > tlbool ).
tff(func_def_130,type,
'none$b': 'A_option$' ).
tff(func_def_131,type,
'the$a': 'C_option_c_fun$' ).
tff(func_def_132,type,
'fun_app$u': ( 'C_option_c_option_fun$' * 'C_option$' ) > 'C_option$' ).
tff(func_def_133,type,
'bot$': 'A_set$' ).
tff(func_def_134,type,
'comp$w': ( 'C_b_fun$' * 'A_c_fun$' ) > 'A_b_fun$' ).
tff(func_def_135,type,
def_9: ( 'Bool_bool_fun$' * tlbool ) > tlbool ).
tff(func_def_136,type,
'fun_app$ak': ( 'C_option_c_fun$' * 'C_option$' ) > 'C$' ).
tff(func_def_137,type,
'id$d': 'B_option_b_option_fun$' ).
tff(func_def_138,type,
'map_option$g': 'C_a_fun$' > 'C_option_a_option_fun$' ).
tff(func_def_139,type,
'map_option$l': ( 'C_c_option_fun$' * 'C_option$' ) > 'C_option_option$' ).
tff(func_def_140,type,
'uut$': 'C_c_c_option_fun_fun$' > 'C_c_c_option_fun_fun$' ).
tff(func_def_141,type,
'uvq$': ( 'A_a_option_fun_b_b_option_fun_fun$' * 'B$' ) > 'A_bool_fun$' ).
tff(func_def_142,type,
'fun_upd$': ( 'A_a_fun$' * 'A$' ) > 'A_a_a_fun_fun$' ).
tff(func_def_143,type,
'f$': 'A_a_option_fun_b_b_option_fun_fun$' ).
tff(func_def_144,type,
'combine_options$a': ( 'C_c_c_fun_fun$' * 'C_option$' ) > 'C_option_c_option_fun$' ).
tff(func_def_145,type,
'update1$a': 'C$' > 'C_c_c_option_fun_fun$' ).
tff(func_def_146,type,
'fun_app$at': ( 'C_c_option_fun_b_b_option_fun_fun$' * 'C_c_option_fun$' ) > 'B_b_option_fun$' ).
tff(func_def_147,type,
tltrue: tlbool ).
tff(func_def_148,type,
'register_from_getter_setter$b': ( 'B_b_fun$' * 'B_b_b_fun_fun$' ) > 'B_b_option_fun_b_b_option_fun_fun$' ).
tff(func_def_149,type,
def_11: ( tlbool * 'B_bool_fun$' * 'B_option$' ) > tlbool ).
tff(func_def_150,type,
'comp$ab': ( 'B_option_c_option_fun$' * 'B_option_b_option_fun$' ) > 'B_option_c_option_fun$' ).
tff(func_def_151,type,
'case_option$b': ( 'A_option$' * 'A_a_option_fun$' * 'A_option$' ) > 'A_option$' ).
tff(func_def_152,type,
'uuz$': ( 'C_c_c_fun_fun$' * 'C_option$' ) > 'C_c_option_fun$' ).
tff(func_def_153,type,
'top$c': 'B_set$' ).
tff(func_def_154,type,
'comp$ad': ( 'B_option_c_option_fun$' * 'A_option_b_option_fun$' ) > 'A_option_c_option_fun$' ).
tff(func_def_155,type,
'case_sum$c': ( 'B_c_option_fun$' * 'B_c_option_fun$' ) > 'B_b_sum_c_option_fun$' ).
tff(func_def_156,type,
'uun$': ( 'Bool_b_option_fun$' * 'B_bool_fun$' ) > 'B_b_option_fun$' ).
tff(func_def_157,type,
'set_option$b': 'A_option$' > 'A_set$' ).
tff(func_def_158,type,
'uvz$': ( 'B_c_option_fun$' * 'C_c_option_fun$' ) > 'B_c_option_fun$' ).
tff(func_def_159,type,
'getter$a': 'A_a_option_fun_b_b_option_fun_fun$' > 'B_a_fun$' ).
tff(func_def_160,type,
'fun_app$bm': ( 'A_c_option_fun$' * 'A$' ) > 'C_option$' ).
tff(func_def_161,type,
'uuc$': 'C_bool_fun$' ).
tff(func_def_162,type,
'the$e': 'B_option_option$' > 'B_option$' ).
tff(func_def_163,type,
'uuw$': ( 'A_a_a_fun_fun$' * 'A$' ) > 'A_a_option_fun$' ).
tff(func_def_164,type,
'comp$ae': ( 'B_c_fun$' * 'A_b_fun$' ) > 'A_c_fun$' ).
tff(func_def_165,type,
'fun_app$aq': ( 'B_b_option_fun_a_a_option_fun_fun$' * 'B_b_option_fun$' ) > 'A_a_option_fun$' ).
tff(func_def_166,type,
'set_option$d': 'B_option$' > 'B_set$' ).
tff(func_def_167,type,
'comp$j': ( 'B_bool_fun$' * 'C_b_fun$' ) > 'C_bool_fun$' ).
tff(func_def_168,type,
def_5: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_169,type,
'uvo$': 'A_a_a_fun_fun$' ).
tff(func_def_170,type,
'fun_app$ad': ( 'B_b_option_fun_b_b_option_fun_fun$' * 'B_b_option_fun$' ) > 'B_b_option_fun$' ).
tff(func_def_171,type,
'bind$g': ( 'B_option$' * 'B_a_option_fun$' ) > 'A_option$' ).
tff(func_def_172,type,
'map_option$b': 'B_b_fun$' > 'B_option_b_option_fun$' ).
tff(func_def_173,type,
'uwc$': 'C_c_option_fun$' ).
tff(func_def_174,type,
'uws$': 'C_option_c_option_bool_fun_fun$' ).
tff(func_def_175,type,
'id$': 'A_a_fun$' ).
tff(func_def_176,type,
'insert$a': ( 'C$' * 'C_set$' ) > 'C_set$' ).
tff(func_def_177,type,
def_13: ( tlbool * 'C_bool_fun$' * 'C_option$' ) > tlbool ).
tff(func_def_178,type,
'fun_app$ax': ( 'C_option_a_option_bool_fun_fun$' * 'C_option$' ) > 'A_option_bool_fun$' ).
tff(func_def_179,type,
'comp$at': ( 'C_option_b_option_fun$' * 'B_c_option_fun$' ) > 'B_b_option_fun$' ).
tff(func_def_180,type,
'fun_app$af': ( 'Bool_b_option_fun$' * tlbool ) > 'B_option$' ).
tff(func_def_181,type,
'uvi$': 'B_set$' > 'B_bool_fun$' ).
tff(func_def_182,type,
def_21: ( 'B_bool_fun$' * 'B_option$' ) > tlbool ).
tff(func_def_183,type,
'uvd$': 'A_a_fun$' > 'A_a_option_fun$' ).
tff(func_def_184,type,
'undefined$a': 'B$' ).
tff(func_def_185,type,
'uuy$': 'C_c_c_fun_fun$' > 'C_c_c_option_fun_fun$' ).
tff(func_def_186,type,
'comp$bf': ( 'B_option_b_option_fun$' * 'A_b_option_fun$' ) > 'A_b_option_fun$' ).
tff(func_def_187,type,
'uvu$': ( 'C_b_option_fun$' * 'B_b_option_fun$' ) > 'C_b_option_fun$' ).
tff(func_def_188,type,
'comp$ac': ( 'B_c_fun$' * 'B_b_fun$' ) > 'B_c_fun$' ).
tff(func_def_189,type,
'bot$c': 'C_set$' ).
tff(func_def_190,type,
'case_option$a': ( 'C_option$' * 'C_c_option_fun$' ) > 'C_option_c_option_fun$' ).
tff(func_def_191,type,
'id$e': 'A_option_a_option_fun$' ).
tff(func_def_192,type,
'comp$af': ( 'B_option_b_option_fun$' * 'C_option_b_option_fun$' ) > 'C_option_b_option_fun$' ).
tff(func_def_193,type,
'top$b': 'B_option_set$' ).
tff(func_def_194,type,
'comp$y': ( 'C_b_fun$' * 'B_c_fun$' ) > 'B_b_fun$' ).
tff(func_def_195,type,
'insert$c': ( 'C_option$' * 'C_option_set$' ) > 'C_option_set$' ).
tff(func_def_196,type,
'uwe$': 'C_b_option_fun$' ).
tff(func_def_197,type,
'bind$f': ( 'C_option$' * 'C_a_option_fun$' ) > 'A_option$' ).
tff(func_def_198,type,
'update1$b': 'B$' > 'B_b_b_option_fun_fun$' ).
tff(func_def_199,type,
'uwo$': 'C_option_c_option_bool_fun_fun$' ).
tff(func_def_200,type,
'comp$bi': ( 'A_option_a_fun$' * 'A_a_option_fun$' ) > 'A_a_fun$' ).
tff(func_def_201,type,
'fun_app$ap': ( 'C_c_option_fun_a_a_option_fun_fun$' * 'C_c_option_fun$' ) > 'A_a_option_fun$' ).
tff(func_def_202,type,
'some$d': 'C_option$' > 'C_option_option$' ).
tff(func_def_203,type,
'uvl$': 'C_option_set$' > 'C_option_bool_fun$' ).
tff(func_def_204,type,
'uvj$': 'C_set$' > 'C_bool_fun$' ).
tff(func_def_205,type,
'case_option$e': ( tlbool * 'B_bool_fun$' ) > 'B_option_bool_fun$' ).
tff(func_def_206,type,
'bot$b': 'C_option_set$' ).
tff(func_def_207,type,
'case_option$f': ( tlbool * 'C_bool_fun$' ) > 'C_option_bool_fun$' ).
tff(func_def_208,type,
'comp$b': ( 'C_c_option_fun$' * 'B_c_fun$' ) > 'B_c_option_fun$' ).
tff(func_def_209,type,
'fun_app$bf': ( 'A_option_a_fun$' * 'A_option$' ) > 'A$' ).
tff(func_def_210,type,
'uwh$': 'B_option$' > 'A_b_option_fun$' ).
tff(func_def_211,type,
'case_option$j': ( 'B$' * 'B_b_fun$' ) > 'B_option_b_fun$' ).
tff(func_def_212,type,
'fun_app$k': ( 'C_c_fun$' * 'C$' ) > 'C$' ).
tff(func_def_213,type,
'fun_app$bb': ( 'A_option_a_option_bool_fun_fun$' * 'A_option$' ) > 'A_option_bool_fun$' ).
tff(func_def_214,type,
'comp$c': ( 'B_b_option_fun$' * 'B_b_fun$' ) > 'B_b_option_fun$' ).
tff(func_def_215,type,
'uul$': ( 'C_option_bool_fun$' * 'B_c_option_fun$' ) > 'B_bool_fun$' ).
tff(func_def_216,type,
'fun_app$n': ( 'B_c_option_fun$' * 'B$' ) > 'C_option$' ).
tff(func_def_217,type,
'fun_app$am': ( 'B_b_option_fun_c_c_option_fun_fun$' * 'B_b_option_fun$' ) > 'C_c_option_fun$' ).
tff(func_def_218,type,
'fun_app$ae': ( 'Bool_c_option_fun$' * tlbool ) > 'C_option$' ).
tff(func_def_219,type,
'comp$ap': ( 'B_c_option_fun$' * 'C_b_fun$' ) > 'C_c_option_fun$' ).
tff(func_def_220,type,
'uvp$': 'B_b_b_fun_fun$' ).
tff(func_def_221,type,
'uuh$': ( 'C_option_c_option_fun$' * 'B_c_option_fun$' ) > 'B_c_option_fun$' ).
tff(func_def_222,type,
'uvb$': ( 'B_b_b_fun_fun$' * 'B_option$' ) > 'B_b_option_fun$' ).
tff(func_def_223,type,
'uuk$': ( 'Bool_bool_fun$' * 'C_bool_fun$' ) > 'C_bool_fun$' ).
tff(func_def_224,type,
'uvf$': 'C_c_fun$' > 'C_c_option_fun$' ).
tff(func_def_225,type,
'comp$q': ( 'C_c_fun$' * 'B_c_fun$' ) > 'B_c_fun$' ).
tff(func_def_226,type,
'case_option$g': ( tlbool * 'A_bool_fun$' ) > 'A_option_bool_fun$' ).
tff(func_def_227,type,
'comp$o': ( 'C_b_option_fun$' * 'B_c_fun$' ) > 'B_b_option_fun$' ).
tff(func_def_228,type,
'uuf$': 'C_bool_fun$' ).
tff(func_def_229,type,
'comp$bk': ( 'B_c_option_fun$' * 'B_b_sum_b_fun$' ) > 'B_b_sum_c_option_fun$' ).
tff(func_def_230,type,
'the$d': 'B_bool_fun$' > 'B$' ).
tff(func_def_231,type,
'uuj$': ( 'Bool_bool_fun$' * 'B_bool_fun$' ) > 'B_bool_fun$' ).
tff(func_def_232,type,
'set_option$': 'B_option_option$' > 'B_option_set$' ).
tff(func_def_233,type,
'map_option$h': 'B_a_fun$' > 'B_option_a_option_fun$' ).
tff(func_def_234,type,
'comp$aj': ( 'A_a_option_fun_b_b_option_fun_fun$' * 'A_a_option_fun_a_a_option_fun_fun$' ) > 'A_a_option_fun_b_b_option_fun_fun$' ).
tff(func_def_235,type,
'fun_app$bl': ( 'C_a_fun$' * 'C$' ) > 'A$' ).
tff(func_def_236,type,
'fun_app$s': ( 'B_option_b_option_fun$' * 'B_option$' ) > 'B_option$' ).
tff(func_def_237,type,
'setter$a': 'A_a_option_fun_b_b_option_fun_fun$' > 'A_b_b_fun_fun$' ).
tff(func_def_238,type,
'comp$u': ( 'C_b_fun$' * 'C_c_fun$' ) > 'C_b_fun$' ).
tff(func_def_239,type,
'comp$d': ( 'B_b_option_fun$' * 'A_b_fun$' ) > 'A_b_option_fun$' ).
tff(func_def_240,type,
'fun_app$h': ( 'B_b_fun$' * 'B$' ) > 'B$' ).
tff(func_def_241,type,
def_6: ( tlbool * 'B_bool_fun$' * 'B_option$' ) > tlbool ).
tff(func_def_242,type,
'insert$b': ( 'B_option$' * 'B_option_set$' ) > 'B_option_set$' ).
tff(func_def_243,type,
'bind$c': 'B_option$' > 'B_b_option_fun_b_option_fun$' ).
tff(func_def_244,type,
'fun_app$ah': ( 'C_c_c_fun_fun$' * 'C$' ) > 'C_c_fun$' ).
tff(func_def_245,type,
'comp$': ( 'C_c_option_fun$' * 'C_c_fun$' ) > 'C_c_option_fun$' ).
tff(func_def_246,type,
'comp$av': ( 'B_option_c_option_fun$' * 'B_b_option_fun$' ) > 'B_c_option_fun$' ).
tff(func_def_247,type,
'uwp$': 'B$' > 'B_bool_fun$' ).
tff(func_def_248,type,
'id$f': 'B_b_option_fun_b_b_option_fun_fun$' ).
tff(func_def_249,type,
'uvx$': ( 'B_b_option_fun$' * 'B_c_option_fun$' ) > 'B_c_option_fun$' ).
tff(func_def_250,type,
'fun_app$as': ( 'A_a_option_fun_a_a_option_fun_fun$' * 'A_a_option_fun$' ) > 'A_a_option_fun$' ).
tff(func_def_251,type,
'fun_app$bh': ( 'A_option_c_option_fun$' * 'A_option$' ) > 'C_option$' ).
tff(func_def_252,type,
'uwf$': 'B_option_bool_fun$' ).
tff(func_def_253,type,
'uwr$': 'B_option_b_option_bool_fun_fun$' ).
tff(func_def_254,type,
'uvv$': ( 'B_c_option_fun$' * 'C_b_option_fun$' ) > 'B_b_option_fun$' ).
tff(func_def_255,type,
'fun_upd$c': ( 'B_c_option_fun$' * 'B$' * 'C_option$' ) > 'B_c_option_fun$' ).
tff(func_def_256,type,
'bind$a': ( 'C_option$' * 'C_b_option_fun$' ) > 'B_option$' ).
tff(func_def_257,type,
'getter$': 'B_b_option_fun_c_c_option_fun_fun$' > 'C_b_fun$' ).
tff(func_def_258,type,
'fun_app$ay': ( 'B_option_a_option_bool_fun_fun$' * 'B_option$' ) > 'A_option_bool_fun$' ).
tff(func_def_259,type,
'case_option$c': ( 'C_option$' * 'B_c_option_fun$' ) > 'B_option_c_option_fun$' ).
tff(func_def_260,type,
'uvw$': ( 'C_c_option_fun$' * 'C_b_option_fun$' ) > 'C_b_option_fun$' ).
tff(func_def_261,type,
def_16: ( tlbool * 'B_bool_fun$' * 'B_option$' ) > tlbool ).
tff(func_def_262,type,
'case_option$': ( 'B_option$' * 'B_b_option_fun$' ) > 'B_option_b_option_fun$' ).
tff(func_def_263,type,
'comp$m': ( 'B_option_b_fun$' * 'B_b_option_fun$' ) > 'B_b_fun$' ).
tff(func_def_264,type,
tlfalse: tlbool ).
tff(func_def_265,type,
def_20: ( tlbool * 'B_bool_fun$' * 'B_option$' ) > tlbool ).
tff(func_def_266,type,
'comp$as': 'C_option_c_option_fun$' > 'C_c_option_fun_c_c_option_fun_fun$' ).
tff(func_def_267,type,
'is_none$': 'B_option_bool_fun$' ).
tff(func_def_268,type,
'collect$b': 'B_option_bool_fun$' > 'B_option_set$' ).
tff(func_def_269,type,
'comp$ar': ( 'C_option_c_option_fun$' * 'B_c_option_fun$' ) > 'B_c_option_fun$' ).
tff(func_def_270,type,
'uvn$': 'A_a_fun$' ).
tff(func_def_271,type,
'bot$h': 'C_option_bool_fun$' ).
tff(func_def_272,type,
'uwn$': 'B_option_b_option_bool_fun_fun$' ).
tff(func_def_273,type,
'fun_app$bg': ( 'C_option_b_option_fun$' * 'C_option$' ) > 'B_option$' ).
tff(func_def_274,type,
def_3: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_275,type,
def_22: ( tlbool * 'C_bool_fun$' * 'C_option$' ) > tlbool ).
tff(func_def_276,type,
'uum$': ( 'Bool_c_option_fun$' * 'B_bool_fun$' ) > 'B_c_option_fun$' ).
tff(func_def_277,type,
'uwl$': 'B$' > 'B_bool_fun$' ).
tff(func_def_278,type,
'comp$ai': ( 'B_b_fun$' * 'B_b_fun$' ) > 'B_b_fun$' ).
tff(func_def_279,type,
'map_option$k': ( 'B_b_option_fun$' * 'B_option$' ) > 'B_option_option$' ).
tff(func_def_280,type,
'none$d': 'C_option_option$' ).
tff(func_def_281,type,
'comp$bb': ( 'B_b_fun$' * 'B_option_b_fun$' ) > 'B_option_b_fun$' ).
tff(func_def_282,type,
'comp$az': ( 'A_option_b_option_fun$' * 'B_a_option_fun$' ) > 'B_b_option_fun$' ).
tff(func_def_283,type,
'register_from_getter_setter$a': ( 'C_b_fun$' * 'B_c_c_fun_fun$' ) > 'B_b_option_fun_c_c_option_fun_fun$' ).
tff(func_def_284,type,
'uva$': 'B_b_b_fun_fun$' > 'B_b_b_option_fun_fun$' ).
tff(func_def_285,type,
'fun_upd$f': ( 'C_c_fun$' * 'C$' ) > 'C_c_c_fun_fun$' ).
tff(func_def_286,type,
'bind$': 'C_option$' > 'C_c_option_fun_c_option_fun$' ).
tff(func_def_287,type,
'case_sum$f': ( 'C_c_fun$' * 'C_c_fun$' ) > 'C_c_sum_c_fun$' ).
tff(func_def_288,type,
'setter$': 'B_b_option_fun_c_c_option_fun_fun$' > 'B_c_c_fun_fun$' ).
tff(func_def_289,type,
'uwi$': 'C_option$' > 'B_c_option_fun$' ).
tff(func_def_290,type,
'the$b': 'A_option_a_fun$' ).
tff(func_def_291,type,
'fun_app$au': ( 'A_a_option_fun_b_b_option_fun_fun$' * 'A_a_option_fun$' ) > 'B_b_option_fun$' ).
tff(func_def_292,type,
'fun_app$y': ( 'B_c_c_fun_fun$' * 'B$' ) > 'C_c_fun$' ).
tff(func_def_293,type,
'undefined$b': 'C$' ).
tff(func_def_294,type,
'uvc$': 'C_b_fun$' > 'C_b_option_fun$' ).
tff(func_def_295,type,
'comp$bm': ( 'C_option_c_fun$' * 'C_c_sum_c_option_fun$' ) > 'C_c_sum_c_fun$' ).
tff(func_def_296,type,
'is_none$b': 'A_option_bool_fun$' ).
tff(func_def_297,type,
'id$a': 'C_c_fun$' ).
tff(func_def_298,type,
'image$a': ( 'B_b_option_fun$' * 'B_set$' ) > 'B_option_set$' ).
tff(func_def_299,type,
'fun_app$m': ( 'C_b_fun$' * 'C$' ) > 'B$' ).
tff(func_def_300,type,
'uve$': 'B_b_fun$' > 'B_b_option_fun$' ).
tff(func_def_301,type,
'fun_app$ai': ( 'B_b_b_fun_fun$' * 'B$' ) > 'B_b_fun$' ).
tff(func_def_302,type,
'register_from_getter_setter$': ( 'B_a_fun$' * 'A_b_b_fun_fun$' ) > 'A_a_option_fun_b_b_option_fun_fun$' ).
tff(func_def_303,type,
'map_option$a': 'A_a_fun$' > 'A_option_a_option_fun$' ).
tff(func_def_304,type,
'uup$': ( 'B_option_bool_fun$' * 'B_b_option_fun$' ) > 'B_bool_fun$' ).
tff(func_def_305,type,
'fun_app$aa': ( 'C_c_option_fun_c_c_option_fun_fun$' * 'C_c_option_fun$' ) > 'C_c_option_fun$' ).
tff(func_def_306,type,
'uwk$': 'C$' > 'C_option_c_fun$' ).
tff(func_def_307,type,
'some$b': 'A_a_option_fun$' ).
tff(func_def_308,type,
'fun_app$l': ( 'C_b_option_fun$' * 'C$' ) > 'B_option$' ).
tff(func_def_309,type,
'uuu$': ( 'B_c_c_option_fun_fun$' * 'C$' ) > 'B_c_option_fun$' ).
tff(func_def_310,type,
'comp$bg': ( 'B_c_option_fun$' * 'B_option_b_fun$' ) > 'B_option_c_option_fun$' ).
tff(func_def_311,type,
'comp$ah': ( 'B_option_b_option_fun$' * 'B_option_b_option_fun$' ) > 'B_option_b_option_fun$' ).
tff(func_def_312,type,
'case_sum$a': ( 'A_b_option_fun$' * 'A_b_option_fun$' ) > 'A_a_sum_b_option_fun$' ).
tff(func_def_313,type,
'comp$ay': ( 'B_option_b_option_fun$' * 'C_b_option_fun$' ) > 'C_b_option_fun$' ).
tff(func_def_314,type,
'comp$v': ( 'C_option_b_option_fun$' * 'A_option_c_option_fun$' ) > 'A_option_b_option_fun$' ).
tff(func_def_315,type,
'case_sum$d': ( 'B_b_option_fun$' * 'B_b_option_fun$' ) > 'B_b_sum_b_option_fun$' ).
tff(func_def_316,type,
'comp$ak': ( 'B_b_option_fun_c_c_option_fun_fun$' * 'B_b_option_fun_b_b_option_fun_fun$' ) > 'B_b_option_fun_c_c_option_fun_fun$' ).
tff(func_def_317,type,
'bot$f': 'C_bool_fun$' ).
tff(func_def_318,type,
'comp$bj': ( 'A_b_option_fun$' * 'A_a_sum_a_fun$' ) > 'A_a_sum_b_option_fun$' ).
tff(func_def_319,type,
'the$f': 'C_option_option$' > 'C_option$' ).
tff(func_def_320,type,
'fun_upd$a': ( 'A_b_option_fun$' * 'A$' * 'B_option$' ) > 'A_b_option_fun$' ).
tff(func_def_321,type,
'is_none$a': 'C_option_bool_fun$' ).
tff(func_def_322,type,
'uu$': ( 'B_c_c_fun_fun$' * 'C$' ) > 'B_c_option_fun$' ).
tff(func_def_323,type,
'fun_app$av': ( 'A_option_b_option_fun$' * 'A_option$' ) > 'B_option$' ).
tff(func_def_324,type,
'comp$aq': ( 'B_c_option_fun$' * 'A_b_fun$' ) > 'A_c_option_fun$' ).
tff(func_def_325,type,
'fun_app$az': ( 'A_option_c_option_bool_fun_fun$' * 'A_option$' ) > 'C_option_bool_fun$' ).
tff(func_def_326,type,
'comp$am': ( 'B_b_option_fun_c_c_option_fun_fun$' * 'A_a_option_fun_b_b_option_fun_fun$' ) > 'A_a_option_fun_c_c_option_fun_fun$' ).
tff(func_def_327,type,
'undefined$': 'A$' ).
tff(func_def_328,type,
'fun_app$w': ( 'B_c_c_option_fun_fun$' * 'B$' ) > 'C_c_option_fun$' ).
tff(func_def_329,type,
'uwa$': 'C_c_option_fun$' > 'C_c_option_fun_c_c_option_fun_fun$' ).
tff(func_def_330,type,
'sF$': 'A_b_b_fun_fun$' ).
tff(func_def_331,type,
'map_option$i': ( 'B_option_b_option_fun$' * 'B_option_option$' ) > 'B_option_option$' ).
tff(func_def_332,type,
'fun_app$j': ( 'C_c_option_fun$' * 'C$' ) > 'C_option$' ).
tff(func_def_333,type,
'uue$': 'A_bool_fun$' ).
tff(func_def_334,type,
'fun_app$be': ( 'A_option_a_option_fun$' * 'A_option$' ) > 'A_option$' ).
tff(func_def_335,type,
'combine_options$b': ( 'B_b_b_fun_fun$' * 'B_option$' ) > 'B_option_b_option_fun$' ).
tff(func_def_336,type,
'none$c': 'B_option_option$' ).
tff(func_def_337,type,
'comp$f': ( 'B_c_option_fun$' * 'B_b_fun$' ) > 'B_c_option_fun$' ).
tff(func_def_338,type,
'comp$au': ( 'C_option_b_option_fun$' * 'C_c_option_fun$' ) > 'C_b_option_fun$' ).
tff(func_def_339,type,
'comp$k': ( 'C_bool_fun$' * 'B_c_fun$' ) > 'B_bool_fun$' ).
tff(func_def_340,type,
'case_sum$b': ( 'B_b_fun$' * 'B_b_fun$' ) > 'B_b_sum_b_fun$' ).
tff(func_def_341,type,
'fun_upd$e': ( 'C_c_option_fun$' * 'C$' * 'C_option$' ) > 'C_c_option_fun$' ).
tff(func_def_342,type,
'gF$': 'B_a_fun$' ).
tff(func_def_343,type,
'fun_app$g': ( 'B_b_option_fun$' * 'B$' ) > 'B_option$' ).
tff(func_def_344,type,
'fun_app$o': ( 'B_c_fun$' * 'B$' ) > 'C$' ).
tff(func_def_345,type,
'bot$g': 'B_option_bool_fun$' ).
tff(func_def_346,type,
'uwb$': 'B_c_option_fun$' ).
tff(func_def_347,type,
'fun_app$x': ( 'A_b_b_option_fun_fun$' * 'A$' ) > 'B_b_option_fun$' ).
tff(func_def_348,type,
'register_from_getter_setter$c': ( 'B_c_fun$' * 'C_b_b_fun_fun$' ) > 'C_c_option_fun_b_b_option_fun_fun$' ).
tff(func_def_349,type,
'comp$g': ( 'A_b_option_fun$' * 'A_a_fun$' ) > 'A_b_option_fun$' ).
tff(func_def_350,type,
'fun_app$q': ( 'A_a_option_fun$' * 'A$' ) > 'A_option$' ).
tff(func_def_351,type,
def_18: ( tlbool * 'C_bool_fun$' * 'C_option$' ) > tlbool ).
tff(func_def_352,type,
'comp$i': ( 'B_bool_fun$' * 'B_b_fun$' ) > 'B_bool_fun$' ).
tff(func_def_353,type,
'comp$ao': ( 'C_b_option_fun$' * 'C_c_fun$' ) > 'C_b_option_fun$' ).
tff(func_def_354,type,
'uuo$': ( 'Bool_c_option_fun$' * 'C_bool_fun$' ) > 'C_c_option_fun$' ).
tff(func_def_355,type,
def_15: ( 'C_option_bool_fun$' * 'C_option$' ) > tlbool ).
tff(func_def_356,type,
'uwm$': 'C$' > 'C_bool_fun$' ).
tff(func_def_357,type,
sK44: ( 'B_c_c_fun_fun$' * 'C_b_fun$' ) > 'B_b_option_fun$' ).
tff(func_def_358,type,
sK45: ( 'B_c_c_fun_fun$' * 'C_b_fun$' ) > 'C$' ).
tff(func_def_359,type,
sK46: 'A_b_b_fun_fun$' ).
tff(func_def_360,type,
sK47: 'B_a_fun$' ).
tff(func_def_361,type,
sK48: 'A_option$' > 'A$' ).
tff(func_def_362,type,
sK49: 'C_option$' > 'C$' ).
tff(func_def_363,type,
sK50: 'B_option$' > 'B$' ).
tff(func_def_364,type,
sK51: 'C_option_set$' > 'C_option$' ).
tff(func_def_365,type,
sK52: 'B_option_set$' > 'B_option$' ).
tff(func_def_366,type,
sK53: 'C_set$' > 'C$' ).
tff(func_def_367,type,
sK54: 'B_set$' > 'B$' ).
tff(func_def_368,type,
sK55: ( 'C_c_option_fun_c_c_option_fun_fun$' * 'C_c_fun$' * 'C_c_c_option_fun_fun$' ) > 'C_c_option_fun$' ).
tff(func_def_369,type,
sK56: ( 'C_c_option_fun_c_c_option_fun_fun$' * 'C_c_fun$' * 'C_c_c_option_fun_fun$' ) > 'C$' ).
tff(func_def_370,type,
sK57: 'C_c_option_fun_c_c_option_fun_fun$' > 'C_c_fun$' ).
tff(func_def_371,type,
sK58: 'C_c_option_fun_c_c_option_fun_fun$' > 'C_c_c_option_fun_fun$' ).
tff(func_def_372,type,
sK59: 'C_c_option_fun_c_c_option_fun_fun$' > 'C_c_fun$' ).
tff(func_def_373,type,
sK60: 'C_c_option_fun_c_c_option_fun_fun$' > 'C_c_c_fun_fun$' ).
tff(func_def_374,type,
sK61: 'B_b_option_fun_b_b_option_fun_fun$' > 'B_b_fun$' ).
tff(func_def_375,type,
sK62: 'B_b_option_fun_b_b_option_fun_fun$' > 'B_b_b_fun_fun$' ).
tff(func_def_376,type,
sK63: 'B_b_option_fun_c_c_option_fun_fun$' > 'C_b_fun$' ).
tff(func_def_377,type,
sK64: 'B_b_option_fun_c_c_option_fun_fun$' > 'B_c_c_fun_fun$' ).
tff(func_def_378,type,
sK65: 'A_a_option_fun_b_b_option_fun_fun$' > 'B_a_fun$' ).
tff(func_def_379,type,
sK66: 'A_a_option_fun_b_b_option_fun_fun$' > 'A_b_b_fun_fun$' ).
tff(func_def_380,type,
sK67: ( 'B_b_option_fun_b_b_option_fun_fun$' * 'B_b_fun$' * 'B_b_b_option_fun_fun$' ) > 'B_b_option_fun$' ).
tff(func_def_381,type,
sK68: ( 'B_b_option_fun_b_b_option_fun_fun$' * 'B_b_fun$' * 'B_b_b_option_fun_fun$' ) > 'B$' ).
tff(func_def_382,type,
sK69: 'B_b_option_fun_b_b_option_fun_fun$' > 'B_b_fun$' ).
tff(func_def_383,type,
sK70: 'B_b_option_fun_b_b_option_fun_fun$' > 'B_b_b_option_fun_fun$' ).
tff(func_def_384,type,
sK71: ( 'B_b_option_fun_c_c_option_fun_fun$' * 'C_b_fun$' * 'B_c_c_option_fun_fun$' ) > 'B_b_option_fun$' ).
tff(func_def_385,type,
sK72: ( 'B_b_option_fun_c_c_option_fun_fun$' * 'C_b_fun$' * 'B_c_c_option_fun_fun$' ) > 'C$' ).
tff(func_def_386,type,
sK73: 'B_b_option_fun_c_c_option_fun_fun$' > 'C_b_fun$' ).
tff(func_def_387,type,
sK74: 'B_b_option_fun_c_c_option_fun_fun$' > 'B_c_c_option_fun_fun$' ).
tff(func_def_388,type,
sK75: ( 'A_a_option_fun_b_b_option_fun_fun$' * 'B_a_fun$' * 'A_b_b_option_fun_fun$' ) > 'A_a_option_fun$' ).
tff(func_def_389,type,
sK76: ( 'A_a_option_fun_b_b_option_fun_fun$' * 'B_a_fun$' * 'A_b_b_option_fun_fun$' ) > 'B$' ).
tff(func_def_390,type,
sK77: 'A_a_option_fun_b_b_option_fun_fun$' > 'B_a_fun$' ).
tff(func_def_391,type,
sK78: 'A_a_option_fun_b_b_option_fun_fun$' > 'A_b_b_option_fun_fun$' ).
tff(func_def_392,type,
sK79: 'A_option$' > 'A$' ).
tff(func_def_393,type,
sK80: 'C_option$' > 'C$' ).
tff(func_def_394,type,
sK81: 'B_option$' > 'B$' ).
tff(func_def_395,type,
sK82: 'C_bool_fun$' > 'C$' ).
tff(func_def_396,type,
sK83: 'C_bool_fun$' > 'C$' ).
tff(func_def_397,type,
sK84: 'B_bool_fun$' > 'B$' ).
tff(func_def_398,type,
sK85: 'B_bool_fun$' > 'B$' ).
tff(func_def_399,type,
sK86: 'C_option_bool_fun$' > 'C_option$' ).
tff(func_def_400,type,
sK87: 'C_option_bool_fun$' > 'C_option$' ).
tff(func_def_401,type,
sK88: 'B_option_bool_fun$' > 'B_option$' ).
tff(func_def_402,type,
sK89: 'B_option_bool_fun$' > 'B_option$' ).
tff(func_def_403,type,
sK90: 'B_option_set$' > 'B_option$' ).
tff(func_def_404,type,
sK91: 'C_option_set$' > 'C_option$' ).
tff(func_def_405,type,
sK92: 'C_set$' > 'C$' ).
tff(func_def_406,type,
sK93: 'B_set$' > 'B$' ).
tff(func_def_407,type,
sK94: 'A_option_bool_fun$' > 'A$' ).
tff(func_def_408,type,
sK95: 'A_option_bool_fun$' > 'A_option$' ).
tff(func_def_409,type,
sK96: 'C_option_bool_fun$' > 'C$' ).
tff(func_def_410,type,
sK97: 'C_option_bool_fun$' > 'C_option$' ).
tff(func_def_411,type,
sK98: 'B_option_bool_fun$' > 'B$' ).
tff(func_def_412,type,
sK99: 'B_option_bool_fun$' > 'B_option$' ).
tff(func_def_413,type,
sK100: 'A_option$' > 'A$' ).
tff(func_def_414,type,
sK101: 'C_option$' > 'C$' ).
tff(func_def_415,type,
sK102: 'B_option$' > 'B$' ).
tff(func_def_416,type,
sK103: 'B_option_set$' > 'B_option$' ).
tff(func_def_417,type,
sK104: 'C_option_set$' > 'C_option$' ).
tff(func_def_418,type,
sK105: 'A_option_bool_fun$' > 'A_option$' ).
tff(func_def_419,type,
sK106: 'A_option_bool_fun$' > 'A$' ).
tff(func_def_420,type,
sK107: 'C_option_bool_fun$' > 'C_option$' ).
tff(func_def_421,type,
sK108: 'C_option_bool_fun$' > 'C$' ).
tff(func_def_422,type,
sK109: 'B_option_bool_fun$' > 'B_option$' ).
tff(func_def_423,type,
sK110: 'B_option_bool_fun$' > 'B$' ).
tff(func_def_424,type,
sK111: 'C_set$' > 'C$' ).
tff(func_def_425,type,
sK112: 'B_set$' > 'B$' ).
tff(func_def_426,type,
sK113: ( 'A_a_option_fun_b_b_option_fun_fun$' * 'A_a_option_fun_b_b_option_fun_fun$' ) > 'A$' ).
tff(func_def_427,type,
sK114: ( 'A_a_option_fun_b_b_option_fun_fun$' * 'A_a_option_fun_b_b_option_fun_fun$' ) > 'A$' ).
tff(func_def_428,type,
sK115: ( 'B_b_option_fun_c_c_option_fun_fun$' * 'B_b_option_fun_c_c_option_fun_fun$' ) > 'B$' ).
tff(func_def_429,type,
sK116: ( 'B_b_option_fun_c_c_option_fun_fun$' * 'B_b_option_fun_c_c_option_fun_fun$' ) > 'B$' ).
tff(func_def_430,type,
sK117: ( 'C_option_option$' * 'C_option_c_option_fun$' ) > 'C_option$' ).
tff(func_def_431,type,
sK118: ( 'B_option_option$' * 'B_option_b_option_fun$' ) > 'B_option$' ).
tff(func_def_432,type,
sK119: ( 'A_option$' * 'A_a_fun$' ) > 'A$' ).
tff(func_def_433,type,
sK120: ( 'C_option$' * 'C_c_fun$' ) > 'C$' ).
tff(func_def_434,type,
sK121: ( 'B_option$' * 'B_b_fun$' ) > 'B$' ).
tff(func_def_435,type,
sK122: 'B_c_c_fun_fun$' > 'B$' ).
tff(func_def_436,type,
sK123: 'B_c_c_fun_fun$' > 'B$' ).
tff(func_def_437,type,
sK124: 'B_c_c_fun_fun$' > 'C$' ).
tff(func_def_438,type,
sK125: ( 'C_b_fun$' * 'B_c_c_fun_fun$' ) > 'B$' ).
tff(func_def_439,type,
sK126: ( 'C_b_fun$' * 'B_c_c_fun_fun$' ) > 'C$' ).
tff(func_def_440,type,
sK127: ( 'C_b_fun$' * 'B_c_c_fun_fun$' ) > 'C$' ).
tff(func_def_441,type,
sK128: 'A_b_b_fun_fun$' > 'A$' ).
tff(func_def_442,type,
sK129: 'A_b_b_fun_fun$' > 'A$' ).
tff(func_def_443,type,
sK130: 'A_b_b_fun_fun$' > 'B$' ).
tff(func_def_444,type,
sK131: ( 'B_a_fun$' * 'A_b_b_fun_fun$' ) > 'A$' ).
tff(func_def_445,type,
sK132: ( 'B_a_fun$' * 'A_b_b_fun_fun$' ) > 'B$' ).
tff(func_def_446,type,
sK133: ( 'B_a_fun$' * 'A_b_b_fun_fun$' ) > 'B$' ).
tff(func_def_447,type,
sK134: ( 'A_bool_fun$' * 'A_option$' ) > 'A$' ).
tff(func_def_448,type,
sK135: ( 'C_bool_fun$' * 'C_option$' ) > 'C$' ).
tff(func_def_449,type,
sK136: ( 'B_bool_fun$' * 'B_option$' ) > 'B$' ).
tff(func_def_450,type,
sK137: ( 'A_option$' * 'A_option$' * 'A_option_a_option_bool_fun_fun$' ) > 'A$' ).
tff(func_def_451,type,
sK138: ( 'A_option$' * 'A_option$' * 'A_option_a_option_bool_fun_fun$' ) > 'A$' ).
tff(func_def_452,type,
sK139: ( 'C_option$' * 'A_option$' * 'A_option_c_option_bool_fun_fun$' ) > 'A$' ).
tff(func_def_453,type,
sK140: ( 'C_option$' * 'A_option$' * 'A_option_c_option_bool_fun_fun$' ) > 'C$' ).
tff(func_def_454,type,
sK141: ( 'B_option$' * 'A_option$' * 'A_option_b_option_bool_fun_fun$' ) > 'A$' ).
tff(func_def_455,type,
sK142: ( 'B_option$' * 'A_option$' * 'A_option_b_option_bool_fun_fun$' ) > 'B$' ).
tff(func_def_456,type,
sK143: ( 'A_option$' * 'C_option$' * 'C_option_a_option_bool_fun_fun$' ) > 'C$' ).
tff(func_def_457,type,
sK144: ( 'A_option$' * 'C_option$' * 'C_option_a_option_bool_fun_fun$' ) > 'A$' ).
tff(func_def_458,type,
sK145: ( 'C_option$' * 'C_option$' * 'C_option_c_option_bool_fun_fun$' ) > 'C$' ).
tff(func_def_459,type,
sK146: ( 'C_option$' * 'C_option$' * 'C_option_c_option_bool_fun_fun$' ) > 'C$' ).
tff(func_def_460,type,
sK147: ( 'B_option$' * 'C_option$' * 'C_option_b_option_bool_fun_fun$' ) > 'C$' ).
tff(func_def_461,type,
sK148: ( 'B_option$' * 'C_option$' * 'C_option_b_option_bool_fun_fun$' ) > 'B$' ).
tff(func_def_462,type,
sK149: ( 'A_option$' * 'B_option$' * 'B_option_a_option_bool_fun_fun$' ) > 'B$' ).
tff(func_def_463,type,
sK150: ( 'A_option$' * 'B_option$' * 'B_option_a_option_bool_fun_fun$' ) > 'A$' ).
tff(func_def_464,type,
sK151: ( 'C_option$' * 'B_option$' * 'B_option_c_option_bool_fun_fun$' ) > 'B$' ).
tff(func_def_465,type,
sK152: ( 'C_option$' * 'B_option$' * 'B_option_c_option_bool_fun_fun$' ) > 'C$' ).
tff(func_def_466,type,
sK153: ( 'B_option$' * 'B_option$' * 'B_option_b_option_bool_fun_fun$' ) > 'B$' ).
tff(func_def_467,type,
sK154: ( 'B_option$' * 'B_option$' * 'B_option_b_option_bool_fun_fun$' ) > 'B$' ).
tff(func_def_468,type,
sK155: ( 'C_option_option$' * 'C_option_bool_fun$' ) > 'C_option$' ).
tff(func_def_469,type,
sK156: ( 'B_option_option$' * 'B_option_bool_fun$' ) > 'B_option$' ).
tff(func_def_470,type,
sK157: ( 'A_option$' * 'A_bool_fun$' ) > 'A$' ).
tff(func_def_471,type,
sK158: ( 'C_option$' * 'C_bool_fun$' ) > 'C$' ).
tff(func_def_472,type,
sK159: ( 'B_option$' * 'B_bool_fun$' ) > 'B$' ).
tff(func_def_473,type,
sK160: ( 'A_option$' * 'A_b_fun$' * 'A_b_fun$' ) > 'A$' ).
tff(func_def_474,type,
sK161: ( 'A_option$' * 'A_a_fun$' * 'A_a_fun$' ) > 'A$' ).
tff(func_def_475,type,
sK162: ( 'C_option$' * 'C_b_fun$' * 'C_b_fun$' ) > 'C$' ).
tff(func_def_476,type,
sK163: ( 'B_option$' * 'B_c_fun$' * 'B_c_fun$' ) > 'B$' ).
tff(func_def_477,type,
sK164: ( 'B_option$' * 'B_b_fun$' * 'B_b_fun$' ) > 'B$' ).
tff(func_def_478,type,
sK165: 'C_c_c_fun_fun$' > 'C$' ).
tff(func_def_479,type,
sK166: 'C_c_c_fun_fun$' > 'C$' ).
tff(func_def_480,type,
sK167: 'B_b_b_fun_fun$' > 'B$' ).
tff(func_def_481,type,
sK168: 'B_b_b_fun_fun$' > 'B$' ).
tff(func_def_482,type,
sK169: ( 'C_a_option_fun$' * 'A_option_bool_fun$' * 'C_option$' ) > 'C$' ).
tff(func_def_483,type,
sK170: ( 'B_a_option_fun$' * 'A_option_bool_fun$' * 'B_option$' ) > 'B$' ).
tff(func_def_484,type,
sK171: ( 'C_a_option_fun$' * 'A_option_bool_fun$' * 'C_option$' ) > 'C$' ).
tff(func_def_485,type,
sK172: ( 'B_a_option_fun$' * 'A_option_bool_fun$' * 'B_option$' ) > 'B$' ).
tff(func_def_486,type,
sK173: ( 'A_c_option_fun$' * 'C_option_bool_fun$' * 'A_option$' ) > 'A$' ).
tff(func_def_487,type,
sK174: ( 'A_c_option_fun$' * 'C_option_bool_fun$' * 'A_option$' ) > 'A$' ).
tff(func_def_488,type,
sK175: ( 'B_c_option_fun$' * 'C_option_bool_fun$' * 'B_option$' ) > 'B$' ).
tff(func_def_489,type,
sK176: ( 'B_c_option_fun$' * 'C_option_bool_fun$' * 'B_option$' ) > 'B$' ).
tff(func_def_490,type,
sK177: ( 'A_b_option_fun$' * 'B_option_bool_fun$' * 'A_option$' ) > 'A$' ).
tff(func_def_491,type,
sK178: ( 'A_b_option_fun$' * 'B_option_bool_fun$' * 'A_option$' ) > 'A$' ).
tff(func_def_492,type,
sK179: ( 'C_b_option_fun$' * 'B_option_bool_fun$' * 'C_option$' ) > 'C$' ).
tff(func_def_493,type,
sK180: ( 'C_b_option_fun$' * 'B_option_bool_fun$' * 'C_option$' ) > 'C$' ).
tff(func_def_494,type,
sK181: ( 'A_a_option_fun$' * 'A_option_bool_fun$' * 'A_option$' ) > 'A$' ).
tff(func_def_495,type,
sK182: ( 'A_a_option_fun$' * 'A_option_bool_fun$' * 'A_option$' ) > 'A$' ).
tff(func_def_496,type,
sK183: ( 'C_c_option_fun$' * 'C_option_bool_fun$' * 'C_option$' ) > 'C$' ).
tff(func_def_497,type,
sK184: ( 'C_c_option_fun$' * 'C_option_bool_fun$' * 'C_option$' ) > 'C$' ).
tff(func_def_498,type,
sK185: ( 'B_b_option_fun$' * 'B_option_bool_fun$' * 'B_option$' ) > 'B$' ).
tff(func_def_499,type,
sK186: ( 'B_b_option_fun$' * 'B_option_bool_fun$' * 'B_option$' ) > 'B$' ).
tff(func_def_500,type,
sK187: ( 'C_option$' * 'C_a_option_fun$' * 'A$' ) > 'C$' ).
tff(func_def_501,type,
sK188: ( 'B_option$' * 'B_a_option_fun$' * 'A$' ) > 'B$' ).
tff(func_def_502,type,
sK189: ( 'A_option$' * 'A_c_option_fun$' * 'C$' ) > 'A$' ).
tff(func_def_503,type,
sK190: ( 'B_option$' * 'B_c_option_fun$' * 'C$' ) > 'B$' ).
tff(func_def_504,type,
sK191: ( 'A_option$' * 'A_b_option_fun$' * 'B$' ) > 'A$' ).
tff(func_def_505,type,
sK192: ( 'C_option$' * 'C_b_option_fun$' * 'B$' ) > 'C$' ).
tff(func_def_506,type,
sK193: ( 'A_option$' * 'A_a_option_fun$' * 'A$' ) > 'A$' ).
tff(func_def_507,type,
sK194: ( 'C_a_fun$' * 'C_option$' * 'A$' ) > 'C$' ).
tff(func_def_508,type,
sK195: ( 'B_a_fun$' * 'B_option$' * 'A$' ) > 'B$' ).
tff(func_def_509,type,
sK196: ( 'A_a_fun$' * 'A_option$' * 'A$' ) > 'A$' ).
tff(func_def_510,type,
sK197: ( 'A_c_fun$' * 'A_option$' * 'C$' ) > 'A$' ).
tff(func_def_511,type,
sK198: ( 'C_option$' * 'C_c_option_fun$' * 'C$' ) > 'C$' ).
tff(func_def_512,type,
sK199: ( 'C_c_fun$' * 'C_option$' * 'C$' ) > 'C$' ).
tff(func_def_513,type,
sK200: ( 'B_c_fun$' * 'B_option$' * 'C$' ) > 'B$' ).
tff(func_def_514,type,
sK201: ( 'B_option$' * 'B_b_option_fun$' * 'B$' ) > 'B$' ).
tff(func_def_515,type,
sK202: ( 'C_b_fun$' * 'C_option$' * 'B$' ) > 'C$' ).
tff(func_def_516,type,
sK203: ( 'A_b_fun$' * 'A_option$' * 'B$' ) > 'A$' ).
tff(func_def_517,type,
sK204: ( 'B_b_fun$' * 'B_option$' * 'B$' ) > 'B$' ).
tff(func_def_518,type,
sK205: ( 'A_option$' * 'A_b_fun$' * 'A_b_fun$' ) > 'A$' ).
tff(func_def_519,type,
sK206: ( 'A_option$' * 'A_a_fun$' * 'A_a_fun$' ) > 'A$' ).
tff(func_def_520,type,
sK207: ( 'C_option$' * 'C_b_option_fun$' * 'C_b_option_fun$' ) > 'C$' ).
tff(func_def_521,type,
sK208: ( 'C_option$' * 'C_b_fun$' * 'C_b_fun$' ) > 'C$' ).
tff(func_def_522,type,
sK209: ( 'C_option$' * 'C_c_option_fun$' * 'C_c_option_fun$' ) > 'C$' ).
tff(func_def_523,type,
sK210: ( 'B_option$' * 'B_c_fun$' * 'B_c_fun$' ) > 'B$' ).
tff(func_def_524,type,
sK211: ( 'B_option$' * 'B_c_option_fun$' * 'B_c_option_fun$' ) > 'B$' ).
tff(func_def_525,type,
sK212: ( 'B_option$' * 'B_b_fun$' * 'B_b_fun$' ) > 'B$' ).
tff(func_def_526,type,
sK213: ( 'B_option$' * 'B_b_option_fun$' * 'B_b_option_fun$' ) > 'B$' ).
tff(func_def_527,type,
sK214: ( 'A_option$' * 'A_b_fun$' * 'A_b_fun$' ) > 'A$' ).
tff(func_def_528,type,
sK215: ( 'A_option$' * 'A_a_fun$' * 'A_a_fun$' ) > 'A$' ).
tff(func_def_529,type,
sK216: ( 'C_option$' * 'C_b_option_fun$' * 'C_b_option_fun$' ) > 'C$' ).
tff(func_def_530,type,
sK217: ( 'C_option$' * 'C_b_fun$' * 'C_b_fun$' ) > 'C$' ).
tff(func_def_531,type,
sK218: ( 'C_option$' * 'C_c_option_fun$' * 'C_c_option_fun$' ) > 'C$' ).
tff(func_def_532,type,
sK219: ( 'B_option$' * 'B_c_fun$' * 'B_c_fun$' ) > 'B$' ).
tff(func_def_533,type,
sK220: ( 'B_option$' * 'B_c_option_fun$' * 'B_c_option_fun$' ) > 'B$' ).
tff(func_def_534,type,
sK221: ( 'B_option$' * 'B_b_fun$' * 'B_b_fun$' ) > 'B$' ).
tff(func_def_535,type,
sK222: ( 'B_option$' * 'B_b_option_fun$' * 'B_b_option_fun$' ) > 'B$' ).
tff(func_def_536,type,
sK223: 'C_c_c_fun_fun$' > 'C$' ).
tff(func_def_537,type,
sK224: 'C_c_c_fun_fun$' > 'C$' ).
tff(func_def_538,type,
sK225: 'C_c_c_fun_fun$' > 'C$' ).
tff(func_def_539,type,
sK226: 'C_c_c_fun_fun$' > 'C$' ).
tff(func_def_540,type,
sK227: 'C_c_c_fun_fun$' > 'C$' ).
tff(func_def_541,type,
sK228: 'B_b_b_fun_fun$' > 'B$' ).
tff(func_def_542,type,
sK229: 'B_b_b_fun_fun$' > 'B$' ).
tff(func_def_543,type,
sK230: 'B_b_b_fun_fun$' > 'B$' ).
tff(func_def_544,type,
sK231: 'B_b_b_fun_fun$' > 'B$' ).
tff(func_def_545,type,
sK232: 'B_b_b_fun_fun$' > 'B$' ).
tff(func_def_546,type,
sK233: ( 'A_option$' * 'A_option$' * 'A_b_fun$' * 'A_b_fun$' ) > 'A$' ).
tff(func_def_547,type,
sK234: ( 'A_option$' * 'A_option$' * 'A_b_fun$' * 'A_b_fun$' ) > 'A$' ).
tff(func_def_548,type,
sK235: ( 'A_option$' * 'A_option$' * 'A_a_fun$' * 'A_a_fun$' ) > 'A$' ).
tff(func_def_549,type,
sK236: ( 'A_option$' * 'A_option$' * 'A_a_fun$' * 'A_a_fun$' ) > 'A$' ).
tff(func_def_550,type,
sK237: ( 'C_option$' * 'C_option$' * 'C_b_fun$' * 'C_b_fun$' ) > 'C$' ).
tff(func_def_551,type,
sK238: ( 'C_option$' * 'C_option$' * 'C_b_fun$' * 'C_b_fun$' ) > 'C$' ).
tff(func_def_552,type,
sK239: ( 'B_option$' * 'B_option$' * 'B_c_fun$' * 'B_c_fun$' ) > 'B$' ).
tff(func_def_553,type,
sK240: ( 'B_option$' * 'B_option$' * 'B_c_fun$' * 'B_c_fun$' ) > 'B$' ).
tff(func_def_554,type,
sK241: ( 'B_option$' * 'B_option$' * 'B_b_fun$' * 'B_b_fun$' ) > 'B$' ).
tff(func_def_555,type,
sK242: ( 'B_option$' * 'B_option$' * 'B_b_fun$' * 'B_b_fun$' ) > 'B$' ).
tff(func_def_556,type,
sK243: 'C_c_c_fun_fun$' > 'C$' ).
tff(func_def_557,type,
sK244: 'C_c_c_fun_fun$' > 'C$' ).
tff(func_def_558,type,
sK245: 'C_c_c_fun_fun$' > 'C$' ).
tff(func_def_559,type,
sK246: 'B_b_b_fun_fun$' > 'B$' ).
tff(func_def_560,type,
sK247: 'B_b_b_fun_fun$' > 'B$' ).
tff(func_def_561,type,
sK248: 'B_b_b_fun_fun$' > 'B$' ).
tff(pred_def_1,type,
'valid_getter_setter$c': ( 'B_c_fun$' * 'C_b_b_fun_fun$' ) > $o ).
tff(pred_def_2,type,
'member$b': ( 'C$' * 'C_set$' ) > $o ).
tff(pred_def_3,type,
'fun_app$z': ( 'A_bool_fun$' * 'A$' ) > $o ).
tff(pred_def_4,type,
'register$f': 'C_c_option_fun_c_c_option_fun_fun$' > $o ).
tff(pred_def_5,type,
'is_empty$c': 'C_option_set$' > $o ).
tff(pred_def_6,type,
'member$c': ( 'B$' * 'B_set$' ) > $o ).
tff(pred_def_7,type,
'member$d': ( 'A$' * 'A_set$' ) > $o ).
tff(pred_def_8,type,
'member$a': ( 'B_option$' * 'B_option_set$' ) > $o ).
tff(pred_def_9,type,
'inj_on$': ( 'C_c_option_fun$' * 'C_set$' ) > $o ).
tff(pred_def_10,type,
'is_empty$b': 'B_option_set$' > $o ).
tff(pred_def_11,type,
'valid_getter_setter$a': ( 'B_a_fun$' * 'A_b_b_fun_fun$' ) > $o ).
tff(pred_def_12,type,
'preregister$e': 'A_a_option_fun_a_a_option_fun_fun$' > $o ).
tff(pred_def_13,type,
'is_empty$a': 'C_set$' > $o ).
tff(pred_def_14,type,
'is_empty$': 'B_set$' > $o ).
tff(pred_def_15,type,
'fun_app$b': ( 'C_bool_fun$' * 'C$' ) > $o ).
tff(pred_def_16,type,
'preregister$d': 'C_c_option_fun_b_b_option_fun_fun$' > $o ).
tff(pred_def_18,type,
'register$': 'A_a_option_fun_b_b_option_fun_fun$' > $o ).
tff(pred_def_19,type,
'register$d': 'A_a_option_fun_c_c_option_fun_fun$' > $o ).
tff(pred_def_20,type,
'member$': ( 'C_option$' * 'C_option_set$' ) > $o ).
tff(pred_def_21,type,
'valid_getter_setter$b': ( 'B_b_fun$' * 'B_b_b_fun_fun$' ) > $o ).
tff(pred_def_22,type,
'preregister$b': 'B_b_option_fun_c_c_option_fun_fun$' > $o ).
tff(pred_def_23,type,
'preregister$f': 'A_a_option_fun_c_c_option_fun_fun$' > $o ).
tff(pred_def_24,type,
'register$b': 'C_c_option_fun_a_a_option_fun_fun$' > $o ).
tff(pred_def_25,type,
'fun_app$c': ( 'B_bool_fun$' * 'B$' ) > $o ).
tff(pred_def_26,type,
'valid_getter_setter$': ( 'C_b_fun$' * 'B_c_c_fun_fun$' ) > $o ).
tff(pred_def_27,type,
'register$e': 'A_a_option_fun_a_a_option_fun_fun$' > $o ).
tff(pred_def_28,type,
'register$h': 'B_b_option_fun_b_b_option_fun_fun$' > $o ).
tff(pred_def_29,type,
'preregister$a': 'C_c_option_fun_c_c_option_fun_fun$' > $o ).
tff(pred_def_30,type,
'fun_app$aw': ( 'A_option_bool_fun$' * 'A_option$' ) > $o ).
tff(pred_def_31,type,
'register$c': 'B_b_option_fun_a_a_option_fun_fun$' > $o ).
tff(pred_def_32,type,
'inj_on$a': ( 'B_b_option_fun$' * 'B_set$' ) > $o ).
tff(pred_def_33,type,
'fun_app$ag': ( 'Bool_bool_fun$' * tlbool ) > $o ).
tff(pred_def_34,type,
'register$a': 'B_b_option_fun_c_c_option_fun_fun$' > $o ).
tff(pred_def_35,type,
'preregister$': 'B_b_option_fun_b_b_option_fun_fun$' > $o ).
tff(pred_def_36,type,
'preregister$c': 'A_a_option_fun_b_b_option_fun_fun$' > $o ).
tff(pred_def_37,type,
'register$g': 'C_c_option_fun_b_b_option_fun_fun$' > $o ).
tff(pred_def_38,type,
'fun_app$': ( 'C_option_bool_fun$' * 'C_option$' ) > $o ).
tff(pred_def_39,type,
'fun_app$a': ( 'B_option_bool_fun$' * 'B_option$' ) > $o ).
tff(pred_def_40,type,
'valid_getter_setter$d': ( 'C_c_fun$' * 'C_c_c_fun_fun$' ) > $o ).
tff(pred_def_41,type,
sP0: ( 'A_option$' * 'A_option$' ) > $o ).
tff(pred_def_42,type,
sP1: ( 'C_option$' * 'C_option$' ) > $o ).
tff(pred_def_43,type,
sP2: ( 'B_option$' * 'B_option$' ) > $o ).
tff(pred_def_44,type,
sP3: ( 'A_option$' * 'A_option$' * 'A_option_a_option_bool_fun_fun$' ) > $o ).
tff(pred_def_45,type,
sP4: ( 'C_option$' * 'A_option$' * 'A_option_c_option_bool_fun_fun$' ) > $o ).
tff(pred_def_46,type,
sP5: ( 'B_option$' * 'A_option$' * 'A_option_b_option_bool_fun_fun$' ) > $o ).
tff(pred_def_47,type,
sP6: ( 'A_option$' * 'C_option$' * 'C_option_a_option_bool_fun_fun$' ) > $o ).
tff(pred_def_48,type,
sP7: ( 'C_option$' * 'C_option$' * 'C_option_c_option_bool_fun_fun$' ) > $o ).
tff(pred_def_49,type,
sP8: ( 'B_option$' * 'C_option$' * 'C_option_b_option_bool_fun_fun$' ) > $o ).
tff(pred_def_50,type,
sP9: ( 'A_option$' * 'B_option$' * 'B_option_a_option_bool_fun_fun$' ) > $o ).
tff(pred_def_51,type,
sP10: ( 'C_option$' * 'B_option$' * 'B_option_c_option_bool_fun_fun$' ) > $o ).
tff(pred_def_52,type,
sP11: ( 'B_option$' * 'B_option$' * 'B_option_b_option_bool_fun_fun$' ) > $o ).
tff(pred_def_53,type,
sP12: ( 'C_a_option_fun$' * 'A_option_bool_fun$' * 'C_option$' ) > $o ).
tff(pred_def_54,type,
sP13: ( 'B_a_option_fun$' * 'A_option_bool_fun$' * 'B_option$' ) > $o ).
tff(pred_def_55,type,
sP14: ( 'C_a_option_fun$' * 'A_option_bool_fun$' * 'C_option$' ) > $o ).
tff(pred_def_56,type,
sP15: ( 'B_a_option_fun$' * 'A_option_bool_fun$' * 'B_option$' ) > $o ).
tff(pred_def_57,type,
sP16: ( 'A_c_option_fun$' * 'C_option_bool_fun$' * 'A_option$' ) > $o ).
tff(pred_def_58,type,
sP17: ( 'A_c_option_fun$' * 'C_option_bool_fun$' * 'A_option$' ) > $o ).
tff(pred_def_59,type,
sP18: ( 'B_c_option_fun$' * 'C_option_bool_fun$' * 'B_option$' ) > $o ).
tff(pred_def_60,type,
sP19: ( 'B_c_option_fun$' * 'C_option_bool_fun$' * 'B_option$' ) > $o ).
tff(pred_def_61,type,
sP20: ( 'C_option$' * 'C_bool_fun$' * tlbool ) > $o ).
tff(pred_def_62,type,
sP21: ( 'A_b_option_fun$' * 'B_option_bool_fun$' * 'A_option$' ) > $o ).
tff(pred_def_63,type,
sP22: ( 'A_b_option_fun$' * 'B_option_bool_fun$' * 'A_option$' ) > $o ).
tff(pred_def_64,type,
sP23: ( 'C_b_option_fun$' * 'B_option_bool_fun$' * 'C_option$' ) > $o ).
tff(pred_def_65,type,
sP24: ( 'C_b_option_fun$' * 'B_option_bool_fun$' * 'C_option$' ) > $o ).
tff(pred_def_66,type,
sP25: ( 'B_option$' * 'B_bool_fun$' * tlbool ) > $o ).
tff(pred_def_67,type,
sP26: ( 'A_a_option_fun$' * 'A_option_bool_fun$' * 'A_option$' ) > $o ).
tff(pred_def_68,type,
sP27: ( 'A_a_option_fun$' * 'A_option_bool_fun$' * 'A_option$' ) > $o ).
tff(pred_def_69,type,
sP28: ( 'C_c_option_fun$' * 'C_option_bool_fun$' * 'C_option$' ) > $o ).
tff(pred_def_70,type,
sP29: ( 'C_c_option_fun$' * 'C_option_bool_fun$' * 'C_option$' ) > $o ).
tff(pred_def_71,type,
sP30: ( 'B_b_option_fun$' * 'B_option_bool_fun$' * 'B_option$' ) > $o ).
tff(pred_def_72,type,
sP31: ( 'B_b_option_fun$' * 'B_option_bool_fun$' * 'B_option$' ) > $o ).
tff(pred_def_73,type,
sP32: ( 'C_option$' * 'C_bool_fun$' * 'Bool_bool_fun$' * tlbool ) > $o ).
tff(pred_def_74,type,
sP33: ( 'B_option$' * 'B_bool_fun$' * 'Bool_bool_fun$' * tlbool ) > $o ).
tff(pred_def_75,type,
sP34: ( 'C_option$' * 'C_bool_fun$' * 'Bool_bool_fun$' * tlbool ) > $o ).
tff(pred_def_76,type,
sP35: ( 'B_option$' * 'B_bool_fun$' * 'Bool_bool_fun$' * tlbool ) > $o ).
tff(pred_def_77,type,
sP36: ( 'C_option$' * 'C_c_option_fun$' * 'C_option_bool_fun$' * 'C_option$' ) > $o ).
tff(pred_def_78,type,
sP37: ( 'C_option$' * 'C_c_option_fun$' * 'C_option_bool_fun$' * 'C_option$' ) > $o ).
tff(pred_def_79,type,
sP38: ( 'B_option$' * 'B_c_option_fun$' * 'C_option_bool_fun$' * 'C_option$' ) > $o ).
tff(pred_def_80,type,
sP39: ( 'B_option$' * 'B_c_option_fun$' * 'C_option_bool_fun$' * 'C_option$' ) > $o ).
tff(pred_def_81,type,
sP40: ( 'A_option$' * 'A_b_option_fun$' * 'B_option_bool_fun$' * 'B_option$' ) > $o ).
tff(pred_def_82,type,
sP41: ( 'A_option$' * 'A_b_option_fun$' * 'B_option_bool_fun$' * 'B_option$' ) > $o ).
tff(pred_def_83,type,
sP42: ( 'B_option$' * 'B_b_option_fun$' * 'B_option_bool_fun$' * 'B_option$' ) > $o ).
tff(pred_def_84,type,
sP43: ( 'B_option$' * 'B_b_option_fun$' * 'B_option_bool_fun$' * 'B_option$' ) > $o ).
tff(f19036,plain,
$false,
inference(avatar_sat_refutation,[],[f3608,f3613,f3618,f3623,f3628,f3633,f3638,f3643,f3648,f3653,f3658,f3662,f3666,f3670,f3674,f3678,f3682,f3686,f3690,f3694,f3698,f3702,f3706,f3710,f3714,f3718,f3722,f3726,f3730,f3735,f3740,f3745,f3750,f3755,f3760,f3765,f3770,f3775,f3780,f3785,f3790,f3795,f3800,f3805,f3810,f3815,f3820,f3824,f3828,f3832,f3836,f3841,f3846,f3850,f3854,f3858,f3862,f3866,f3870,f3879,f3884,f3889,f3894,f3899,f3903,f3907,f3911,f3915,f3919,f3923,f3927,f3931,f3935,f3939,f3944,f3948,f3952,f3956,f3960,f3964,f3968,f3972,f3976,f3980,f3984,f3989,f3993,f3997,f4001,f4005,f4009,f4013,f4017,f4021,f4025,f4029,f4033,f4038,f4043,f4048,f4053,f4057,f4061,f4065,f4069,f4073,f4077,f4081,f4085,f4089,f4093,f4097,f4101,f4105,f4109,f4113,f4117,f4121,f4125,f4129,f4133,f4137,f4141,f4145,f4149,f4153,f4157,f4161,f4165,f4169,f4173,f4178,f4183,f4187,f4191,f4195,f4199,f4203,f4207,f4211,f4215,f4219,f4223,f4228,f4233,f4254,f4259,f4263,f4267,f4271,f4275,f4279,f4283,f4287,f4291,f4295,f4299,f4303,f4307,f4311,f4315,f4319,f4323,f4327,f4331,f4335,f4339,f4343,f4347,f4351,f4355,f4359,f4363,f4367,f4371,f4375,f4379,f4383,f4387,f4391,f4395,f4399,f4403,f4407,f4411,f4415,f4419,f4423,f4427,f4431,f4435,f4439,f4443,f4447,f4451,f4455,f4459,f4463,f4467,f4471,f4475,f4479,f4483,f4487,f4491,f4495,f4499,f4503,f4507,f4511,f4515,f4519,f4523,f4527,f4531,f4535,f4539,f4543,f4547,f4551,f4555,f4559,f4563,f4567,f4571,f4575,f4579,f4583,f4587,f4591,f4595,f4599,f4603,f4607,f4611,f4615,f4619,f4623,f4627,f4631,f4635,f4639,f4643,f4647,f4651,f4655,f4659,f4668,f4708,f4721,f4734,f4738,f4814,f4818,f4822,f4826,f4830,f4835,f4839,f4843,f4847,f4851,f4855,f4859,f4863,f4867,f4871,f4875,f4879,f4883,f4887,f4891,f4895,f4899,f4903,f4907,f4911,f4915,f4920,f4924,f4928,f4932,f4936,f4940,f4944,f4948,f4952,f4956,f4960,f4965,f4969,f4973,f4977,f4981,f4985,f4989,f4993,f4997,f5001,f5005,f5010,f5014,f5018,f5022,f5026,f5030,f5034,f5038,f5042,f5046,f5050,f5055,f5059,f5063,f5067,f5071,f5075,f5079,f5083,f5087,f5091,f5095,f5099,f5103,f5107,f5111,f5115,f5119,f5123,f5127,f5131,f5230,f5278,f5326,f5355,f5360,f5364,f5368,f5372,f5376,f5380,f5384,f5388,f5394,f5398,f5402,f5406,f5410,f5414,f5418,f5422,f5426,f5430,f5434,f5438,f5442,f5446,f5450,f5454,f5458,f5462,f5466,f5470,f5474,f5478,f5482,f5486,f5490,f5494,f5498,f5502,f5506,f5510,f5514,f5518,f5522,f5526,f5530,f5534,f5538,f5542,f5546,f5550,f5554,f5558,f5562,f5566,f5570,f5574,f5578,f5582,f5586,f5590,f5594,f5598,f5602,f5606,f5612,f5616,f5620,f5624,f5628,f5632,f5636,f5640,f5644,f5648,f5654,f5658,f5662,f5666,f5670,f5674,f5678,f5682,f5686,f5690,f5696,f5700,f5704,f5708,f5712,f5716,f5720,f5724,f5728,f5732,f5738,f5742,f5746,f5750,f5754,f5758,f5762,f5766,f5770,f5774,f5780,f5784,f5788,f5792,f5796,f5888,f5931,f5962,f6009,f6048,f6093,f6306,f6347,f6351,f6355,f6359,f6363,f6367,f6371,f6375,f6379,f6383,f6387,f6391,f6395,f6399,f6403,f6407,f6411,f6415,f6419,f6423,f6427,f6431,f6435,f6439,f6443,f6447,f6451,f6455,f6459,f6463,f6467,f6471,f6475,f6479,f6483,f6487,f6491,f6495,f6499,f6503,f6507,f6511,f6515,f6519,f6523,f6527,f6531,f6535,f6539,f6543,f6547,f6551,f6555,f6559,f6563,f6567,f6571,f6575,f6579,f6583,f6587,f6591,f6595,f6599,f6603,f6607,f6611,f6615,f6620,f6624,f6628,f6632,f6636,f6640,f6644,f6665,f6726,f6756,f6792,f6857,f6940,f7093,f7097,f7101,f7105,f7109,f7113,f7117,f7121,f7125,f7129,f7133,f7137,f7141,f7145,f7149,f7153,f7157,f7161,f7165,f7169,f7173,f7177,f7181,f7185,f7189,f7193,f7197,f7201,f7205,f7209,f7213,f7217,f7221,f7225,f7229,f7233,f7237,f7241,f7245,f7249,f7253,f7257,f7261,f7265,f7269,f7273,f7278,f7282,f7286,f7290,f7294,f7298,f7302,f7306,f7310,f7314,f7318,f7322,f7326,f7330,f7334,f7338,f7342,f7346,f7350,f7354,f7358,f7362,f7366,f7370,f7374,f7378,f7382,f7386,f7390,f7394,f7398,f7402,f7406,f7410,f7414,f7418,f7908,f7912,f7916,f7920,f7924,f7928,f7932,f7936,f7940,f7944,f7948,f7952,f7956,f7960,f7964,f7968,f7972,f7976,f7980,f7984,f7988,f7992,f7996,f8000,f8004,f8008,f8012,f8016,f8020,f8024,f8028,f8032,f8036,f8040,f8044,f8048,f8052,f8056,f8060,f8064,f8068,f8072,f8076,f8080,f8084,f8088,f8092,f8096,f8100,f8104,f8108,f8112,f8116,f8120,f8124,f8128,f8132,f8136,f8140,f8144,f8148,f8152,f8156,f8160,f8164,f8168,f8172,f8176,f8180,f8184,f8188,f8192,f8196,f8202,f8206,f8210,f8214,f8218,f8222,f8226,f8230,f8234,f8238,f8244,f8248,f8252,f8256,f8260,f8264,f8268,f8272,f8276,f8280,f8626,f8672,f8676,f8735,f8891,f9050,f9054,f9058,f9062,f9066,f9070,f9074,f9078,f9082,f9086,f9090,f9094,f9098,f9102,f9106,f9110,f9114,f9118,f9122,f9126,f9130,f9134,f9138,f9142,f9146,f9150,f9154,f9158,f9162,f9166,f9170,f9174,f9178,f9182,f9186,f9190,f9194,f9198,f9202,f9206,f9210,f9214,f9218,f9222,f9226,f9230,f9234,f9238,f9242,f9246,f9250,f9254,f9258,f9262,f9266,f9270,f9274,f9402,f9874,f9878,f9882,f9886,f9890,f9894,f9898,f9902,f9906,f9910,f9914,f9918,f9922,f9926,f9930,f9934,f9938,f9942,f9946,f9950,f9954,f9958,f9962,f9966,f9970,f9974,f9978,f9982,f9986,f9990,f9994,f9998,f10002,f10006,f10010,f10688,f10692,f10696,f10700,f10704,f10708,f10712,f10716,f10720,f10724,f10728,f10732,f10736,f10740,f10744,f10748,f10752,f10756,f10760,f10764,f10768,f10772,f10776,f10780,f10784,f10788,f10792,f10796,f10800,f10804,f10808,f10812,f10816,f10820,f10824,f10828,f10832,f10836,f10840,f10844,f10848,f10852,f10856,f10860,f10864,f10868,f10872,f10876,f10880,f10884,f10888,f10892,f10896,f10900,f10904,f10908,f10912,f10916,f10920,f10924,f10928,f10932,f10936,f10940,f10944,f10948,f10952,f10956,f10960,f10964,f10968,f10972,f10976,f10980,f10984,f10988,f10992,f10996,f11000,f11004,f11008,f11012,f11016,f11020,f11024,f11028,f11032,f11036,f11040,f11044,f11048,f11052,f11056,f11060,f11064,f11068,f11072,f11076,f11080,f11084,f11088,f11092,f11096,f11100,f11104,f11108,f11112,f11116,f11120,f11124,f11128,f11132,f11136,f11140,f11144,f11148,f11152,f11156,f11160,f11164,f11168,f11172,f11176,f11180,f11184,f11188,f11192,f11196,f11200,f11204,f11208,f11212,f11216,f11220,f11224,f11228,f11232,f11236,f11240,f11244,f11248,f11252,f11256,f11260,f11264,f11268,f11272,f11276,f11280,f11284,f11288,f11292,f11296,f11300,f11304,f11308,f11312,f11316,f11320,f11324,f11328,f11332,f11336,f11340,f11344,f11348,f11352,f11356,f11360,f11364,f11425,f11660,f11876,f13532,f13536,f13540,f13544,f13548,f13552,f13556,f13561,f13565,f13569,f13573,f13577,f13581,f13585,f13589,f13593,f13597,f13603,f13607,f13611,f13615,f13619,f13623,f13627,f13631,f13635,f13639,f13643,f13647,f13651,f13655,f13659,f13663,f13667,f13671,f13675,f13679,f13683,f13687,f13691,f13695,f13699,f13703,f13707,f13711,f13715,f13719,f13723,f13727,f13731,f13735,f13739,f13743,f13747,f13751,f13755,f13759,f13763,f13767,f13771,f13775,f13779,f13783,f13787,f13791,f13795,f13799,f13803,f13808,f13812,f13828,f13832,f13968,f14131,f14246,f14413,f14531,f14854,f14954,f14958,f14962,f14966,f14970,f14974,f14978,f14982,f14986,f14990,f14995,f14999,f15003,f15007,f15011,f15015,f15019,f15023,f15027,f15031,f15036,f15040,f15044,f15048,f15052,f15056,f15060,f15064,f15068,f15072,f15077,f15081,f15085,f15089,f15093,f15097,f15101,f15105,f15109,f16221,f16225,f16231,f16235,f16239,f16243,f16247,f16251,f16255,f16274,f16396,f16400,f16404,f16408,f16412,f16416,f16420,f16424,f16428,f16432,f16436,f16440,f16490,f16600,f16604,f16608,f16612,f16616,f16620,f16624,f16628,f16632,f16636,f16640,f16644,f16655,f16803,f16807,f16811,f16820,f16824,f16828,f16832,f16836,f16840,f16847,f16851,f16855,f16859,f16863,f16867,f16871,f16875,f16879,f16883,f16888,f16892,f16896,f16900,f16904,f16908,f16928,f17019,f17099,f17103,f17107,f17111,f17116,f17120,f17124,f17128,f17132,f17136,f17235,f17239,f17243,f17253,f17257,f17261,f17265,f17269,f17348,f17354,f17359,f17363,f17367,f17374,f17378,f17382,f17395,f17399,f17409,f17413,f17417,f17421,f17425,f17442,f17446,f17450,f17454,f17458,f17462,f17466,f17470,f17474,f17478,f17482,f17486,f17490,f17494,f17498,f17502,f17506,f17510,f17514,f17637,f17641,f17645,f17649,f17653,f17658,f17664,f17670,f17675,f17679,f17683,f17687,f17694,f17698,f17702,f17706,f17710,f17714,f17718,f17722,f17726,f17730,f17735,f17740,f17745,f17750,f17754,f17758,f17762,f17766,f17770,f17774,f17778,f17782,f17786,f17790,f17794,f17798,f17802,f17810,f17814,f17818,f17822,f17826,f17830,f17834,f17838,f17842,f17846,f17850,f17854,f17858,f17862,f17866,f17870,f17874,f17878,f17882,f17886,f17890,f17894,f17898,f17902,f17906,f17910,f17914,f17918,f17922,f17926,f17930,f17938,f17942,f17946,f17950,f17954,f17958,f17962,f17966,f17970,f17974,f17978,f17982,f17986,f17990,f17994,f17998,f18002,f18006,f18010,f18014,f18018,f18022,f18026,f18030,f18034,f18038,f18042,f18046,f18050,f18054,f18058,f18062,f18066,f18070,f18074,f18078,f18082,f18086,f18090,f18094,f18098,f18102,f18106,f18110,f18114,f18118,f18122,f18126,f18130,f18141,f18175,f18205,f18233,f18461,f19035]) ).
tff(f19035,plain,
( ~ spl249_4
| ~ spl249_167
| spl249_1332 ),
inference(avatar_split_clause,[],[f18818,f18458,f4337,f3620]) ).
tff(f3620,plain,
( spl249_4
<=> 'register$a'('g$') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_4])]) ).
tff(f4337,plain,
( spl249_167
<=> ! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( 'valid_getter_setter$'(sK63(X0),sK64(X0))
| ~ 'register$a'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_167])]) ).
tff(f18458,plain,
( spl249_1332
<=> 'valid_getter_setter$'(sK63('g$'),sK64('g$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1332])]) ).
tff(f18818,plain,
( ~ 'register$a'('g$')
| ~ spl249_167
| spl249_1332 ),
inference(resolution,[],[f18460,f4338]) ).
tff(f4338,plain,
( ! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( 'valid_getter_setter$'(sK63(X0),sK64(X0))
| ~ 'register$a'(X0) )
| ~ spl249_167 ),
inference(avatar_component_clause,[],[f4337]) ).
tff(f18460,plain,
( ~ 'valid_getter_setter$'(sK63('g$'),sK64('g$'))
| spl249_1332 ),
inference(avatar_component_clause,[],[f18458]) ).
tff(f18461,plain,
( ~ spl249_1332
| ~ spl249_1177
| ~ spl249_1233 ),
inference(avatar_split_clause,[],[f18196,f17742,f17357,f18458]) ).
tff(f17357,plain,
( spl249_1177
<=> ! [X0: 'B_c_c_fun_fun$',X1: 'C_b_fun$'] :
( ( 'fun_app$j'('fun_app$am'('g$',sK44(X0,X1)),sK45(X0,X1)) != 'fun_app$j'('fun_app$am'('register_from_getter_setter$a'(X1,X0),sK44(X0,X1)),sK45(X0,X1)) )
| ~ 'valid_getter_setter$'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1177])]) ).
tff(f17742,plain,
( spl249_1233
<=> ( 'g$' = 'register_from_getter_setter$a'(sK63('g$'),sK64('g$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1233])]) ).
tff(f18196,plain,
( ~ 'valid_getter_setter$'(sK63('g$'),sK64('g$'))
| ~ spl249_1177
| ~ spl249_1233 ),
inference(trivial_inequality_removal,[],[f18194]) ).
tff(f18194,plain,
( ( 'fun_app$j'('fun_app$am'('g$',sK44(sK64('g$'),sK63('g$'))),sK45(sK64('g$'),sK63('g$'))) != 'fun_app$j'('fun_app$am'('g$',sK44(sK64('g$'),sK63('g$'))),sK45(sK64('g$'),sK63('g$'))) )
| ~ 'valid_getter_setter$'(sK63('g$'),sK64('g$'))
| ~ spl249_1177
| ~ spl249_1233 ),
inference(superposition,[],[f17358,f17744]) ).
tff(f17744,plain,
( ( 'g$' = 'register_from_getter_setter$a'(sK63('g$'),sK64('g$')) )
| ~ spl249_1233 ),
inference(avatar_component_clause,[],[f17742]) ).
tff(f17358,plain,
( ! [X0: 'B_c_c_fun_fun$',X1: 'C_b_fun$'] :
( ( 'fun_app$j'('fun_app$am'('g$',sK44(X0,X1)),sK45(X0,X1)) != 'fun_app$j'('fun_app$am'('register_from_getter_setter$a'(X1,X0),sK44(X0,X1)),sK45(X0,X1)) )
| ~ 'valid_getter_setter$'(X1,X0) )
| ~ spl249_1177 ),
inference(avatar_component_clause,[],[f17357]) ).
tff(f18233,plain,
( spl249_1331
| ~ spl249_1213 ),
inference(avatar_split_clause,[],[f18137,f17651,f18231]) ).
tff(f18231,plain,
( spl249_1331
<=> ! [X0: 'B_option$'] : ~ 'fun_app$a'('uvk$'('bot$a'),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1331])]) ).
tff(f17651,plain,
( spl249_1213
<=> ! [X0: 'B_option_set$',X1: 'B_option$'] :
( ( 'bot$a' != X0 )
| ~ 'fun_app$a'('uvk$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1213])]) ).
tff(f18137,plain,
( ! [X0: 'B_option$'] : ~ 'fun_app$a'('uvk$'('bot$a'),X0)
| ~ spl249_1213 ),
inference(equality_resolution,[],[f17652]) ).
tff(f17652,plain,
( ! [X0: 'B_option_set$',X1: 'B_option$'] :
( ( 'bot$a' != X0 )
| ~ 'fun_app$a'('uvk$'(X0),X1) )
| ~ spl249_1213 ),
inference(avatar_component_clause,[],[f17651]) ).
tff(f18205,plain,
( spl249_1330
| ~ spl249_1212 ),
inference(avatar_split_clause,[],[f18136,f17647,f18203]) ).
tff(f18203,plain,
( spl249_1330
<=> ! [X0: 'C_option$'] : ~ 'fun_app$'('uvl$'('bot$b'),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1330])]) ).
tff(f17647,plain,
( spl249_1212
<=> ! [X0: 'C_option_set$',X1: 'C_option$'] :
( ( 'bot$b' != X0 )
| ~ 'fun_app$'('uvl$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1212])]) ).
tff(f18136,plain,
( ! [X0: 'C_option$'] : ~ 'fun_app$'('uvl$'('bot$b'),X0)
| ~ spl249_1212 ),
inference(equality_resolution,[],[f17648]) ).
tff(f17648,plain,
( ! [X0: 'C_option_set$',X1: 'C_option$'] :
( ( 'bot$b' != X0 )
| ~ 'fun_app$'('uvl$'(X0),X1) )
| ~ spl249_1212 ),
inference(avatar_component_clause,[],[f17647]) ).
tff(f18175,plain,
( spl249_1329
| ~ spl249_1211 ),
inference(avatar_split_clause,[],[f18135,f17643,f18173]) ).
tff(f18173,plain,
( spl249_1329
<=> ! [X0: 'B$'] : ~ 'fun_app$c'('uvi$'('bot$d'),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1329])]) ).
tff(f17643,plain,
( spl249_1211
<=> ! [X0: 'B_set$',X1: 'B$'] :
( ( 'bot$d' != X0 )
| ~ 'fun_app$c'('uvi$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1211])]) ).
tff(f18135,plain,
( ! [X0: 'B$'] : ~ 'fun_app$c'('uvi$'('bot$d'),X0)
| ~ spl249_1211 ),
inference(equality_resolution,[],[f17644]) ).
tff(f17644,plain,
( ! [X0: 'B_set$',X1: 'B$'] :
( ( 'bot$d' != X0 )
| ~ 'fun_app$c'('uvi$'(X0),X1) )
| ~ spl249_1211 ),
inference(avatar_component_clause,[],[f17643]) ).
tff(f18141,plain,
( spl249_1328
| ~ spl249_1210 ),
inference(avatar_split_clause,[],[f18134,f17639,f18139]) ).
tff(f18139,plain,
( spl249_1328
<=> ! [X0: 'C$'] : ~ 'fun_app$b'('uvj$'('bot$c'),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1328])]) ).
tff(f17639,plain,
( spl249_1210
<=> ! [X0: 'C_set$',X1: 'C$'] :
( ( 'bot$c' != X0 )
| ~ 'fun_app$b'('uvj$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1210])]) ).
tff(f18134,plain,
( ! [X0: 'C$'] : ~ 'fun_app$b'('uvj$'('bot$c'),X0)
| ~ spl249_1210 ),
inference(equality_resolution,[],[f17640]) ).
tff(f17640,plain,
( ! [X0: 'C_set$',X1: 'C$'] :
( ( 'bot$c' != X0 )
| ~ 'fun_app$b'('uvj$'(X0),X1) )
| ~ spl249_1210 ),
inference(avatar_component_clause,[],[f17639]) ).
tff(f18130,plain,
( spl249_1327
| ~ spl249_201
| ~ spl249_770 ),
inference(avatar_split_clause,[],[f10021,f9876,f4473,f18128]) ).
tff(f18128,plain,
( spl249_1327
<=> ! [X0: 'B_b_b_fun_fun$',X1: 'B_option_option$'] : ( 'map_option$i'('combine_options$b'(X0,'none$a'),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1327])]) ).
tff(f4473,plain,
( spl249_201
<=> ! [X0: 'B_b_b_fun_fun$',X1: 'B_option$'] : ( 'fun_app$s'('combine_options$b'(X0,'none$a'),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_201])]) ).
tff(f9876,plain,
( spl249_770
<=> ! [X0: 'B_option_option$',X1: 'B_option_b_option_fun$'] :
( ( 'map_option$i'(X1,X0) = X0 )
| ( sK118(X0,X1) != 'fun_app$s'(X1,sK118(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_770])]) ).
tff(f10021,plain,
( ! [X0: 'B_b_b_fun_fun$',X1: 'B_option_option$'] : ( 'map_option$i'('combine_options$b'(X0,'none$a'),X1) = X1 )
| ~ spl249_201
| ~ spl249_770 ),
inference(trivial_inequality_removal,[],[f10020]) ).
tff(f10020,plain,
( ! [X0: 'B_b_b_fun_fun$',X1: 'B_option_option$'] :
( ( sK118(X1,'combine_options$b'(X0,'none$a')) != sK118(X1,'combine_options$b'(X0,'none$a')) )
| ( 'map_option$i'('combine_options$b'(X0,'none$a'),X1) = X1 ) )
| ~ spl249_201
| ~ spl249_770 ),
inference(superposition,[],[f9877,f4474]) ).
tff(f4474,plain,
( ! [X0: 'B_b_b_fun_fun$',X1: 'B_option$'] : ( 'fun_app$s'('combine_options$b'(X0,'none$a'),X1) = X1 )
| ~ spl249_201 ),
inference(avatar_component_clause,[],[f4473]) ).
tff(f9877,plain,
( ! [X0: 'B_option_option$',X1: 'B_option_b_option_fun$'] :
( ( sK118(X0,X1) != 'fun_app$s'(X1,sK118(X0,X1)) )
| ( 'map_option$i'(X1,X0) = X0 ) )
| ~ spl249_770 ),
inference(avatar_component_clause,[],[f9876]) ).
tff(f18126,plain,
( spl249_1326
| ~ spl249_196
| ~ spl249_769 ),
inference(avatar_split_clause,[],[f10015,f9872,f4453,f18124]) ).
tff(f18124,plain,
( spl249_1326
<=> ! [X0: 'C_c_c_fun_fun$',X1: 'C_option_option$'] : ( 'map_option$j'('combine_options$a'(X0,'none$'),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1326])]) ).
tff(f4453,plain,
( spl249_196
<=> ! [X0: 'C_c_c_fun_fun$',X1: 'C_option$'] : ( 'fun_app$u'('combine_options$a'(X0,'none$'),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_196])]) ).
tff(f9872,plain,
( spl249_769
<=> ! [X0: 'C_option_option$',X1: 'C_option_c_option_fun$'] :
( ( 'map_option$j'(X1,X0) = X0 )
| ( sK117(X0,X1) != 'fun_app$u'(X1,sK117(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_769])]) ).
tff(f10015,plain,
( ! [X0: 'C_c_c_fun_fun$',X1: 'C_option_option$'] : ( 'map_option$j'('combine_options$a'(X0,'none$'),X1) = X1 )
| ~ spl249_196
| ~ spl249_769 ),
inference(trivial_inequality_removal,[],[f10012]) ).
tff(f10012,plain,
( ! [X0: 'C_c_c_fun_fun$',X1: 'C_option_option$'] :
( ( sK117(X1,'combine_options$a'(X0,'none$')) != sK117(X1,'combine_options$a'(X0,'none$')) )
| ( 'map_option$j'('combine_options$a'(X0,'none$'),X1) = X1 ) )
| ~ spl249_196
| ~ spl249_769 ),
inference(superposition,[],[f9873,f4454]) ).
tff(f4454,plain,
( ! [X0: 'C_c_c_fun_fun$',X1: 'C_option$'] : ( 'fun_app$u'('combine_options$a'(X0,'none$'),X1) = X1 )
| ~ spl249_196 ),
inference(avatar_component_clause,[],[f4453]) ).
tff(f9873,plain,
( ! [X0: 'C_option_option$',X1: 'C_option_c_option_fun$'] :
( ( sK117(X0,X1) != 'fun_app$u'(X1,sK117(X0,X1)) )
| ( 'map_option$j'(X1,X0) = X0 ) )
| ~ spl249_769 ),
inference(avatar_component_clause,[],[f9872]) ).
tff(f18122,plain,
( spl249_1325
| ~ spl249_74
| ~ spl249_79
| ~ spl249_763 ),
inference(avatar_split_clause,[],[f9850,f9256,f3958,f3937,f18120]) ).
tff(f18120,plain,
( spl249_1325
<=> ! [X0: 'B$',X1: 'C_b_option_fun$'] : ( 'none$a' = 'fun_app$g'('uvv$'('uwb$',X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1325])]) ).
tff(f3937,plain,
( spl249_74
<=> ! [X0: 'B_option$'] : ( 'none$' = 'bind$b'(X0,'uwb$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_74])]) ).
tff(f3958,plain,
( spl249_79
<=> ! [X0: 'C_b_option_fun$'] : ( 'none$a' = 'bind$a'('none$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_79])]) ).
tff(f9256,plain,
( spl249_763
<=> ! [X2: 'B$',X0: 'B_c_option_fun$',X1: 'C_b_option_fun$'] : ( 'fun_app$g'('uvv$'(X0,X1),X2) = 'bind$a'('bind$b'('fun_app$g'('some$',X2),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_763])]) ).
tff(f9850,plain,
( ! [X0: 'B$',X1: 'C_b_option_fun$'] : ( 'none$a' = 'fun_app$g'('uvv$'('uwb$',X1),X0) )
| ~ spl249_74
| ~ spl249_79
| ~ spl249_763 ),
inference(forward_demodulation,[],[f9835,f3959]) ).
tff(f3959,plain,
( ! [X0: 'C_b_option_fun$'] : ( 'none$a' = 'bind$a'('none$',X0) )
| ~ spl249_79 ),
inference(avatar_component_clause,[],[f3958]) ).
tff(f9835,plain,
( ! [X0: 'B$',X1: 'C_b_option_fun$'] : ( 'bind$a'('none$',X1) = 'fun_app$g'('uvv$'('uwb$',X1),X0) )
| ~ spl249_74
| ~ spl249_763 ),
inference(superposition,[],[f9257,f3938]) ).
tff(f3938,plain,
( ! [X0: 'B_option$'] : ( 'none$' = 'bind$b'(X0,'uwb$') )
| ~ spl249_74 ),
inference(avatar_component_clause,[],[f3937]) ).
tff(f9257,plain,
( ! [X2: 'B$',X0: 'B_c_option_fun$',X1: 'C_b_option_fun$'] : ( 'fun_app$g'('uvv$'(X0,X1),X2) = 'bind$a'('bind$b'('fun_app$g'('some$',X2),X0),X1) )
| ~ spl249_763 ),
inference(avatar_component_clause,[],[f9256]) ).
tff(f18118,plain,
( spl249_1324
| ~ spl249_78
| ~ spl249_763 ),
inference(avatar_split_clause,[],[f9838,f9256,f3954,f18116]) ).
tff(f18116,plain,
( spl249_1324
<=> ! [X0: 'B$',X1: 'B_c_option_fun$'] : ( 'none$a' = 'fun_app$g'('uvv$'(X1,'uwe$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1324])]) ).
tff(f3954,plain,
( spl249_78
<=> ! [X0: 'C_option$'] : ( 'none$a' = 'bind$a'(X0,'uwe$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_78])]) ).
tff(f9838,plain,
( ! [X0: 'B$',X1: 'B_c_option_fun$'] : ( 'none$a' = 'fun_app$g'('uvv$'(X1,'uwe$'),X0) )
| ~ spl249_78
| ~ spl249_763 ),
inference(superposition,[],[f9257,f3955]) ).
tff(f3955,plain,
( ! [X0: 'C_option$'] : ( 'none$a' = 'bind$a'(X0,'uwe$') )
| ~ spl249_78 ),
inference(avatar_component_clause,[],[f3954]) ).
tff(f18114,plain,
( spl249_1323
| ~ spl249_76
| ~ spl249_78
| ~ spl249_762 ),
inference(avatar_split_clause,[],[f9815,f9252,f3954,f3946,f18112]) ).
tff(f18112,plain,
( spl249_1323
<=> ! [X0: 'C$',X1: 'B_c_option_fun$'] : ( 'none$' = 'fun_app$j'('uvy$'('uwe$',X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1323])]) ).
tff(f3946,plain,
( spl249_76
<=> ! [X0: 'B_c_option_fun$'] : ( 'none$' = 'bind$b'('none$a',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_76])]) ).
tff(f9252,plain,
( spl249_762
<=> ! [X2: 'C$',X0: 'C_b_option_fun$',X1: 'B_c_option_fun$'] : ( 'fun_app$j'('uvy$'(X0,X1),X2) = 'bind$b'('bind$a'('fun_app$j'('some$a',X2),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_762])]) ).
tff(f9815,plain,
( ! [X0: 'C$',X1: 'B_c_option_fun$'] : ( 'none$' = 'fun_app$j'('uvy$'('uwe$',X1),X0) )
| ~ spl249_76
| ~ spl249_78
| ~ spl249_762 ),
inference(forward_demodulation,[],[f9800,f3947]) ).
tff(f3947,plain,
( ! [X0: 'B_c_option_fun$'] : ( 'none$' = 'bind$b'('none$a',X0) )
| ~ spl249_76 ),
inference(avatar_component_clause,[],[f3946]) ).
tff(f9800,plain,
( ! [X0: 'C$',X1: 'B_c_option_fun$'] : ( 'bind$b'('none$a',X1) = 'fun_app$j'('uvy$'('uwe$',X1),X0) )
| ~ spl249_78
| ~ spl249_762 ),
inference(superposition,[],[f9253,f3955]) ).
tff(f9253,plain,
( ! [X2: 'C$',X0: 'C_b_option_fun$',X1: 'B_c_option_fun$'] : ( 'fun_app$j'('uvy$'(X0,X1),X2) = 'bind$b'('bind$a'('fun_app$j'('some$a',X2),X0),X1) )
| ~ spl249_762 ),
inference(avatar_component_clause,[],[f9252]) ).
tff(f18110,plain,
( spl249_1322
| ~ spl249_74
| ~ spl249_762 ),
inference(avatar_split_clause,[],[f9802,f9252,f3937,f18108]) ).
tff(f18108,plain,
( spl249_1322
<=> ! [X0: 'C$',X1: 'C_b_option_fun$'] : ( 'none$' = 'fun_app$j'('uvy$'(X1,'uwb$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1322])]) ).
tff(f9802,plain,
( ! [X0: 'C$',X1: 'C_b_option_fun$'] : ( 'none$' = 'fun_app$j'('uvy$'(X1,'uwb$'),X0) )
| ~ spl249_74
| ~ spl249_762 ),
inference(superposition,[],[f9253,f3938]) ).
tff(f18106,plain,
( spl249_1321
| ~ spl249_121
| ~ spl249_736 ),
inference(avatar_split_clause,[],[f9593,f9148,f4131,f18104]) ).
tff(f18104,plain,
( spl249_1321
<=> ! [X0: 'A_b_fun$',X1: 'A_option$'] : ( 'none$a' = 'bind$e'(X1,'comp$d'('uwd$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1321])]) ).
tff(f4131,plain,
( spl249_121
<=> ! [X0: 'B_option$'] : ( 'none$a' = 'fun_app$ac'('bind$c'(X0),'uwd$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_121])]) ).
tff(f9148,plain,
( spl249_736
<=> ! [X2: 'B_b_option_fun$',X0: 'A_b_fun$',X1: 'A_option$'] : ( 'fun_app$ac'('bind$c'('fun_app$av'('map_option$e'(X0),X1)),X2) = 'bind$e'(X1,'comp$d'(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_736])]) ).
tff(f9593,plain,
( ! [X0: 'A_b_fun$',X1: 'A_option$'] : ( 'none$a' = 'bind$e'(X1,'comp$d'('uwd$',X0)) )
| ~ spl249_121
| ~ spl249_736 ),
inference(superposition,[],[f9149,f4132]) ).
tff(f4132,plain,
( ! [X0: 'B_option$'] : ( 'none$a' = 'fun_app$ac'('bind$c'(X0),'uwd$') )
| ~ spl249_121 ),
inference(avatar_component_clause,[],[f4131]) ).
tff(f9149,plain,
( ! [X2: 'B_b_option_fun$',X0: 'A_b_fun$',X1: 'A_option$'] : ( 'fun_app$ac'('bind$c'('fun_app$av'('map_option$e'(X0),X1)),X2) = 'bind$e'(X1,'comp$d'(X2,X0)) )
| ~ spl249_736 ),
inference(avatar_component_clause,[],[f9148]) ).
tff(f18102,plain,
( spl249_1320
| ~ spl249_121
| ~ spl249_735 ),
inference(avatar_split_clause,[],[f9570,f9144,f4131,f18100]) ).
tff(f18100,plain,
( spl249_1320
<=> ! [X0: 'C_b_fun$',X1: 'C_option$'] : ( 'none$a' = 'bind$a'(X1,'comp$a'('uwd$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1320])]) ).
tff(f9144,plain,
( spl249_735
<=> ! [X2: 'B_b_option_fun$',X0: 'C_b_fun$',X1: 'C_option$'] : ( 'fun_app$ac'('bind$c'('fun_app$bg'('map_option$'(X0),X1)),X2) = 'bind$a'(X1,'comp$a'(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_735])]) ).
tff(f9570,plain,
( ! [X0: 'C_b_fun$',X1: 'C_option$'] : ( 'none$a' = 'bind$a'(X1,'comp$a'('uwd$',X0)) )
| ~ spl249_121
| ~ spl249_735 ),
inference(superposition,[],[f9145,f4132]) ).
tff(f9145,plain,
( ! [X2: 'B_b_option_fun$',X0: 'C_b_fun$',X1: 'C_option$'] : ( 'fun_app$ac'('bind$c'('fun_app$bg'('map_option$'(X0),X1)),X2) = 'bind$a'(X1,'comp$a'(X2,X0)) )
| ~ spl249_735 ),
inference(avatar_component_clause,[],[f9144]) ).
tff(f18098,plain,
( spl249_1319
| ~ spl249_117
| ~ spl249_733 ),
inference(avatar_split_clause,[],[f9550,f9136,f4115,f18096]) ).
tff(f18096,plain,
( spl249_1319
<=> ! [X0: 'B_c_fun$',X1: 'B_option$'] : ( 'none$' = 'bind$b'(X1,'comp$b'('uwc$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1319])]) ).
tff(f4115,plain,
( spl249_117
<=> ! [X0: 'C_option$'] : ( 'none$' = 'fun_app$ab'('bind$'(X0),'uwc$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_117])]) ).
tff(f9136,plain,
( spl249_733
<=> ! [X2: 'C_c_option_fun$',X0: 'B_c_fun$',X1: 'B_option$'] : ( 'fun_app$ab'('bind$'('fun_app$an'('map_option$d'(X0),X1)),X2) = 'bind$b'(X1,'comp$b'(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_733])]) ).
tff(f9550,plain,
( ! [X0: 'B_c_fun$',X1: 'B_option$'] : ( 'none$' = 'bind$b'(X1,'comp$b'('uwc$',X0)) )
| ~ spl249_117
| ~ spl249_733 ),
inference(superposition,[],[f9137,f4116]) ).
tff(f4116,plain,
( ! [X0: 'C_option$'] : ( 'none$' = 'fun_app$ab'('bind$'(X0),'uwc$') )
| ~ spl249_117 ),
inference(avatar_component_clause,[],[f4115]) ).
tff(f9137,plain,
( ! [X2: 'C_c_option_fun$',X0: 'B_c_fun$',X1: 'B_option$'] : ( 'fun_app$ab'('bind$'('fun_app$an'('map_option$d'(X0),X1)),X2) = 'bind$b'(X1,'comp$b'(X2,X0)) )
| ~ spl249_733 ),
inference(avatar_component_clause,[],[f9136]) ).
tff(f18094,plain,
( spl249_1318
| ~ spl249_68
| ~ spl249_725 ),
inference(avatar_split_clause,[],[f9425,f9104,f3913,f18092]) ).
tff(f18092,plain,
( spl249_1318
<=> ! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A$'] : ~ 'fun_app$aw'('is_none$b','fun_app$q'('uuw$'(X0,X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1318])]) ).
tff(f3913,plain,
( spl249_68
<=> ! [X0: 'A$'] : ~ 'fun_app$aw'('is_none$b','fun_app$q'('some$b',X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_68])]) ).
tff(f9104,plain,
( spl249_725
<=> ! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A$'] : ( 'fun_app$q'('uuw$'(X0,X1),X2) = 'fun_app$q'('some$b','fun_app$r'('fun_app$aj'(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_725])]) ).
tff(f9425,plain,
( ! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A$'] : ~ 'fun_app$aw'('is_none$b','fun_app$q'('uuw$'(X0,X1),X2))
| ~ spl249_68
| ~ spl249_725 ),
inference(superposition,[],[f3914,f9105]) ).
tff(f9105,plain,
( ! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A$'] : ( 'fun_app$q'('uuw$'(X0,X1),X2) = 'fun_app$q'('some$b','fun_app$r'('fun_app$aj'(X0,X1),X2)) )
| ~ spl249_725 ),
inference(avatar_component_clause,[],[f9104]) ).
tff(f3914,plain,
( ! [X0: 'A$'] : ~ 'fun_app$aw'('is_none$b','fun_app$q'('some$b',X0))
| ~ spl249_68 ),
inference(avatar_component_clause,[],[f3913]) ).
tff(f18090,plain,
( spl249_1317
| ~ spl249_65
| ~ spl249_725 ),
inference(avatar_split_clause,[],[f9424,f9104,f3901,f18088]) ).
tff(f18088,plain,
( spl249_1317
<=> ! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A$'] : ( 'fun_app$q'('uuw$'(X0,X1),X2) != 'none$b' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1317])]) ).
tff(f3901,plain,
( spl249_65
<=> ! [X0: 'A$'] : ( 'none$b' != 'fun_app$q'('some$b',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_65])]) ).
tff(f9424,plain,
( ! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A$'] : ( 'fun_app$q'('uuw$'(X0,X1),X2) != 'none$b' )
| ~ spl249_65
| ~ spl249_725 ),
inference(superposition,[],[f3902,f9105]) ).
tff(f3902,plain,
( ! [X0: 'A$'] : ( 'none$b' != 'fun_app$q'('some$b',X0) )
| ~ spl249_65 ),
inference(avatar_component_clause,[],[f3901]) ).
tff(f18086,plain,
( spl249_1316
| ~ spl249_70
| ~ spl249_721 ),
inference(avatar_split_clause,[],[f9367,f9088,f3921,f18084]) ).
tff(f18084,plain,
( spl249_1316
<=> ! [X2: 'B$',X0: 'A_b_b_fun_fun$',X1: 'A$'] : ~ 'fun_app$a'('is_none$','fun_app$f'('uua$'(X0,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1316])]) ).
tff(f3921,plain,
( spl249_70
<=> ! [X0: 'B$'] : ~ 'fun_app$a'('is_none$','fun_app$g'('some$',X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_70])]) ).
tff(f9088,plain,
( spl249_721
<=> ! [X2: 'A$',X0: 'A_b_b_fun_fun$',X1: 'B$'] : ( 'fun_app$f'('uua$'(X0,X1),X2) = 'fun_app$g'('some$','fun_app$h'('fun_app$i'(X0,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_721])]) ).
tff(f9367,plain,
( ! [X2: 'B$',X0: 'A_b_b_fun_fun$',X1: 'A$'] : ~ 'fun_app$a'('is_none$','fun_app$f'('uua$'(X0,X2),X1))
| ~ spl249_70
| ~ spl249_721 ),
inference(superposition,[],[f3922,f9089]) ).
tff(f9089,plain,
( ! [X2: 'A$',X0: 'A_b_b_fun_fun$',X1: 'B$'] : ( 'fun_app$f'('uua$'(X0,X1),X2) = 'fun_app$g'('some$','fun_app$h'('fun_app$i'(X0,X2),X1)) )
| ~ spl249_721 ),
inference(avatar_component_clause,[],[f9088]) ).
tff(f3922,plain,
( ! [X0: 'B$'] : ~ 'fun_app$a'('is_none$','fun_app$g'('some$',X0))
| ~ spl249_70 ),
inference(avatar_component_clause,[],[f3921]) ).
tff(f18082,plain,
( spl249_1315
| ~ spl249_67
| ~ spl249_721 ),
inference(avatar_split_clause,[],[f9366,f9088,f3909,f18080]) ).
tff(f18080,plain,
( spl249_1315
<=> ! [X2: 'B$',X0: 'A_b_b_fun_fun$',X1: 'A$'] : ( 'none$a' != 'fun_app$f'('uua$'(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1315])]) ).
tff(f3909,plain,
( spl249_67
<=> ! [X0: 'B$'] : ( 'none$a' != 'fun_app$g'('some$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_67])]) ).
tff(f9366,plain,
( ! [X2: 'B$',X0: 'A_b_b_fun_fun$',X1: 'A$'] : ( 'none$a' != 'fun_app$f'('uua$'(X0,X2),X1) )
| ~ spl249_67
| ~ spl249_721 ),
inference(superposition,[],[f3910,f9089]) ).
tff(f3910,plain,
( ! [X0: 'B$'] : ( 'none$a' != 'fun_app$g'('some$',X0) )
| ~ spl249_67 ),
inference(avatar_component_clause,[],[f3909]) ).
tff(f18078,plain,
( spl249_1314
| ~ spl249_20
| ~ spl249_683 ),
inference(avatar_split_clause,[],[f8687,f8186,f3692,f18076]) ).
tff(f18076,plain,
( spl249_1314
<=> ! [X0: 'B_option$',X1: tlbool] :
( sP25(X0,'uug$',X1)
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1314])]) ).
tff(f3692,plain,
( spl249_20
<=> ! [X0: 'B$'] : 'fun_app$c'('uug$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_20])]) ).
tff(f8186,plain,
( spl249_683
<=> ! [X2: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( sP25(X0,X1,X2)
| ~ 'fun_app$c'(X1,'fun_app$al'('the$',X0))
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_683])]) ).
tff(f8687,plain,
( ! [X0: 'B_option$',X1: tlbool] :
( sP25(X0,'uug$',X1)
| ( 'none$a' = X0 ) )
| ~ spl249_20
| ~ spl249_683 ),
inference(resolution,[],[f8187,f3693]) ).
tff(f3693,plain,
( ! [X0: 'B$'] : 'fun_app$c'('uug$',X0)
| ~ spl249_20 ),
inference(avatar_component_clause,[],[f3692]) ).
tff(f8187,plain,
( ! [X2: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( ~ 'fun_app$c'(X1,'fun_app$al'('the$',X0))
| sP25(X0,X1,X2)
| ( 'none$a' = X0 ) )
| ~ spl249_683 ),
inference(avatar_component_clause,[],[f8186]) ).
tff(f18074,plain,
( spl249_1313
| ~ spl249_18
| ~ spl249_681 ),
inference(avatar_split_clause,[],[f8679,f8178,f3684,f18072]) ).
tff(f18072,plain,
( spl249_1313
<=> ! [X0: 'C_option$',X1: tlbool] :
( sP20(X0,'uuf$',X1)
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1313])]) ).
tff(f3684,plain,
( spl249_18
<=> ! [X0: 'C$'] : 'fun_app$b'('uuf$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_18])]) ).
tff(f8178,plain,
( spl249_681
<=> ! [X2: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( sP20(X0,X1,X2)
| ~ 'fun_app$b'(X1,'fun_app$ak'('the$a',X0))
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_681])]) ).
tff(f8679,plain,
( ! [X0: 'C_option$',X1: tlbool] :
( sP20(X0,'uuf$',X1)
| ( 'none$' = X0 ) )
| ~ spl249_18
| ~ spl249_681 ),
inference(resolution,[],[f8179,f3685]) ).
tff(f3685,plain,
( ! [X0: 'C$'] : 'fun_app$b'('uuf$',X0)
| ~ spl249_18 ),
inference(avatar_component_clause,[],[f3684]) ).
tff(f8179,plain,
( ! [X2: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( ~ 'fun_app$b'(X1,'fun_app$ak'('the$a',X0))
| sP20(X0,X1,X2)
| ( 'none$' = X0 ) )
| ~ spl249_681 ),
inference(avatar_component_clause,[],[f8178]) ).
tff(f18070,plain,
( spl249_1312
| ~ spl249_78
| ~ spl249_120
| ~ spl249_657 ),
inference(avatar_split_clause,[],[f8646,f8082,f4127,f3954,f18068]) ).
tff(f18068,plain,
( spl249_1312
<=> ! [X0: 'C_option$',X1: 'B_b_option_fun$'] : ( 'none$a' = 'bind$a'(X0,'uvu$'('uwe$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1312])]) ).
tff(f4127,plain,
( spl249_120
<=> ! [X0: 'B_b_option_fun$'] : ( 'none$a' = 'fun_app$ac'('bind$c'('none$a'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_120])]) ).
tff(f8082,plain,
( spl249_657
<=> ! [X2: 'B_b_option_fun$',X0: 'C_option$',X1: 'C_b_option_fun$'] : ( 'fun_app$ac'('bind$c'('bind$a'(X0,X1)),X2) = 'bind$a'(X0,'uvu$'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_657])]) ).
tff(f8646,plain,
( ! [X0: 'C_option$',X1: 'B_b_option_fun$'] : ( 'none$a' = 'bind$a'(X0,'uvu$'('uwe$',X1)) )
| ~ spl249_78
| ~ spl249_120
| ~ spl249_657 ),
inference(forward_demodulation,[],[f8627,f4128]) ).
tff(f4128,plain,
( ! [X0: 'B_b_option_fun$'] : ( 'none$a' = 'fun_app$ac'('bind$c'('none$a'),X0) )
| ~ spl249_120 ),
inference(avatar_component_clause,[],[f4127]) ).
tff(f8627,plain,
( ! [X0: 'C_option$',X1: 'B_b_option_fun$'] : ( 'fun_app$ac'('bind$c'('none$a'),X1) = 'bind$a'(X0,'uvu$'('uwe$',X1)) )
| ~ spl249_78
| ~ spl249_657 ),
inference(superposition,[],[f8083,f3955]) ).
tff(f8083,plain,
( ! [X2: 'B_b_option_fun$',X0: 'C_option$',X1: 'C_b_option_fun$'] : ( 'fun_app$ac'('bind$c'('bind$a'(X0,X1)),X2) = 'bind$a'(X0,'uvu$'(X1,X2)) )
| ~ spl249_657 ),
inference(avatar_component_clause,[],[f8082]) ).
tff(f18066,plain,
( spl249_1311
| ~ spl249_121
| ~ spl249_657 ),
inference(avatar_split_clause,[],[f8632,f8082,f4131,f18064]) ).
tff(f18064,plain,
( spl249_1311
<=> ! [X0: 'C_option$',X1: 'C_b_option_fun$'] : ( 'none$a' = 'bind$a'(X0,'uvu$'(X1,'uwd$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1311])]) ).
tff(f8632,plain,
( ! [X0: 'C_option$',X1: 'C_b_option_fun$'] : ( 'none$a' = 'bind$a'(X0,'uvu$'(X1,'uwd$')) )
| ~ spl249_121
| ~ spl249_657 ),
inference(superposition,[],[f8083,f4132]) ).
tff(f18062,plain,
( spl249_1310
| ~ spl249_74
| ~ spl249_656 ),
inference(avatar_split_clause,[],[f8607,f8078,f3937,f18060]) ).
tff(f18060,plain,
( spl249_1310
<=> ! [X0: 'B_b_fun$',X1: 'B_option$'] : ( 'none$' = 'bind$b'(X1,'comp$f'('uwb$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1310])]) ).
tff(f8078,plain,
( spl249_656
<=> ! [X2: 'B_c_option_fun$',X0: 'B_b_fun$',X1: 'B_option$'] : ( 'bind$b'('fun_app$s'('map_option$b'(X0),X1),X2) = 'bind$b'(X1,'comp$f'(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_656])]) ).
tff(f8607,plain,
( ! [X0: 'B_b_fun$',X1: 'B_option$'] : ( 'none$' = 'bind$b'(X1,'comp$f'('uwb$',X0)) )
| ~ spl249_74
| ~ spl249_656 ),
inference(superposition,[],[f8079,f3938]) ).
tff(f8079,plain,
( ! [X2: 'B_c_option_fun$',X0: 'B_b_fun$',X1: 'B_option$'] : ( 'bind$b'('fun_app$s'('map_option$b'(X0),X1),X2) = 'bind$b'(X1,'comp$f'(X2,X0)) )
| ~ spl249_656 ),
inference(avatar_component_clause,[],[f8078]) ).
tff(f18058,plain,
( spl249_1309
| ~ spl249_78
| ~ spl249_654 ),
inference(avatar_split_clause,[],[f8589,f8070,f3954,f18056]) ).
tff(f18056,plain,
( spl249_1309
<=> ! [X0: 'C_c_fun$',X1: 'C_option$'] : ( 'none$a' = 'bind$a'(X1,'comp$ao'('uwe$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1309])]) ).
tff(f8070,plain,
( spl249_654
<=> ! [X2: 'C_b_option_fun$',X0: 'C_c_fun$',X1: 'C_option$'] : ( 'bind$a'('fun_app$u'('map_option$c'(X0),X1),X2) = 'bind$a'(X1,'comp$ao'(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_654])]) ).
tff(f8589,plain,
( ! [X0: 'C_c_fun$',X1: 'C_option$'] : ( 'none$a' = 'bind$a'(X1,'comp$ao'('uwe$',X0)) )
| ~ spl249_78
| ~ spl249_654 ),
inference(superposition,[],[f8071,f3955]) ).
tff(f8071,plain,
( ! [X2: 'C_b_option_fun$',X0: 'C_c_fun$',X1: 'C_option$'] : ( 'bind$a'('fun_app$u'('map_option$c'(X0),X1),X2) = 'bind$a'(X1,'comp$ao'(X2,X0)) )
| ~ spl249_654 ),
inference(avatar_component_clause,[],[f8070]) ).
tff(f18054,plain,
( spl249_1308
| ~ spl249_74
| ~ spl249_653 ),
inference(avatar_split_clause,[],[f8572,f8066,f3937,f18052]) ).
tff(f18052,plain,
( spl249_1308
<=> ! [X0: 'A_b_fun$',X1: 'A_option$'] : ( 'none$' = 'bind$d'(X1,'comp$aq'('uwb$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1308])]) ).
tff(f8066,plain,
( spl249_653
<=> ! [X2: 'B_c_option_fun$',X0: 'A_b_fun$',X1: 'A_option$'] : ( 'bind$b'('fun_app$av'('map_option$e'(X0),X1),X2) = 'bind$d'(X1,'comp$aq'(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_653])]) ).
tff(f8572,plain,
( ! [X0: 'A_b_fun$',X1: 'A_option$'] : ( 'none$' = 'bind$d'(X1,'comp$aq'('uwb$',X0)) )
| ~ spl249_74
| ~ spl249_653 ),
inference(superposition,[],[f8067,f3938]) ).
tff(f8067,plain,
( ! [X2: 'B_c_option_fun$',X0: 'A_b_fun$',X1: 'A_option$'] : ( 'bind$b'('fun_app$av'('map_option$e'(X0),X1),X2) = 'bind$d'(X1,'comp$aq'(X2,X0)) )
| ~ spl249_653 ),
inference(avatar_component_clause,[],[f8066]) ).
tff(f18050,plain,
( spl249_1307
| ~ spl249_76
| ~ spl249_121
| ~ spl249_652 ),
inference(avatar_split_clause,[],[f8564,f8062,f4131,f3946,f18048]) ).
tff(f18048,plain,
( spl249_1307
<=> ! [X0: 'B_option$',X1: 'B_c_option_fun$'] : ( 'none$' = 'bind$b'(X0,'uvx$'('uwd$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1307])]) ).
tff(f8062,plain,
( spl249_652
<=> ! [X2: 'B_c_option_fun$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ( 'bind$b'('fun_app$ac'('bind$c'(X0),X1),X2) = 'bind$b'(X0,'uvx$'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_652])]) ).
tff(f8564,plain,
( ! [X0: 'B_option$',X1: 'B_c_option_fun$'] : ( 'none$' = 'bind$b'(X0,'uvx$'('uwd$',X1)) )
| ~ spl249_76
| ~ spl249_121
| ~ spl249_652 ),
inference(forward_demodulation,[],[f8548,f3947]) ).
tff(f8548,plain,
( ! [X0: 'B_option$',X1: 'B_c_option_fun$'] : ( 'bind$b'('none$a',X1) = 'bind$b'(X0,'uvx$'('uwd$',X1)) )
| ~ spl249_121
| ~ spl249_652 ),
inference(superposition,[],[f8063,f4132]) ).
tff(f8063,plain,
( ! [X2: 'B_c_option_fun$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ( 'bind$b'('fun_app$ac'('bind$c'(X0),X1),X2) = 'bind$b'(X0,'uvx$'(X1,X2)) )
| ~ spl249_652 ),
inference(avatar_component_clause,[],[f8062]) ).
tff(f18046,plain,
( spl249_1306
| ~ spl249_74
| ~ spl249_652 ),
inference(avatar_split_clause,[],[f8553,f8062,f3937,f18044]) ).
tff(f18044,plain,
( spl249_1306
<=> ! [X0: 'B_option$',X1: 'B_b_option_fun$'] : ( 'none$' = 'bind$b'(X0,'uvx$'(X1,'uwb$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1306])]) ).
tff(f8553,plain,
( ! [X0: 'B_option$',X1: 'B_b_option_fun$'] : ( 'none$' = 'bind$b'(X0,'uvx$'(X1,'uwb$')) )
| ~ spl249_74
| ~ spl249_652 ),
inference(superposition,[],[f8063,f3938]) ).
tff(f18042,plain,
( spl249_1305
| ~ spl249_79
| ~ spl249_117
| ~ spl249_651 ),
inference(avatar_split_clause,[],[f8542,f8058,f4115,f3958,f18040]) ).
tff(f18040,plain,
( spl249_1305
<=> ! [X0: 'C_option$',X1: 'C_b_option_fun$'] : ( 'none$a' = 'bind$a'(X0,'uvw$'('uwc$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1305])]) ).
tff(f8058,plain,
( spl249_651
<=> ! [X2: 'C_b_option_fun$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ( 'bind$a'('fun_app$ab'('bind$'(X0),X1),X2) = 'bind$a'(X0,'uvw$'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_651])]) ).
tff(f8542,plain,
( ! [X0: 'C_option$',X1: 'C_b_option_fun$'] : ( 'none$a' = 'bind$a'(X0,'uvw$'('uwc$',X1)) )
| ~ spl249_79
| ~ spl249_117
| ~ spl249_651 ),
inference(forward_demodulation,[],[f8528,f3959]) ).
tff(f8528,plain,
( ! [X0: 'C_option$',X1: 'C_b_option_fun$'] : ( 'bind$a'('none$',X1) = 'bind$a'(X0,'uvw$'('uwc$',X1)) )
| ~ spl249_117
| ~ spl249_651 ),
inference(superposition,[],[f8059,f4116]) ).
tff(f8059,plain,
( ! [X2: 'C_b_option_fun$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ( 'bind$a'('fun_app$ab'('bind$'(X0),X1),X2) = 'bind$a'(X0,'uvw$'(X1,X2)) )
| ~ spl249_651 ),
inference(avatar_component_clause,[],[f8058]) ).
tff(f18038,plain,
( spl249_1304
| ~ spl249_78
| ~ spl249_651 ),
inference(avatar_split_clause,[],[f8533,f8058,f3954,f18036]) ).
tff(f18036,plain,
( spl249_1304
<=> ! [X0: 'C_option$',X1: 'C_c_option_fun$'] : ( 'none$a' = 'bind$a'(X0,'uvw$'(X1,'uwe$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1304])]) ).
tff(f8533,plain,
( ! [X0: 'C_option$',X1: 'C_c_option_fun$'] : ( 'none$a' = 'bind$a'(X0,'uvw$'(X1,'uwe$')) )
| ~ spl249_78
| ~ spl249_651 ),
inference(superposition,[],[f8059,f3955]) ).
tff(f18034,plain,
( spl249_1303
| ~ spl249_74
| ~ spl249_116
| ~ spl249_650 ),
inference(avatar_split_clause,[],[f8523,f8054,f4111,f3937,f18032]) ).
tff(f18032,plain,
( spl249_1303
<=> ! [X0: 'B_option$',X1: 'C_c_option_fun$'] : ( 'none$' = 'bind$b'(X0,'uvz$'('uwb$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1303])]) ).
tff(f4111,plain,
( spl249_116
<=> ! [X0: 'C_c_option_fun$'] : ( 'none$' = 'fun_app$ab'('bind$'('none$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_116])]) ).
tff(f8054,plain,
( spl249_650
<=> ! [X2: 'C_c_option_fun$',X0: 'B_option$',X1: 'B_c_option_fun$'] : ( 'fun_app$ab'('bind$'('bind$b'(X0,X1)),X2) = 'bind$b'(X0,'uvz$'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_650])]) ).
tff(f8523,plain,
( ! [X0: 'B_option$',X1: 'C_c_option_fun$'] : ( 'none$' = 'bind$b'(X0,'uvz$'('uwb$',X1)) )
| ~ spl249_74
| ~ spl249_116
| ~ spl249_650 ),
inference(forward_demodulation,[],[f8505,f4112]) ).
tff(f4112,plain,
( ! [X0: 'C_c_option_fun$'] : ( 'none$' = 'fun_app$ab'('bind$'('none$'),X0) )
| ~ spl249_116 ),
inference(avatar_component_clause,[],[f4111]) ).
tff(f8505,plain,
( ! [X0: 'B_option$',X1: 'C_c_option_fun$'] : ( 'fun_app$ab'('bind$'('none$'),X1) = 'bind$b'(X0,'uvz$'('uwb$',X1)) )
| ~ spl249_74
| ~ spl249_650 ),
inference(superposition,[],[f8055,f3938]) ).
tff(f8055,plain,
( ! [X2: 'C_c_option_fun$',X0: 'B_option$',X1: 'B_c_option_fun$'] : ( 'fun_app$ab'('bind$'('bind$b'(X0,X1)),X2) = 'bind$b'(X0,'uvz$'(X1,X2)) )
| ~ spl249_650 ),
inference(avatar_component_clause,[],[f8054]) ).
tff(f18030,plain,
( spl249_1302
| ~ spl249_117
| ~ spl249_650 ),
inference(avatar_split_clause,[],[f8512,f8054,f4115,f18028]) ).
tff(f18028,plain,
( spl249_1302
<=> ! [X0: 'B_option$',X1: 'B_c_option_fun$'] : ( 'none$' = 'bind$b'(X0,'uvz$'(X1,'uwc$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1302])]) ).
tff(f8512,plain,
( ! [X0: 'B_option$',X1: 'B_c_option_fun$'] : ( 'none$' = 'bind$b'(X0,'uvz$'(X1,'uwc$')) )
| ~ spl249_117
| ~ spl249_650 ),
inference(superposition,[],[f8055,f4116]) ).
tff(f18026,plain,
( spl249_1301
| ~ spl249_63
| ~ spl249_88
| ~ spl249_552 ),
inference(avatar_split_clause,[],[f7529,f7175,f3995,f3891,f18024]) ).
tff(f18024,plain,
( spl249_1301
<=> ! [X0: 'B_c_option_fun$'] : ( 'comp$av'('comp$bg'(X0,'the$'),'some$') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1301])]) ).
tff(f3891,plain,
( spl249_63
<=> ( 'comp$m'('the$','some$') = 'id$b' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_63])]) ).
tff(f3995,plain,
( spl249_88
<=> ! [X0: 'B_c_option_fun$'] : ( 'comp$f'(X0,'id$b') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_88])]) ).
tff(f7175,plain,
( spl249_552
<=> ! [X2: 'B_b_option_fun$',X0: 'B_c_option_fun$',X1: 'B_option_b_fun$'] : ( 'comp$f'(X0,'comp$m'(X1,X2)) = 'comp$av'('comp$bg'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_552])]) ).
tff(f7529,plain,
( ! [X0: 'B_c_option_fun$'] : ( 'comp$av'('comp$bg'(X0,'the$'),'some$') = X0 )
| ~ spl249_63
| ~ spl249_88
| ~ spl249_552 ),
inference(forward_demodulation,[],[f7521,f3996]) ).
tff(f3996,plain,
( ! [X0: 'B_c_option_fun$'] : ( 'comp$f'(X0,'id$b') = X0 )
| ~ spl249_88 ),
inference(avatar_component_clause,[],[f3995]) ).
tff(f7521,plain,
( ! [X0: 'B_c_option_fun$'] : ( 'comp$f'(X0,'id$b') = 'comp$av'('comp$bg'(X0,'the$'),'some$') )
| ~ spl249_63
| ~ spl249_552 ),
inference(superposition,[],[f7176,f3893]) ).
tff(f3893,plain,
( ( 'comp$m'('the$','some$') = 'id$b' )
| ~ spl249_63 ),
inference(avatar_component_clause,[],[f3891]) ).
tff(f7176,plain,
( ! [X2: 'B_b_option_fun$',X0: 'B_c_option_fun$',X1: 'B_option_b_fun$'] : ( 'comp$f'(X0,'comp$m'(X1,X2)) = 'comp$av'('comp$bg'(X0,X1),X2) )
| ~ spl249_552 ),
inference(avatar_component_clause,[],[f7175]) ).
tff(f18022,plain,
( spl249_1300
| ~ spl249_129
| ~ spl249_513 ),
inference(avatar_split_clause,[],[f7014,f6597,f4163,f18020]) ).
tff(f18020,plain,
( spl249_1300
<=> ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,X0)
| ~ sP31('some$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1300])]) ).
tff(f4163,plain,
( spl249_129
<=> ! [X0: 'B_option$'] : ( 'fun_app$ac'('bind$c'(X0),'some$') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_129])]) ).
tff(f6597,plain,
( spl249_513
<=> ! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
| ~ sP31(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_513])]) ).
tff(f7014,plain,
( ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,X0)
| ~ sP31('some$',X1,X0) )
| ~ spl249_129
| ~ spl249_513 ),
inference(superposition,[],[f6598,f4164]) ).
tff(f4164,plain,
( ! [X0: 'B_option$'] : ( 'fun_app$ac'('bind$c'(X0),'some$') = X0 )
| ~ spl249_129 ),
inference(avatar_component_clause,[],[f4163]) ).
tff(f6598,plain,
( ! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
| ~ sP31(X2,X0,X1) )
| ~ spl249_513 ),
inference(avatar_component_clause,[],[f6597]) ).
tff(f18018,plain,
( spl249_1299
| ~ spl249_121
| ~ spl249_513 ),
inference(avatar_split_clause,[],[f7013,f6597,f4131,f18016]) ).
tff(f18016,plain,
( spl249_1299
<=> ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP31('uwd$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1299])]) ).
tff(f7013,plain,
( ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP31('uwd$',X1,X0) )
| ~ spl249_121
| ~ spl249_513 ),
inference(superposition,[],[f6598,f4132]) ).
tff(f18014,plain,
( spl249_1298
| ~ spl249_129
| ~ spl249_512 ),
inference(avatar_split_clause,[],[f6996,f6593,f4163,f18012]) ).
tff(f18012,plain,
( spl249_1298
<=> ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,X0)
| sP31('some$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1298])]) ).
tff(f6593,plain,
( spl249_512
<=> ! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( sP31(X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_512])]) ).
tff(f6996,plain,
( ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,X0)
| sP31('some$',X1,X0) )
| ~ spl249_129
| ~ spl249_512 ),
inference(superposition,[],[f6594,f4164]) ).
tff(f6594,plain,
( ! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ~ 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
| sP31(X2,X0,X1) )
| ~ spl249_512 ),
inference(avatar_component_clause,[],[f6593]) ).
tff(f18010,plain,
( spl249_1297
| ~ spl249_121
| ~ spl249_512 ),
inference(avatar_split_clause,[],[f6995,f6593,f4131,f18008]) ).
tff(f18008,plain,
( spl249_1297
<=> ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP31('uwd$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1297])]) ).
tff(f6995,plain,
( ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP31('uwd$',X1,X0) )
| ~ spl249_121
| ~ spl249_512 ),
inference(superposition,[],[f6594,f4132]) ).
tff(f18006,plain,
( spl249_1296
| ~ spl249_120
| ~ spl249_512 ),
inference(avatar_split_clause,[],[f6994,f6593,f4127,f18004]) ).
tff(f18004,plain,
( spl249_1296
<=> ! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP31(X0,X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1296])]) ).
tff(f6994,plain,
( ! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP31(X0,X1,'none$a') )
| ~ spl249_120
| ~ spl249_512 ),
inference(superposition,[],[f6594,f4128]) ).
tff(f18002,plain,
( spl249_1295
| ~ spl249_394
| ~ spl249_512 ),
inference(avatar_split_clause,[],[f6993,f6593,f5592,f18000]) ).
tff(f18000,plain,
( spl249_1295
<=> ! [X0: 'B_b_option_fun$',X1: 'B_option$'] :
( sP31(X0,'is_none$',X1)
| ~ 'fun_app$a'('is_none$',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1295])]) ).
tff(f5592,plain,
( spl249_394
<=> ! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'('is_none$','fun_app$ac'('bind$c'(X0),X1))
| ~ 'fun_app$a'('is_none$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_394])]) ).
tff(f6993,plain,
( ! [X0: 'B_b_option_fun$',X1: 'B_option$'] :
( sP31(X0,'is_none$',X1)
| ~ 'fun_app$a'('is_none$',X1) )
| ~ spl249_394
| ~ spl249_512 ),
inference(resolution,[],[f6594,f5593]) ).
tff(f5593,plain,
( ! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'('is_none$','fun_app$ac'('bind$c'(X0),X1))
| ~ 'fun_app$a'('is_none$',X0) )
| ~ spl249_394 ),
inference(avatar_component_clause,[],[f5592]) ).
tff(f17998,plain,
( spl249_1294
| ~ spl249_129
| ~ spl249_511 ),
inference(avatar_split_clause,[],[f6985,f6589,f4163,f17996]) ).
tff(f17996,plain,
( spl249_1294
<=> ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,X0)
| ~ sP30('some$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1294])]) ).
tff(f6589,plain,
( spl249_511
<=> ! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
| ~ sP30(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_511])]) ).
tff(f6985,plain,
( ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,X0)
| ~ sP30('some$',X1,X0) )
| ~ spl249_129
| ~ spl249_511 ),
inference(superposition,[],[f6590,f4164]) ).
tff(f6590,plain,
( ! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
| ~ sP30(X2,X0,X1) )
| ~ spl249_511 ),
inference(avatar_component_clause,[],[f6589]) ).
tff(f17994,plain,
( spl249_1293
| ~ spl249_121
| ~ spl249_511 ),
inference(avatar_split_clause,[],[f6984,f6589,f4131,f17992]) ).
tff(f17992,plain,
( spl249_1293
<=> ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP30('uwd$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1293])]) ).
tff(f6984,plain,
( ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP30('uwd$',X1,X0) )
| ~ spl249_121
| ~ spl249_511 ),
inference(superposition,[],[f6590,f4132]) ).
tff(f17990,plain,
( spl249_1292
| ~ spl249_129
| ~ spl249_510 ),
inference(avatar_split_clause,[],[f6968,f6585,f4163,f17988]) ).
tff(f17988,plain,
( spl249_1292
<=> ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,X0)
| sP30('some$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1292])]) ).
tff(f6585,plain,
( spl249_510
<=> ! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( sP30(X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_510])]) ).
tff(f6968,plain,
( ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,X0)
| sP30('some$',X1,X0) )
| ~ spl249_129
| ~ spl249_510 ),
inference(superposition,[],[f6586,f4164]) ).
tff(f6586,plain,
( ! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ~ 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
| sP30(X2,X0,X1) )
| ~ spl249_510 ),
inference(avatar_component_clause,[],[f6585]) ).
tff(f17986,plain,
( spl249_1291
| ~ spl249_121
| ~ spl249_510 ),
inference(avatar_split_clause,[],[f6967,f6585,f4131,f17984]) ).
tff(f17984,plain,
( spl249_1291
<=> ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP30('uwd$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1291])]) ).
tff(f6967,plain,
( ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP30('uwd$',X1,X0) )
| ~ spl249_121
| ~ spl249_510 ),
inference(superposition,[],[f6586,f4132]) ).
tff(f17982,plain,
( spl249_1290
| ~ spl249_120
| ~ spl249_510 ),
inference(avatar_split_clause,[],[f6966,f6585,f4127,f17980]) ).
tff(f17980,plain,
( spl249_1290
<=> ! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP30(X0,X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1290])]) ).
tff(f6966,plain,
( ! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP30(X0,X1,'none$a') )
| ~ spl249_120
| ~ spl249_510 ),
inference(superposition,[],[f6586,f4128]) ).
tff(f17978,plain,
( spl249_1289
| ~ spl249_394
| ~ spl249_510 ),
inference(avatar_split_clause,[],[f6965,f6585,f5592,f17976]) ).
tff(f17976,plain,
( spl249_1289
<=> ! [X0: 'B_b_option_fun$',X1: 'B_option$'] :
( sP30(X0,'is_none$',X1)
| ~ 'fun_app$a'('is_none$',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1289])]) ).
tff(f6965,plain,
( ! [X0: 'B_b_option_fun$',X1: 'B_option$'] :
( sP30(X0,'is_none$',X1)
| ~ 'fun_app$a'('is_none$',X1) )
| ~ spl249_394
| ~ spl249_510 ),
inference(resolution,[],[f6586,f5593]) ).
tff(f17974,plain,
( spl249_1288
| ~ spl249_128
| ~ spl249_509 ),
inference(avatar_split_clause,[],[f6958,f6581,f4159,f17972]) ).
tff(f17972,plain,
( spl249_1288
<=> ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,X0)
| ~ sP29('some$a',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1288])]) ).
tff(f4159,plain,
( spl249_128
<=> ! [X0: 'C_option$'] : ( 'fun_app$ab'('bind$'(X0),'some$a') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_128])]) ).
tff(f6581,plain,
( spl249_509
<=> ! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
| ~ sP29(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_509])]) ).
tff(f6958,plain,
( ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,X0)
| ~ sP29('some$a',X1,X0) )
| ~ spl249_128
| ~ spl249_509 ),
inference(superposition,[],[f6582,f4160]) ).
tff(f4160,plain,
( ! [X0: 'C_option$'] : ( 'fun_app$ab'('bind$'(X0),'some$a') = X0 )
| ~ spl249_128 ),
inference(avatar_component_clause,[],[f4159]) ).
tff(f6582,plain,
( ! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
| ~ sP29(X2,X0,X1) )
| ~ spl249_509 ),
inference(avatar_component_clause,[],[f6581]) ).
tff(f17970,plain,
( spl249_1287
| ~ spl249_117
| ~ spl249_509 ),
inference(avatar_split_clause,[],[f6957,f6581,f4115,f17968]) ).
tff(f17968,plain,
( spl249_1287
<=> ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP29('uwc$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1287])]) ).
tff(f6957,plain,
( ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP29('uwc$',X1,X0) )
| ~ spl249_117
| ~ spl249_509 ),
inference(superposition,[],[f6582,f4116]) ).
tff(f17966,plain,
( spl249_1286
| ~ spl249_128
| ~ spl249_508 ),
inference(avatar_split_clause,[],[f6935,f6577,f4159,f17964]) ).
tff(f17964,plain,
( spl249_1286
<=> ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,X0)
| sP29('some$a',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1286])]) ).
tff(f6577,plain,
( spl249_508
<=> ! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( sP29(X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_508])]) ).
tff(f6935,plain,
( ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,X0)
| sP29('some$a',X1,X0) )
| ~ spl249_128
| ~ spl249_508 ),
inference(superposition,[],[f6578,f4160]) ).
tff(f6578,plain,
( ! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ~ 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
| sP29(X2,X0,X1) )
| ~ spl249_508 ),
inference(avatar_component_clause,[],[f6577]) ).
tff(f17962,plain,
( spl249_1285
| ~ spl249_117
| ~ spl249_508 ),
inference(avatar_split_clause,[],[f6934,f6577,f4115,f17960]) ).
tff(f17960,plain,
( spl249_1285
<=> ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP29('uwc$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1285])]) ).
tff(f6934,plain,
( ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP29('uwc$',X1,X0) )
| ~ spl249_117
| ~ spl249_508 ),
inference(superposition,[],[f6578,f4116]) ).
tff(f17958,plain,
( spl249_1284
| ~ spl249_116
| ~ spl249_508 ),
inference(avatar_split_clause,[],[f6933,f6577,f4111,f17956]) ).
tff(f17956,plain,
( spl249_1284
<=> ! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP29(X0,X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1284])]) ).
tff(f6933,plain,
( ! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP29(X0,X1,'none$') )
| ~ spl249_116
| ~ spl249_508 ),
inference(superposition,[],[f6578,f4112]) ).
tff(f17954,plain,
( spl249_1283
| ~ spl249_389
| ~ spl249_508 ),
inference(avatar_split_clause,[],[f6932,f6577,f5572,f17952]) ).
tff(f17952,plain,
( spl249_1283
<=> ! [X0: 'C_c_option_fun$',X1: 'C_option$'] :
( sP29(X0,'is_none$a',X1)
| ~ 'fun_app$'('is_none$a',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1283])]) ).
tff(f5572,plain,
( spl249_389
<=> ! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( 'fun_app$'('is_none$a','fun_app$ab'('bind$'(X0),X1))
| ~ 'fun_app$'('is_none$a',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_389])]) ).
tff(f6932,plain,
( ! [X0: 'C_c_option_fun$',X1: 'C_option$'] :
( sP29(X0,'is_none$a',X1)
| ~ 'fun_app$'('is_none$a',X1) )
| ~ spl249_389
| ~ spl249_508 ),
inference(resolution,[],[f6578,f5573]) ).
tff(f5573,plain,
( ! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( 'fun_app$'('is_none$a','fun_app$ab'('bind$'(X0),X1))
| ~ 'fun_app$'('is_none$a',X0) )
| ~ spl249_389 ),
inference(avatar_component_clause,[],[f5572]) ).
tff(f17950,plain,
( spl249_1282
| ~ spl249_128
| ~ spl249_506 ),
inference(avatar_split_clause,[],[f6924,f6569,f4159,f17948]) ).
tff(f17948,plain,
( spl249_1282
<=> ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,X0)
| ~ sP28('some$a',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1282])]) ).
tff(f6569,plain,
( spl249_506
<=> ! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
| ~ sP28(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_506])]) ).
tff(f6924,plain,
( ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,X0)
| ~ sP28('some$a',X1,X0) )
| ~ spl249_128
| ~ spl249_506 ),
inference(superposition,[],[f6570,f4160]) ).
tff(f6570,plain,
( ! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
| ~ sP28(X2,X0,X1) )
| ~ spl249_506 ),
inference(avatar_component_clause,[],[f6569]) ).
tff(f17946,plain,
( spl249_1281
| ~ spl249_117
| ~ spl249_506 ),
inference(avatar_split_clause,[],[f6923,f6569,f4115,f17944]) ).
tff(f17944,plain,
( spl249_1281
<=> ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP28('uwc$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1281])]) ).
tff(f6923,plain,
( ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP28('uwc$',X1,X0) )
| ~ spl249_117
| ~ spl249_506 ),
inference(superposition,[],[f6570,f4116]) ).
tff(f17942,plain,
( spl249_1280
| ~ spl249_128
| ~ spl249_505 ),
inference(avatar_split_clause,[],[f6906,f6565,f4159,f17940]) ).
tff(f17940,plain,
( spl249_1280
<=> ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,X0)
| sP28('some$a',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1280])]) ).
tff(f6565,plain,
( spl249_505
<=> ! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( sP28(X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_505])]) ).
tff(f6906,plain,
( ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,X0)
| sP28('some$a',X1,X0) )
| ~ spl249_128
| ~ spl249_505 ),
inference(superposition,[],[f6566,f4160]) ).
tff(f6566,plain,
( ! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ~ 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
| sP28(X2,X0,X1) )
| ~ spl249_505 ),
inference(avatar_component_clause,[],[f6565]) ).
tff(f17938,plain,
( spl249_1279
| ~ spl249_117
| ~ spl249_505 ),
inference(avatar_split_clause,[],[f6905,f6565,f4115,f17936]) ).
tff(f17936,plain,
( spl249_1279
<=> ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP28('uwc$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1279])]) ).
tff(f6905,plain,
( ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP28('uwc$',X1,X0) )
| ~ spl249_117
| ~ spl249_505 ),
inference(superposition,[],[f6566,f4116]) ).
tff(f17930,plain,
( spl249_1278
| ~ spl249_116
| ~ spl249_505 ),
inference(avatar_split_clause,[],[f6904,f6565,f4111,f17928]) ).
tff(f17928,plain,
( spl249_1278
<=> ! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP28(X0,X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1278])]) ).
tff(f6904,plain,
( ! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP28(X0,X1,'none$') )
| ~ spl249_116
| ~ spl249_505 ),
inference(superposition,[],[f6566,f4112]) ).
tff(f17926,plain,
( spl249_1277
| ~ spl249_389
| ~ spl249_505 ),
inference(avatar_split_clause,[],[f6903,f6565,f5572,f17924]) ).
tff(f17924,plain,
( spl249_1277
<=> ! [X0: 'C_c_option_fun$',X1: 'C_option$'] :
( sP28(X0,'is_none$a',X1)
| ~ 'fun_app$'('is_none$a',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1277])]) ).
tff(f6903,plain,
( ! [X0: 'C_c_option_fun$',X1: 'C_option$'] :
( sP28(X0,'is_none$a',X1)
| ~ 'fun_app$'('is_none$a',X1) )
| ~ spl249_389
| ~ spl249_505 ),
inference(resolution,[],[f6566,f5573]) ).
tff(f17922,plain,
( spl249_1276
| ~ spl249_127
| ~ spl249_504 ),
inference(avatar_split_clause,[],[f6897,f6561,f4155,f17920]) ).
tff(f17920,plain,
( spl249_1276
<=> ! [X0: 'A_option$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,X0)
| ~ sP27('some$b',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1276])]) ).
tff(f4155,plain,
( spl249_127
<=> ! [X0: 'A_option$'] : ( 'fun_app$bp'('bind$h'(X0),'some$b') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_127])]) ).
tff(f6561,plain,
( spl249_504
<=> ! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
| ~ sP27(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_504])]) ).
tff(f6897,plain,
( ! [X0: 'A_option$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,X0)
| ~ sP27('some$b',X1,X0) )
| ~ spl249_127
| ~ spl249_504 ),
inference(superposition,[],[f6562,f4156]) ).
tff(f4156,plain,
( ! [X0: 'A_option$'] : ( 'fun_app$bp'('bind$h'(X0),'some$b') = X0 )
| ~ spl249_127 ),
inference(avatar_component_clause,[],[f4155]) ).
tff(f6562,plain,
( ! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
| ~ sP27(X2,X0,X1) )
| ~ spl249_504 ),
inference(avatar_component_clause,[],[f6561]) ).
tff(f17918,plain,
( spl249_1275
| ~ spl249_127
| ~ spl249_503 ),
inference(avatar_split_clause,[],[f6888,f6557,f4155,f17916]) ).
tff(f17916,plain,
( spl249_1275
<=> ! [X0: 'A_option$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,X0)
| sP27('some$b',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1275])]) ).
tff(f6557,plain,
( spl249_503
<=> ! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( sP27(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_503])]) ).
tff(f6888,plain,
( ! [X0: 'A_option$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,X0)
| sP27('some$b',X1,X0) )
| ~ spl249_127
| ~ spl249_503 ),
inference(superposition,[],[f6558,f4156]) ).
tff(f6558,plain,
( ! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( ~ 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
| sP27(X2,X0,X1) )
| ~ spl249_503 ),
inference(avatar_component_clause,[],[f6557]) ).
tff(f17914,plain,
( spl249_1274
| ~ spl249_111
| ~ spl249_503 ),
inference(avatar_split_clause,[],[f6887,f6557,f4091,f17912]) ).
tff(f17912,plain,
( spl249_1274
<=> ! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,'none$b')
| sP27(X0,X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1274])]) ).
tff(f4091,plain,
( spl249_111
<=> ! [X0: 'A_a_option_fun$'] : ( 'none$b' = 'fun_app$bp'('bind$h'('none$b'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_111])]) ).
tff(f6887,plain,
( ! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,'none$b')
| sP27(X0,X1,'none$b') )
| ~ spl249_111
| ~ spl249_503 ),
inference(superposition,[],[f6558,f4092]) ).
tff(f4092,plain,
( ! [X0: 'A_a_option_fun$'] : ( 'none$b' = 'fun_app$bp'('bind$h'('none$b'),X0) )
| ~ spl249_111 ),
inference(avatar_component_clause,[],[f4091]) ).
tff(f17910,plain,
( spl249_1273
| ~ spl249_127
| ~ spl249_502 ),
inference(avatar_split_clause,[],[f6884,f6553,f4155,f17908]) ).
tff(f17908,plain,
( spl249_1273
<=> ! [X0: 'A_option$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,X0)
| ~ sP26('some$b',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1273])]) ).
tff(f6553,plain,
( spl249_502
<=> ! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
| ~ sP26(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_502])]) ).
tff(f6884,plain,
( ! [X0: 'A_option$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,X0)
| ~ sP26('some$b',X1,X0) )
| ~ spl249_127
| ~ spl249_502 ),
inference(superposition,[],[f6554,f4156]) ).
tff(f6554,plain,
( ! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
| ~ sP26(X2,X0,X1) )
| ~ spl249_502 ),
inference(avatar_component_clause,[],[f6553]) ).
tff(f17906,plain,
( spl249_1272
| ~ spl249_127
| ~ spl249_501 ),
inference(avatar_split_clause,[],[f6876,f6549,f4155,f17904]) ).
tff(f17904,plain,
( spl249_1272
<=> ! [X0: 'A_option$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,X0)
| sP26('some$b',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1272])]) ).
tff(f6549,plain,
( spl249_501
<=> ! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( sP26(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_501])]) ).
tff(f6876,plain,
( ! [X0: 'A_option$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,X0)
| sP26('some$b',X1,X0) )
| ~ spl249_127
| ~ spl249_501 ),
inference(superposition,[],[f6550,f4156]) ).
tff(f6550,plain,
( ! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( ~ 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
| sP26(X2,X0,X1) )
| ~ spl249_501 ),
inference(avatar_component_clause,[],[f6549]) ).
tff(f17902,plain,
( spl249_1271
| ~ spl249_111
| ~ spl249_501 ),
inference(avatar_split_clause,[],[f6875,f6549,f4091,f17900]) ).
tff(f17900,plain,
( spl249_1271
<=> ! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,'none$b')
| sP26(X0,X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1271])]) ).
tff(f6875,plain,
( ! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,'none$b')
| sP26(X0,X1,'none$b') )
| ~ spl249_111
| ~ spl249_501 ),
inference(superposition,[],[f6550,f4092]) ).
tff(f17898,plain,
( spl249_1270
| ~ spl249_57
| ~ spl249_442 ),
inference(avatar_split_clause,[],[f6341,f5794,f3860,f17896]) ).
tff(f17896,plain,
( spl249_1270
<=> ! [X0: 'B_option$'] : sP25(X0,'uwl$'('fun_app$al'('the$',X0)),tltrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1270])]) ).
tff(f3860,plain,
( spl249_57
<=> ! [X1: 'B$'] : 'fun_app$c'('uwl$'(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_57])]) ).
tff(f5794,plain,
( spl249_442
<=> ! [X0: 'B_option$',X1: 'B_bool_fun$'] :
( sP25(X0,X1,tltrue)
| ~ 'fun_app$c'(X1,'fun_app$al'('the$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_442])]) ).
tff(f6341,plain,
( ! [X0: 'B_option$'] : sP25(X0,'uwl$'('fun_app$al'('the$',X0)),tltrue)
| ~ spl249_57
| ~ spl249_442 ),
inference(resolution,[],[f5795,f3861]) ).
tff(f3861,plain,
( ! [X1: 'B$'] : 'fun_app$c'('uwl$'(X1),X1)
| ~ spl249_57 ),
inference(avatar_component_clause,[],[f3860]) ).
tff(f5795,plain,
( ! [X0: 'B_option$',X1: 'B_bool_fun$'] :
( ~ 'fun_app$c'(X1,'fun_app$al'('the$',X0))
| sP25(X0,X1,tltrue) )
| ~ spl249_442 ),
inference(avatar_component_clause,[],[f5794]) ).
tff(f17894,plain,
( spl249_1269
| ~ spl249_56
| ~ spl249_442 ),
inference(avatar_split_clause,[],[f6340,f5794,f3856,f17892]) ).
tff(f17892,plain,
( spl249_1269
<=> ! [X0: 'B_option$'] : sP25(X0,'uwp$'('fun_app$al'('the$',X0)),tltrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1269])]) ).
tff(f3856,plain,
( spl249_56
<=> ! [X1: 'B$'] : 'fun_app$c'('uwp$'(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_56])]) ).
tff(f6340,plain,
( ! [X0: 'B_option$'] : sP25(X0,'uwp$'('fun_app$al'('the$',X0)),tltrue)
| ~ spl249_56
| ~ spl249_442 ),
inference(resolution,[],[f5795,f3857]) ).
tff(f3857,plain,
( ! [X1: 'B$'] : 'fun_app$c'('uwp$'(X1),X1)
| ~ spl249_56 ),
inference(avatar_component_clause,[],[f3856]) ).
tff(f17890,plain,
( spl249_1268
| ~ spl249_271
| ~ spl249_1054 ),
inference(avatar_split_clause,[],[f16226,f14852,f4885,f17888]) ).
tff(f17888,plain,
( spl249_1268
<=> ! [X0: 'B_c_option_fun$'] : ( 'bot$d' = 'collect$'('uul$'('bot$h',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1268])]) ).
tff(f4885,plain,
( spl249_271
<=> ! [X0: 'B_bool_fun$'] :
( ( 'bot$d' = 'collect$'(X0) )
| 'fun_app$c'(X0,sK84(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_271])]) ).
tff(f14852,plain,
( spl249_1054
<=> ! [X0: 'B_c_option_fun$',X1: 'B$'] : ~ 'fun_app$c'('uul$'('bot$h',X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1054])]) ).
tff(f16226,plain,
( ! [X0: 'B_c_option_fun$'] : ( 'bot$d' = 'collect$'('uul$'('bot$h',X0)) )
| ~ spl249_271
| ~ spl249_1054 ),
inference(resolution,[],[f14853,f4886]) ).
tff(f4886,plain,
( ! [X0: 'B_bool_fun$'] :
( 'fun_app$c'(X0,sK84(X0))
| ( 'bot$d' = 'collect$'(X0) ) )
| ~ spl249_271 ),
inference(avatar_component_clause,[],[f4885]) ).
tff(f14853,plain,
( ! [X0: 'B_c_option_fun$',X1: 'B$'] : ~ 'fun_app$c'('uul$'('bot$h',X0),X1)
| ~ spl249_1054 ),
inference(avatar_component_clause,[],[f14852]) ).
tff(f17886,plain,
( spl249_1267
| ~ spl249_55
| ~ spl249_441 ),
inference(avatar_split_clause,[],[f6336,f5790,f3852,f17884]) ).
tff(f17884,plain,
( spl249_1267
<=> ! [X0: 'C_option$'] : sP20(X0,'uwm$'('fun_app$ak'('the$a',X0)),tltrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1267])]) ).
tff(f3852,plain,
( spl249_55
<=> ! [X1: 'C$'] : 'fun_app$b'('uwm$'(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_55])]) ).
tff(f5790,plain,
( spl249_441
<=> ! [X0: 'C_option$',X1: 'C_bool_fun$'] :
( sP20(X0,X1,tltrue)
| ~ 'fun_app$b'(X1,'fun_app$ak'('the$a',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_441])]) ).
tff(f6336,plain,
( ! [X0: 'C_option$'] : sP20(X0,'uwm$'('fun_app$ak'('the$a',X0)),tltrue)
| ~ spl249_55
| ~ spl249_441 ),
inference(resolution,[],[f5791,f3853]) ).
tff(f3853,plain,
( ! [X1: 'C$'] : 'fun_app$b'('uwm$'(X1),X1)
| ~ spl249_55 ),
inference(avatar_component_clause,[],[f3852]) ).
tff(f5791,plain,
( ! [X0: 'C_option$',X1: 'C_bool_fun$'] :
( ~ 'fun_app$b'(X1,'fun_app$ak'('the$a',X0))
| sP20(X0,X1,tltrue) )
| ~ spl249_441 ),
inference(avatar_component_clause,[],[f5790]) ).
tff(f17882,plain,
( spl249_1266
| ~ spl249_54
| ~ spl249_441 ),
inference(avatar_split_clause,[],[f6335,f5790,f3848,f17880]) ).
tff(f17880,plain,
( spl249_1266
<=> ! [X0: 'C_option$'] : sP20(X0,'uwq$'('fun_app$ak'('the$a',X0)),tltrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1266])]) ).
tff(f3848,plain,
( spl249_54
<=> ! [X1: 'C$'] : 'fun_app$b'('uwq$'(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_54])]) ).
tff(f6335,plain,
( ! [X0: 'C_option$'] : sP20(X0,'uwq$'('fun_app$ak'('the$a',X0)),tltrue)
| ~ spl249_54
| ~ spl249_441 ),
inference(resolution,[],[f5791,f3849]) ).
tff(f3849,plain,
( ! [X1: 'C$'] : 'fun_app$b'('uwq$'(X1),X1)
| ~ spl249_54 ),
inference(avatar_component_clause,[],[f3848]) ).
tff(f17878,plain,
( spl249_1265
| ~ spl249_268
| ~ spl249_437 ),
inference(avatar_split_clause,[],[f6318,f5772,f4873,f17876]) ).
tff(f17876,plain,
( spl249_1265
<=> ! [X0: 'B_option$'] :
( ~ sP25(X0,'uud$',tltrue)
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1265])]) ).
tff(f4873,plain,
( spl249_268
<=> ! [X0: 'B_option$'] :
( ( 'none$a' = X0 )
| ~ 'fun_app$a'('case_option$e'(tltrue,'uud$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_268])]) ).
tff(f5772,plain,
( spl249_437
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ~ sP25(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_437])]) ).
tff(f6318,plain,
( ! [X0: 'B_option$'] :
( ~ sP25(X0,'uud$',tltrue)
| ( 'none$a' = X0 ) )
| ~ spl249_268
| ~ spl249_437 ),
inference(resolution,[],[f5773,f4874]) ).
tff(f4874,plain,
( ! [X0: 'B_option$'] :
( ~ 'fun_app$a'('case_option$e'(tltrue,'uud$'),X0)
| ( 'none$a' = X0 ) )
| ~ spl249_268 ),
inference(avatar_component_clause,[],[f4873]) ).
tff(f5773,plain,
( ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ~ sP25(X2,X1,X0) )
| ~ spl249_437 ),
inference(avatar_component_clause,[],[f5772]) ).
tff(f17874,plain,
( spl249_1264
| ~ spl249_78
| ~ spl249_435 ),
inference(avatar_split_clause,[],[f6301,f5764,f3954,f17872]) ).
tff(f17872,plain,
( spl249_1264
<=> ! [X0: 'C_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP24('uwe$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1264])]) ).
tff(f5764,plain,
( spl249_435
<=> ! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$a'(X0,'bind$a'(X1,X2))
| ~ sP24(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_435])]) ).
tff(f6301,plain,
( ! [X0: 'C_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP24('uwe$',X1,X0) )
| ~ spl249_78
| ~ spl249_435 ),
inference(superposition,[],[f5765,f3955]) ).
tff(f5765,plain,
( ! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$a'(X0,'bind$a'(X1,X2))
| ~ sP24(X2,X0,X1) )
| ~ spl249_435 ),
inference(avatar_component_clause,[],[f5764]) ).
tff(f17870,plain,
( spl249_1263
| ~ spl249_79
| ~ spl249_434 ),
inference(avatar_split_clause,[],[f6287,f5760,f3958,f17868]) ).
tff(f17868,plain,
( spl249_1263
<=> ! [X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP24(X0,X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1263])]) ).
tff(f5760,plain,
( spl249_434
<=> ! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( sP24(X2,X0,X1)
| ~ 'fun_app$a'(X0,'bind$a'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_434])]) ).
tff(f6287,plain,
( ! [X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP24(X0,X1,'none$') )
| ~ spl249_79
| ~ spl249_434 ),
inference(superposition,[],[f5761,f3959]) ).
tff(f5761,plain,
( ! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( ~ 'fun_app$a'(X0,'bind$a'(X1,X2))
| sP24(X2,X0,X1) )
| ~ spl249_434 ),
inference(avatar_component_clause,[],[f5760]) ).
tff(f17866,plain,
( spl249_1262
| ~ spl249_78
| ~ spl249_434 ),
inference(avatar_split_clause,[],[f6286,f5760,f3954,f17864]) ).
tff(f17864,plain,
( spl249_1262
<=> ! [X0: 'C_option$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP24('uwe$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1262])]) ).
tff(f6286,plain,
( ! [X0: 'C_option$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP24('uwe$',X1,X0) )
| ~ spl249_78
| ~ spl249_434 ),
inference(superposition,[],[f5761,f3955]) ).
tff(f17862,plain,
( spl249_1261
| ~ spl249_311
| ~ spl249_434 ),
inference(avatar_split_clause,[],[f6285,f5760,f5048,f17860]) ).
tff(f17860,plain,
( spl249_1261
<=> ! [X0: 'C_b_option_fun$',X1: 'C_option$'] :
( sP24(X0,'is_none$',X1)
| ~ 'fun_app$'('is_none$a',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1261])]) ).
tff(f5048,plain,
( spl249_311
<=> ! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$a'(X0,X1))
| ~ 'fun_app$'('is_none$a',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_311])]) ).
tff(f6285,plain,
( ! [X0: 'C_b_option_fun$',X1: 'C_option$'] :
( sP24(X0,'is_none$',X1)
| ~ 'fun_app$'('is_none$a',X1) )
| ~ spl249_311
| ~ spl249_434 ),
inference(resolution,[],[f5761,f5049]) ).
tff(f5049,plain,
( ! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$a'(X0,X1))
| ~ 'fun_app$'('is_none$a',X0) )
| ~ spl249_311 ),
inference(avatar_component_clause,[],[f5048]) ).
tff(f17858,plain,
( spl249_1260
| ~ spl249_78
| ~ spl249_433 ),
inference(avatar_split_clause,[],[f6278,f5756,f3954,f17856]) ).
tff(f17856,plain,
( spl249_1260
<=> ! [X0: 'C_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP23('uwe$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1260])]) ).
tff(f5756,plain,
( spl249_433
<=> ! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$a'(X0,'bind$a'(X1,X2))
| ~ sP23(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_433])]) ).
tff(f6278,plain,
( ! [X0: 'C_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP23('uwe$',X1,X0) )
| ~ spl249_78
| ~ spl249_433 ),
inference(superposition,[],[f5757,f3955]) ).
tff(f5757,plain,
( ! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$a'(X0,'bind$a'(X1,X2))
| ~ sP23(X2,X0,X1) )
| ~ spl249_433 ),
inference(avatar_component_clause,[],[f5756]) ).
tff(f17854,plain,
( spl249_1259
| ~ spl249_79
| ~ spl249_432 ),
inference(avatar_split_clause,[],[f6265,f5752,f3958,f17852]) ).
tff(f17852,plain,
( spl249_1259
<=> ! [X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP23(X0,X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1259])]) ).
tff(f5752,plain,
( spl249_432
<=> ! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( sP23(X2,X0,X1)
| ~ 'fun_app$a'(X0,'bind$a'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_432])]) ).
tff(f6265,plain,
( ! [X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP23(X0,X1,'none$') )
| ~ spl249_79
| ~ spl249_432 ),
inference(superposition,[],[f5753,f3959]) ).
tff(f5753,plain,
( ! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( ~ 'fun_app$a'(X0,'bind$a'(X1,X2))
| sP23(X2,X0,X1) )
| ~ spl249_432 ),
inference(avatar_component_clause,[],[f5752]) ).
tff(f17850,plain,
( spl249_1258
| ~ spl249_78
| ~ spl249_432 ),
inference(avatar_split_clause,[],[f6264,f5752,f3954,f17848]) ).
tff(f17848,plain,
( spl249_1258
<=> ! [X0: 'C_option$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP23('uwe$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1258])]) ).
tff(f6264,plain,
( ! [X0: 'C_option$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP23('uwe$',X1,X0) )
| ~ spl249_78
| ~ spl249_432 ),
inference(superposition,[],[f5753,f3955]) ).
tff(f17846,plain,
( spl249_1257
| ~ spl249_311
| ~ spl249_432 ),
inference(avatar_split_clause,[],[f6263,f5752,f5048,f17844]) ).
tff(f17844,plain,
( spl249_1257
<=> ! [X0: 'C_b_option_fun$',X1: 'C_option$'] :
( sP23(X0,'is_none$',X1)
| ~ 'fun_app$'('is_none$a',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1257])]) ).
tff(f6263,plain,
( ! [X0: 'C_b_option_fun$',X1: 'C_option$'] :
( sP23(X0,'is_none$',X1)
| ~ 'fun_app$'('is_none$a',X1) )
| ~ spl249_311
| ~ spl249_432 ),
inference(resolution,[],[f5753,f5049]) ).
tff(f17842,plain,
( spl249_1256
| ~ spl249_77
| ~ spl249_430 ),
inference(avatar_split_clause,[],[f6244,f5744,f3950,f17840]) ).
tff(f17840,plain,
( spl249_1256
<=> ! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP22(X0,X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1256])]) ).
tff(f3950,plain,
( spl249_77
<=> ! [X0: 'A_b_option_fun$'] : ( 'none$a' = 'bind$e'('none$b',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_77])]) ).
tff(f5744,plain,
( spl249_430
<=> ! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( sP22(X2,X0,X1)
| ~ 'fun_app$a'(X0,'bind$e'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_430])]) ).
tff(f6244,plain,
( ! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP22(X0,X1,'none$b') )
| ~ spl249_77
| ~ spl249_430 ),
inference(superposition,[],[f5745,f3951]) ).
tff(f3951,plain,
( ! [X0: 'A_b_option_fun$'] : ( 'none$a' = 'bind$e'('none$b',X0) )
| ~ spl249_77 ),
inference(avatar_component_clause,[],[f3950]) ).
tff(f5745,plain,
( ! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( ~ 'fun_app$a'(X0,'bind$e'(X1,X2))
| sP22(X2,X0,X1) )
| ~ spl249_430 ),
inference(avatar_component_clause,[],[f5744]) ).
tff(f17838,plain,
( spl249_1255
| ~ spl249_310
| ~ spl249_430 ),
inference(avatar_split_clause,[],[f6243,f5744,f5044,f17836]) ).
tff(f17836,plain,
( spl249_1255
<=> ! [X0: 'A_b_option_fun$',X1: 'A_option$'] :
( sP22(X0,'is_none$',X1)
| ~ 'fun_app$aw'('is_none$b',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1255])]) ).
tff(f5044,plain,
( spl249_310
<=> ! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$e'(X0,X1))
| ~ 'fun_app$aw'('is_none$b',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_310])]) ).
tff(f6243,plain,
( ! [X0: 'A_b_option_fun$',X1: 'A_option$'] :
( sP22(X0,'is_none$',X1)
| ~ 'fun_app$aw'('is_none$b',X1) )
| ~ spl249_310
| ~ spl249_430 ),
inference(resolution,[],[f5745,f5045]) ).
tff(f5045,plain,
( ! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$e'(X0,X1))
| ~ 'fun_app$aw'('is_none$b',X0) )
| ~ spl249_310 ),
inference(avatar_component_clause,[],[f5044]) ).
tff(f17834,plain,
( spl249_1254
| ~ spl249_77
| ~ spl249_428 ),
inference(avatar_split_clause,[],[f6224,f5736,f3950,f17832]) ).
tff(f17832,plain,
( spl249_1254
<=> ! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP21(X0,X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1254])]) ).
tff(f5736,plain,
( spl249_428
<=> ! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( sP21(X2,X0,X1)
| ~ 'fun_app$a'(X0,'bind$e'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_428])]) ).
tff(f6224,plain,
( ! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X1,'none$a')
| sP21(X0,X1,'none$b') )
| ~ spl249_77
| ~ spl249_428 ),
inference(superposition,[],[f5737,f3951]) ).
tff(f5737,plain,
( ! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( ~ 'fun_app$a'(X0,'bind$e'(X1,X2))
| sP21(X2,X0,X1) )
| ~ spl249_428 ),
inference(avatar_component_clause,[],[f5736]) ).
tff(f17830,plain,
( spl249_1253
| ~ spl249_310
| ~ spl249_428 ),
inference(avatar_split_clause,[],[f6223,f5736,f5044,f17828]) ).
tff(f17828,plain,
( spl249_1253
<=> ! [X0: 'A_b_option_fun$',X1: 'A_option$'] :
( sP21(X0,'is_none$',X1)
| ~ 'fun_app$aw'('is_none$b',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1253])]) ).
tff(f6223,plain,
( ! [X0: 'A_b_option_fun$',X1: 'A_option$'] :
( sP21(X0,'is_none$',X1)
| ~ 'fun_app$aw'('is_none$b',X1) )
| ~ spl249_310
| ~ spl249_428 ),
inference(resolution,[],[f5737,f5045]) ).
tff(f17826,plain,
( spl249_1252
| ~ spl249_267
| ~ spl249_427 ),
inference(avatar_split_clause,[],[f6208,f5730,f4869,f17824]) ).
tff(f17824,plain,
( spl249_1252
<=> ! [X0: 'C_option$'] :
( ~ sP20(X0,'uuc$',tltrue)
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1252])]) ).
tff(f4869,plain,
( spl249_267
<=> ! [X0: 'C_option$'] :
( ( 'none$' = X0 )
| ~ 'fun_app$'('case_option$f'(tltrue,'uuc$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_267])]) ).
tff(f5730,plain,
( spl249_427
<=> ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),X2)
| ~ sP20(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_427])]) ).
tff(f6208,plain,
( ! [X0: 'C_option$'] :
( ~ sP20(X0,'uuc$',tltrue)
| ( 'none$' = X0 ) )
| ~ spl249_267
| ~ spl249_427 ),
inference(resolution,[],[f5731,f4870]) ).
tff(f4870,plain,
( ! [X0: 'C_option$'] :
( ~ 'fun_app$'('case_option$f'(tltrue,'uuc$'),X0)
| ( 'none$' = X0 ) )
| ~ spl249_267 ),
inference(avatar_component_clause,[],[f4869]) ).
tff(f5731,plain,
( ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),X2)
| ~ sP20(X2,X1,X0) )
| ~ spl249_427 ),
inference(avatar_component_clause,[],[f5730]) ).
tff(f17822,plain,
( spl249_1251
| ~ spl249_74
| ~ spl249_425 ),
inference(avatar_split_clause,[],[f6194,f5722,f3937,f17820]) ).
tff(f17820,plain,
( spl249_1251
<=> ! [X0: 'B_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP19('uwb$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1251])]) ).
tff(f5722,plain,
( spl249_425
<=> ! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$'(X0,'bind$b'(X1,X2))
| ~ sP19(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_425])]) ).
tff(f6194,plain,
( ! [X0: 'B_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP19('uwb$',X1,X0) )
| ~ spl249_74
| ~ spl249_425 ),
inference(superposition,[],[f5723,f3938]) ).
tff(f5723,plain,
( ! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$'(X0,'bind$b'(X1,X2))
| ~ sP19(X2,X0,X1) )
| ~ spl249_425 ),
inference(avatar_component_clause,[],[f5722]) ).
tff(f17818,plain,
( spl249_1250
| ~ spl249_76
| ~ spl249_424 ),
inference(avatar_split_clause,[],[f6178,f5718,f3946,f17816]) ).
tff(f17816,plain,
( spl249_1250
<=> ! [X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP19(X0,X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1250])]) ).
tff(f5718,plain,
( spl249_424
<=> ! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( sP19(X2,X0,X1)
| ~ 'fun_app$'(X0,'bind$b'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_424])]) ).
tff(f6178,plain,
( ! [X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP19(X0,X1,'none$a') )
| ~ spl249_76
| ~ spl249_424 ),
inference(superposition,[],[f5719,f3947]) ).
tff(f5719,plain,
( ! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( ~ 'fun_app$'(X0,'bind$b'(X1,X2))
| sP19(X2,X0,X1) )
| ~ spl249_424 ),
inference(avatar_component_clause,[],[f5718]) ).
tff(f17814,plain,
( spl249_1249
| ~ spl249_74
| ~ spl249_424 ),
inference(avatar_split_clause,[],[f6177,f5718,f3937,f17812]) ).
tff(f17812,plain,
( spl249_1249
<=> ! [X0: 'B_option$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP19('uwb$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1249])]) ).
tff(f6177,plain,
( ! [X0: 'B_option$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP19('uwb$',X1,X0) )
| ~ spl249_74
| ~ spl249_424 ),
inference(superposition,[],[f5719,f3938]) ).
tff(f17810,plain,
( spl249_1248
| ~ spl249_306
| ~ spl249_424 ),
inference(avatar_split_clause,[],[f6176,f5718,f5028,f17808]) ).
tff(f17808,plain,
( spl249_1248
<=> ! [X0: 'B_c_option_fun$',X1: 'B_option$'] :
( sP19(X0,'is_none$a',X1)
| ~ 'fun_app$a'('is_none$',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1248])]) ).
tff(f5028,plain,
( spl249_306
<=> ! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$b'(X0,X1))
| ~ 'fun_app$a'('is_none$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_306])]) ).
tff(f6176,plain,
( ! [X0: 'B_c_option_fun$',X1: 'B_option$'] :
( sP19(X0,'is_none$a',X1)
| ~ 'fun_app$a'('is_none$',X1) )
| ~ spl249_306
| ~ spl249_424 ),
inference(resolution,[],[f5719,f5029]) ).
tff(f5029,plain,
( ! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$b'(X0,X1))
| ~ 'fun_app$a'('is_none$',X0) )
| ~ spl249_306 ),
inference(avatar_component_clause,[],[f5028]) ).
tff(f17802,plain,
( spl249_1247
| ~ spl249_74
| ~ spl249_423 ),
inference(avatar_split_clause,[],[f6168,f5714,f3937,f17800]) ).
tff(f17800,plain,
( spl249_1247
<=> ! [X0: 'B_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP18('uwb$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1247])]) ).
tff(f5714,plain,
( spl249_423
<=> ! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$'(X0,'bind$b'(X1,X2))
| ~ sP18(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_423])]) ).
tff(f6168,plain,
( ! [X0: 'B_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP18('uwb$',X1,X0) )
| ~ spl249_74
| ~ spl249_423 ),
inference(superposition,[],[f5715,f3938]) ).
tff(f5715,plain,
( ! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$'(X0,'bind$b'(X1,X2))
| ~ sP18(X2,X0,X1) )
| ~ spl249_423 ),
inference(avatar_component_clause,[],[f5714]) ).
tff(f17798,plain,
( spl249_1246
| ~ spl249_76
| ~ spl249_422 ),
inference(avatar_split_clause,[],[f6153,f5710,f3946,f17796]) ).
tff(f17796,plain,
( spl249_1246
<=> ! [X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP18(X0,X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1246])]) ).
tff(f5710,plain,
( spl249_422
<=> ! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( sP18(X2,X0,X1)
| ~ 'fun_app$'(X0,'bind$b'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_422])]) ).
tff(f6153,plain,
( ! [X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP18(X0,X1,'none$a') )
| ~ spl249_76
| ~ spl249_422 ),
inference(superposition,[],[f5711,f3947]) ).
tff(f5711,plain,
( ! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( ~ 'fun_app$'(X0,'bind$b'(X1,X2))
| sP18(X2,X0,X1) )
| ~ spl249_422 ),
inference(avatar_component_clause,[],[f5710]) ).
tff(f17794,plain,
( spl249_1245
| ~ spl249_74
| ~ spl249_422 ),
inference(avatar_split_clause,[],[f6152,f5710,f3937,f17792]) ).
tff(f17792,plain,
( spl249_1245
<=> ! [X0: 'B_option$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP18('uwb$',X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1245])]) ).
tff(f6152,plain,
( ! [X0: 'B_option$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP18('uwb$',X1,X0) )
| ~ spl249_74
| ~ spl249_422 ),
inference(superposition,[],[f5711,f3938]) ).
tff(f17790,plain,
( spl249_1244
| ~ spl249_306
| ~ spl249_422 ),
inference(avatar_split_clause,[],[f6151,f5710,f5028,f17788]) ).
tff(f17788,plain,
( spl249_1244
<=> ! [X0: 'B_c_option_fun$',X1: 'B_option$'] :
( sP18(X0,'is_none$a',X1)
| ~ 'fun_app$a'('is_none$',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1244])]) ).
tff(f6151,plain,
( ! [X0: 'B_c_option_fun$',X1: 'B_option$'] :
( sP18(X0,'is_none$a',X1)
| ~ 'fun_app$a'('is_none$',X1) )
| ~ spl249_306
| ~ spl249_422 ),
inference(resolution,[],[f5711,f5029]) ).
tff(f17786,plain,
( spl249_1243
| ~ spl249_73
| ~ spl249_420 ),
inference(avatar_split_clause,[],[f6131,f5702,f3933,f17784]) ).
tff(f17784,plain,
( spl249_1243
<=> ! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP17(X0,X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1243])]) ).
tff(f3933,plain,
( spl249_73
<=> ! [X0: 'A_c_option_fun$'] : ( 'none$' = 'bind$d'('none$b',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_73])]) ).
tff(f5702,plain,
( spl249_420
<=> ! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( sP17(X2,X0,X1)
| ~ 'fun_app$'(X0,'bind$d'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_420])]) ).
tff(f6131,plain,
( ! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP17(X0,X1,'none$b') )
| ~ spl249_73
| ~ spl249_420 ),
inference(superposition,[],[f5703,f3934]) ).
tff(f3934,plain,
( ! [X0: 'A_c_option_fun$'] : ( 'none$' = 'bind$d'('none$b',X0) )
| ~ spl249_73 ),
inference(avatar_component_clause,[],[f3933]) ).
tff(f5703,plain,
( ! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( ~ 'fun_app$'(X0,'bind$d'(X1,X2))
| sP17(X2,X0,X1) )
| ~ spl249_420 ),
inference(avatar_component_clause,[],[f5702]) ).
tff(f17782,plain,
( spl249_1242
| ~ spl249_305
| ~ spl249_420 ),
inference(avatar_split_clause,[],[f6130,f5702,f5024,f17780]) ).
tff(f17780,plain,
( spl249_1242
<=> ! [X0: 'A_c_option_fun$',X1: 'A_option$'] :
( sP17(X0,'is_none$a',X1)
| ~ 'fun_app$aw'('is_none$b',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1242])]) ).
tff(f5024,plain,
( spl249_305
<=> ! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$d'(X0,X1))
| ~ 'fun_app$aw'('is_none$b',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_305])]) ).
tff(f6130,plain,
( ! [X0: 'A_c_option_fun$',X1: 'A_option$'] :
( sP17(X0,'is_none$a',X1)
| ~ 'fun_app$aw'('is_none$b',X1) )
| ~ spl249_305
| ~ spl249_420 ),
inference(resolution,[],[f5703,f5025]) ).
tff(f5025,plain,
( ! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$d'(X0,X1))
| ~ 'fun_app$aw'('is_none$b',X0) )
| ~ spl249_305 ),
inference(avatar_component_clause,[],[f5024]) ).
tff(f17778,plain,
( spl249_1241
| ~ spl249_73
| ~ spl249_418 ),
inference(avatar_split_clause,[],[f6110,f5694,f3933,f17776]) ).
tff(f17776,plain,
( spl249_1241
<=> ! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP16(X0,X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1241])]) ).
tff(f5694,plain,
( spl249_418
<=> ! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( sP16(X2,X0,X1)
| ~ 'fun_app$'(X0,'bind$d'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_418])]) ).
tff(f6110,plain,
( ! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X1,'none$')
| sP16(X0,X1,'none$b') )
| ~ spl249_73
| ~ spl249_418 ),
inference(superposition,[],[f5695,f3934]) ).
tff(f5695,plain,
( ! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( ~ 'fun_app$'(X0,'bind$d'(X1,X2))
| sP16(X2,X0,X1) )
| ~ spl249_418 ),
inference(avatar_component_clause,[],[f5694]) ).
tff(f17774,plain,
( spl249_1240
| ~ spl249_305
| ~ spl249_418 ),
inference(avatar_split_clause,[],[f6109,f5694,f5024,f17772]) ).
tff(f17772,plain,
( spl249_1240
<=> ! [X0: 'A_c_option_fun$',X1: 'A_option$'] :
( sP16(X0,'is_none$a',X1)
| ~ 'fun_app$aw'('is_none$b',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1240])]) ).
tff(f6109,plain,
( ! [X0: 'A_c_option_fun$',X1: 'A_option$'] :
( sP16(X0,'is_none$a',X1)
| ~ 'fun_app$aw'('is_none$b',X1) )
| ~ spl249_305
| ~ spl249_418 ),
inference(resolution,[],[f5695,f5025]) ).
tff(f17770,plain,
( spl249_1239
| ~ spl249_72
| ~ spl249_416 ),
inference(avatar_split_clause,[],[f6096,f5684,f3929,f17768]) ).
tff(f17768,plain,
( spl249_1239
<=> ! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,'none$b')
| sP15(X0,X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1239])]) ).
tff(f3929,plain,
( spl249_72
<=> ! [X0: 'B_a_option_fun$'] : ( 'none$b' = 'bind$g'('none$a',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_72])]) ).
tff(f5684,plain,
( spl249_416
<=> ! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( sP15(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'bind$g'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_416])]) ).
tff(f6096,plain,
( ! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,'none$b')
| sP15(X0,X1,'none$a') )
| ~ spl249_72
| ~ spl249_416 ),
inference(superposition,[],[f5685,f3930]) ).
tff(f3930,plain,
( ! [X0: 'B_a_option_fun$'] : ( 'none$b' = 'bind$g'('none$a',X0) )
| ~ spl249_72 ),
inference(avatar_component_clause,[],[f3929]) ).
tff(f5685,plain,
( ! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( ~ 'fun_app$aw'(X0,'bind$g'(X1,X2))
| sP15(X2,X0,X1) )
| ~ spl249_416 ),
inference(avatar_component_clause,[],[f5684]) ).
tff(f17766,plain,
( spl249_1238
| ~ spl249_71
| ~ spl249_414 ),
inference(avatar_split_clause,[],[f6081,f5676,f3925,f17764]) ).
tff(f17764,plain,
( spl249_1238
<=> ! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,'none$b')
| sP14(X0,X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1238])]) ).
tff(f3925,plain,
( spl249_71
<=> ! [X0: 'C_a_option_fun$'] : ( 'none$b' = 'bind$f'('none$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_71])]) ).
tff(f5676,plain,
( spl249_414
<=> ! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( sP14(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'bind$f'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_414])]) ).
tff(f6081,plain,
( ! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,'none$b')
| sP14(X0,X1,'none$') )
| ~ spl249_71
| ~ spl249_414 ),
inference(superposition,[],[f5677,f3926]) ).
tff(f3926,plain,
( ! [X0: 'C_a_option_fun$'] : ( 'none$b' = 'bind$f'('none$',X0) )
| ~ spl249_71 ),
inference(avatar_component_clause,[],[f3925]) ).
tff(f5677,plain,
( ! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( ~ 'fun_app$aw'(X0,'bind$f'(X1,X2))
| sP14(X2,X0,X1) )
| ~ spl249_414 ),
inference(avatar_component_clause,[],[f5676]) ).
tff(f17762,plain,
( spl249_1237
| ~ spl249_769
| ~ spl249_1207 ),
inference(avatar_split_clause,[],[f17630,f17508,f9872,f17760]) ).
tff(f17760,plain,
( spl249_1237
<=> ! [X0: 'C_option_option$'] : ( 'map_option$j'('map_option$c'('uvs$'),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1237])]) ).
tff(f17508,plain,
( spl249_1207
<=> ! [X0: 'C_option$'] : ( 'fun_app$u'('map_option$c'('uvs$'),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1207])]) ).
tff(f17630,plain,
( ! [X0: 'C_option_option$'] : ( 'map_option$j'('map_option$c'('uvs$'),X0) = X0 )
| ~ spl249_769
| ~ spl249_1207 ),
inference(trivial_inequality_removal,[],[f17628]) ).
tff(f17628,plain,
( ! [X0: 'C_option_option$'] :
( ( sK117(X0,'map_option$c'('uvs$')) != sK117(X0,'map_option$c'('uvs$')) )
| ( 'map_option$j'('map_option$c'('uvs$'),X0) = X0 ) )
| ~ spl249_769
| ~ spl249_1207 ),
inference(superposition,[],[f9873,f17509]) ).
tff(f17509,plain,
( ! [X0: 'C_option$'] : ( 'fun_app$u'('map_option$c'('uvs$'),X0) = X0 )
| ~ spl249_1207 ),
inference(avatar_component_clause,[],[f17508]) ).
tff(f17758,plain,
( spl249_1236
| ~ spl249_72
| ~ spl249_412 ),
inference(avatar_split_clause,[],[f6071,f5668,f3929,f17756]) ).
tff(f17756,plain,
( spl249_1236
<=> ! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,'none$b')
| sP13(X0,X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1236])]) ).
tff(f5668,plain,
( spl249_412
<=> ! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( sP13(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'bind$g'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_412])]) ).
tff(f6071,plain,
( ! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,'none$b')
| sP13(X0,X1,'none$a') )
| ~ spl249_72
| ~ spl249_412 ),
inference(superposition,[],[f5669,f3930]) ).
tff(f5669,plain,
( ! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( ~ 'fun_app$aw'(X0,'bind$g'(X1,X2))
| sP13(X2,X0,X1) )
| ~ spl249_412 ),
inference(avatar_component_clause,[],[f5668]) ).
tff(f17754,plain,
( spl249_1235
| ~ spl249_71
| ~ spl249_410 ),
inference(avatar_split_clause,[],[f6062,f5660,f3925,f17752]) ).
tff(f17752,plain,
( spl249_1235
<=> ! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,'none$b')
| sP12(X0,X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1235])]) ).
tff(f5660,plain,
( spl249_410
<=> ! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( sP12(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'bind$f'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_410])]) ).
tff(f6062,plain,
( ! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( ~ 'fun_app$aw'(X1,'none$b')
| sP12(X0,X1,'none$') )
| ~ spl249_71
| ~ spl249_410 ),
inference(superposition,[],[f5661,f3926]) ).
tff(f5661,plain,
( ! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( ~ 'fun_app$aw'(X0,'bind$f'(X1,X2))
| sP12(X2,X0,X1) )
| ~ spl249_410 ),
inference(avatar_component_clause,[],[f5660]) ).
tff(f17750,plain,
( spl249_1234
| ~ spl249_5
| ~ spl249_348 ),
inference(avatar_split_clause,[],[f5832,f5408,f3625,f17747]) ).
tff(f17747,plain,
( spl249_1234
<=> ( 'f$' = 'register_from_getter_setter$'(sK65('f$'),sK66('f$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1234])]) ).
tff(f3625,plain,
( spl249_5
<=> 'register$'('f$') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_5])]) ).
tff(f5408,plain,
( spl249_348
<=> ! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( 'register_from_getter_setter$'(sK65(X0),sK66(X0)) = X0 )
| ~ 'register$'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_348])]) ).
tff(f5832,plain,
( ( 'f$' = 'register_from_getter_setter$'(sK65('f$'),sK66('f$')) )
| ~ spl249_5
| ~ spl249_348 ),
inference(resolution,[],[f5409,f3627]) ).
tff(f3627,plain,
( 'register$'('f$')
| ~ spl249_5 ),
inference(avatar_component_clause,[],[f3625]) ).
tff(f5409,plain,
( ! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ~ 'register$'(X0)
| ( 'register_from_getter_setter$'(sK65(X0),sK66(X0)) = X0 ) )
| ~ spl249_348 ),
inference(avatar_component_clause,[],[f5408]) ).
tff(f17745,plain,
( spl249_1233
| ~ spl249_4
| ~ spl249_347 ),
inference(avatar_split_clause,[],[f5830,f5404,f3620,f17742]) ).
tff(f5404,plain,
( spl249_347
<=> ! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( 'register_from_getter_setter$a'(sK63(X0),sK64(X0)) = X0 )
| ~ 'register$a'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_347])]) ).
tff(f5830,plain,
( ( 'g$' = 'register_from_getter_setter$a'(sK63('g$'),sK64('g$')) )
| ~ spl249_4
| ~ spl249_347 ),
inference(resolution,[],[f5405,f3622]) ).
tff(f3622,plain,
( 'register$a'('g$')
| ~ spl249_4 ),
inference(avatar_component_clause,[],[f3620]) ).
tff(f5405,plain,
( ! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ~ 'register$a'(X0)
| ( 'register_from_getter_setter$a'(sK63(X0),sK64(X0)) = X0 ) )
| ~ spl249_347 ),
inference(avatar_component_clause,[],[f5404]) ).
tff(f17740,plain,
( spl249_1232
| ~ spl249_3
| ~ spl249_346 ),
inference(avatar_split_clause,[],[f5828,f5400,f3615,f17737]) ).
tff(f17737,plain,
( spl249_1232
<=> ( 'id$f' = 'register_from_getter_setter$b'(sK61('id$f'),sK62('id$f')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1232])]) ).
tff(f3615,plain,
( spl249_3
<=> 'register$h'('id$f') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_3])]) ).
tff(f5400,plain,
( spl249_346
<=> ! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ( 'register_from_getter_setter$b'(sK61(X0),sK62(X0)) = X0 )
| ~ 'register$h'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_346])]) ).
tff(f5828,plain,
( ( 'id$f' = 'register_from_getter_setter$b'(sK61('id$f'),sK62('id$f')) )
| ~ spl249_3
| ~ spl249_346 ),
inference(resolution,[],[f5401,f3617]) ).
tff(f3617,plain,
( 'register$h'('id$f')
| ~ spl249_3 ),
inference(avatar_component_clause,[],[f3615]) ).
tff(f5401,plain,
( ! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ~ 'register$h'(X0)
| ( 'register_from_getter_setter$b'(sK61(X0),sK62(X0)) = X0 ) )
| ~ spl249_346 ),
inference(avatar_component_clause,[],[f5400]) ).
tff(f17735,plain,
( spl249_1231
| ~ spl249_2
| ~ spl249_345 ),
inference(avatar_split_clause,[],[f5826,f5396,f3610,f17732]) ).
tff(f17732,plain,
( spl249_1231
<=> ( 'id$g' = 'register_from_getter_setter$d'(sK59('id$g'),sK60('id$g')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1231])]) ).
tff(f3610,plain,
( spl249_2
<=> 'register$f'('id$g') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_2])]) ).
tff(f5396,plain,
( spl249_345
<=> ! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ( 'register_from_getter_setter$d'(sK59(X0),sK60(X0)) = X0 )
| ~ 'register$f'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_345])]) ).
tff(f5826,plain,
( ( 'id$g' = 'register_from_getter_setter$d'(sK59('id$g'),sK60('id$g')) )
| ~ spl249_2
| ~ spl249_345 ),
inference(resolution,[],[f5397,f3612]) ).
tff(f3612,plain,
( 'register$f'('id$g')
| ~ spl249_2 ),
inference(avatar_component_clause,[],[f3610]) ).
tff(f5397,plain,
( ! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ~ 'register$f'(X0)
| ( 'register_from_getter_setter$d'(sK59(X0),sK60(X0)) = X0 ) )
| ~ spl249_345 ),
inference(avatar_component_clause,[],[f5396]) ).
tff(f17730,plain,
( spl249_1230
| ~ spl249_107
| ~ spl249_293 ),
inference(avatar_split_clause,[],[f5261,f4975,f4075,f17728]) ).
tff(f17728,plain,
( spl249_1230
<=> ! [X0: 'B_bool_fun$'] : ( tltrue = def_14('case_option$e'(tltrue,X0),'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1230])]) ).
tff(f4075,plain,
( spl249_107
<=> ! [X1: 'B_bool_fun$'] : 'fun_app$a'('case_option$e'(tltrue,X1),'none$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_107])]) ).
tff(f4975,plain,
( spl249_293
<=> ! [X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( tltrue = def_14(X0,X1) )
| ~ 'fun_app$a'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_293])]) ).
tff(f5261,plain,
( ! [X0: 'B_bool_fun$'] : ( tltrue = def_14('case_option$e'(tltrue,X0),'none$a') )
| ~ spl249_107
| ~ spl249_293 ),
inference(resolution,[],[f4976,f4076]) ).
tff(f4076,plain,
( ! [X1: 'B_bool_fun$'] : 'fun_app$a'('case_option$e'(tltrue,X1),'none$a')
| ~ spl249_107 ),
inference(avatar_component_clause,[],[f4075]) ).
tff(f4976,plain,
( ! [X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ~ 'fun_app$a'(X0,X1)
| ( tltrue = def_14(X0,X1) ) )
| ~ spl249_293 ),
inference(avatar_component_clause,[],[f4975]) ).
tff(f17726,plain,
( spl249_1229
| ~ spl249_106
| ~ spl249_293 ),
inference(avatar_split_clause,[],[f5259,f4975,f4071,f17724]) ).
tff(f17724,plain,
( spl249_1229
<=> ! [X0: 'B_option$'] : ( tltrue = def_14('fun_app$e'('uwr$',X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1229])]) ).
tff(f4071,plain,
( spl249_106
<=> ! [X1: 'B_option$'] : 'fun_app$a'('fun_app$e'('uwr$',X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_106])]) ).
tff(f5259,plain,
( ! [X0: 'B_option$'] : ( tltrue = def_14('fun_app$e'('uwr$',X0),X0) )
| ~ spl249_106
| ~ spl249_293 ),
inference(resolution,[],[f4976,f4072]) ).
tff(f4072,plain,
( ! [X1: 'B_option$'] : 'fun_app$a'('fun_app$e'('uwr$',X1),X1)
| ~ spl249_106 ),
inference(avatar_component_clause,[],[f4071]) ).
tff(f17722,plain,
( spl249_1228
| ~ spl249_105
| ~ spl249_293 ),
inference(avatar_split_clause,[],[f5258,f4975,f4067,f17720]) ).
tff(f17720,plain,
( spl249_1228
<=> ! [X0: 'B_option$'] : ( tltrue = def_14('fun_app$e'('uwn$',X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1228])]) ).
tff(f4067,plain,
( spl249_105
<=> ! [X1: 'B_option$'] : 'fun_app$a'('fun_app$e'('uwn$',X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_105])]) ).
tff(f5258,plain,
( ! [X0: 'B_option$'] : ( tltrue = def_14('fun_app$e'('uwn$',X0),X0) )
| ~ spl249_105
| ~ spl249_293 ),
inference(resolution,[],[f4976,f4068]) ).
tff(f4068,plain,
( ! [X1: 'B_option$'] : 'fun_app$a'('fun_app$e'('uwn$',X1),X1)
| ~ spl249_105 ),
inference(avatar_component_clause,[],[f4067]) ).
tff(f17718,plain,
( spl249_1227
| ~ spl249_104
| ~ spl249_291 ),
inference(avatar_split_clause,[],[f5250,f4967,f4063,f17716]) ).
tff(f17716,plain,
( spl249_1227
<=> ! [X0: 'C_bool_fun$'] : ( tltrue = def_10('case_option$f'(tltrue,X0),'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1227])]) ).
tff(f4063,plain,
( spl249_104
<=> ! [X1: 'C_bool_fun$'] : 'fun_app$'('case_option$f'(tltrue,X1),'none$') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_104])]) ).
tff(f4967,plain,
( spl249_291
<=> ! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( tltrue = def_10(X0,X1) )
| ~ 'fun_app$'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_291])]) ).
tff(f5250,plain,
( ! [X0: 'C_bool_fun$'] : ( tltrue = def_10('case_option$f'(tltrue,X0),'none$') )
| ~ spl249_104
| ~ spl249_291 ),
inference(resolution,[],[f4968,f4064]) ).
tff(f4064,plain,
( ! [X1: 'C_bool_fun$'] : 'fun_app$'('case_option$f'(tltrue,X1),'none$')
| ~ spl249_104 ),
inference(avatar_component_clause,[],[f4063]) ).
tff(f4968,plain,
( ! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ~ 'fun_app$'(X0,X1)
| ( tltrue = def_10(X0,X1) ) )
| ~ spl249_291 ),
inference(avatar_component_clause,[],[f4967]) ).
tff(f17714,plain,
( spl249_1226
| ~ spl249_271
| ~ spl249_974 ),
inference(avatar_split_clause,[],[f13598,f11423,f4885,f17712]) ).
tff(f17712,plain,
( spl249_1226
<=> ! [X0: 'B_c_option_fun$'] : ( 'bot$d' = 'collect$'('uul$'('uwg$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1226])]) ).
tff(f11423,plain,
( spl249_974
<=> ! [X0: 'B_c_option_fun$',X1: 'B$'] : ~ 'fun_app$c'('uul$'('uwg$',X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_974])]) ).
tff(f13598,plain,
( ! [X0: 'B_c_option_fun$'] : ( 'bot$d' = 'collect$'('uul$'('uwg$',X0)) )
| ~ spl249_271
| ~ spl249_974 ),
inference(resolution,[],[f11424,f4886]) ).
tff(f11424,plain,
( ! [X0: 'B_c_option_fun$',X1: 'B$'] : ~ 'fun_app$c'('uul$'('uwg$',X0),X1)
| ~ spl249_974 ),
inference(avatar_component_clause,[],[f11423]) ).
tff(f17710,plain,
( spl249_1225
| ~ spl249_103
| ~ spl249_291 ),
inference(avatar_split_clause,[],[f5248,f4967,f4059,f17708]) ).
tff(f17708,plain,
( spl249_1225
<=> ! [X0: 'C_option$'] : ( tltrue = def_10('fun_app$d'('uws$',X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1225])]) ).
tff(f4059,plain,
( spl249_103
<=> ! [X1: 'C_option$'] : 'fun_app$'('fun_app$d'('uws$',X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_103])]) ).
tff(f5248,plain,
( ! [X0: 'C_option$'] : ( tltrue = def_10('fun_app$d'('uws$',X0),X0) )
| ~ spl249_103
| ~ spl249_291 ),
inference(resolution,[],[f4968,f4060]) ).
tff(f4060,plain,
( ! [X1: 'C_option$'] : 'fun_app$'('fun_app$d'('uws$',X1),X1)
| ~ spl249_103 ),
inference(avatar_component_clause,[],[f4059]) ).
tff(f17706,plain,
( spl249_1224
| ~ spl249_102
| ~ spl249_291 ),
inference(avatar_split_clause,[],[f5247,f4967,f4055,f17704]) ).
tff(f17704,plain,
( spl249_1224
<=> ! [X0: 'C_option$'] : ( tltrue = def_10('fun_app$d'('uwo$',X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1224])]) ).
tff(f4055,plain,
( spl249_102
<=> ! [X1: 'C_option$'] : 'fun_app$'('fun_app$d'('uwo$',X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_102])]) ).
tff(f5247,plain,
( ! [X0: 'C_option$'] : ( tltrue = def_10('fun_app$d'('uwo$',X0),X0) )
| ~ spl249_102
| ~ spl249_291 ),
inference(resolution,[],[f4968,f4056]) ).
tff(f4056,plain,
( ! [X1: 'C_option$'] : 'fun_app$'('fun_app$d'('uwo$',X1),X1)
| ~ spl249_102 ),
inference(avatar_component_clause,[],[f4055]) ).
tff(f17702,plain,
( spl249_1223
| ~ spl249_104
| ~ spl249_288 ),
inference(avatar_split_clause,[],[f5239,f4954,f4063,f17700]) ).
tff(f17700,plain,
( spl249_1223
<=> ! [X0: 'C_bool_fun$'] : ( tltrue = def_15('case_option$f'(tltrue,X0),'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1223])]) ).
tff(f4954,plain,
( spl249_288
<=> ! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( tltrue = def_15(X0,X1) )
| ~ 'fun_app$'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_288])]) ).
tff(f5239,plain,
( ! [X0: 'C_bool_fun$'] : ( tltrue = def_15('case_option$f'(tltrue,X0),'none$') )
| ~ spl249_104
| ~ spl249_288 ),
inference(resolution,[],[f4955,f4064]) ).
tff(f4955,plain,
( ! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ~ 'fun_app$'(X0,X1)
| ( tltrue = def_15(X0,X1) ) )
| ~ spl249_288 ),
inference(avatar_component_clause,[],[f4954]) ).
tff(f17698,plain,
( spl249_1222
| ~ spl249_103
| ~ spl249_288 ),
inference(avatar_split_clause,[],[f5237,f4954,f4059,f17696]) ).
tff(f17696,plain,
( spl249_1222
<=> ! [X0: 'C_option$'] : ( tltrue = def_15('fun_app$d'('uws$',X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1222])]) ).
tff(f5237,plain,
( ! [X0: 'C_option$'] : ( tltrue = def_15('fun_app$d'('uws$',X0),X0) )
| ~ spl249_103
| ~ spl249_288 ),
inference(resolution,[],[f4955,f4060]) ).
tff(f17694,plain,
( spl249_1221
| ~ spl249_102
| ~ spl249_288 ),
inference(avatar_split_clause,[],[f5236,f4954,f4055,f17692]) ).
tff(f17692,plain,
( spl249_1221
<=> ! [X0: 'C_option$'] : ( tltrue = def_15('fun_app$d'('uwo$',X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1221])]) ).
tff(f5236,plain,
( ! [X0: 'C_option$'] : ( tltrue = def_15('fun_app$d'('uwo$',X0),X0) )
| ~ spl249_102
| ~ spl249_288 ),
inference(resolution,[],[f4955,f4056]) ).
tff(f17687,plain,
( spl249_1220
| ~ spl249_50
| ~ spl249_227 ),
inference(avatar_split_clause,[],[f4806,f4577,f3830,f17685]) ).
tff(f17685,plain,
( spl249_1220
<=> ! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ~ 'valid_getter_setter$a'(X0,X1)
| 'preregister$c'('register_from_getter_setter$'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1220])]) ).
tff(f3830,plain,
( spl249_50
<=> ! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( 'preregister$c'(X0)
| ~ 'register$'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_50])]) ).
tff(f4577,plain,
( spl249_227
<=> ! [X2: 'A_b_b_fun_fun$',X1: 'B_a_fun$'] :
( 'register$'('register_from_getter_setter$'(X1,X2))
| ~ 'valid_getter_setter$a'(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_227])]) ).
tff(f4806,plain,
( ! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ~ 'valid_getter_setter$a'(X0,X1)
| 'preregister$c'('register_from_getter_setter$'(X0,X1)) )
| ~ spl249_50
| ~ spl249_227 ),
inference(resolution,[],[f4578,f3831]) ).
tff(f3831,plain,
( ! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ~ 'register$'(X0)
| 'preregister$c'(X0) )
| ~ spl249_50 ),
inference(avatar_component_clause,[],[f3830]) ).
tff(f4578,plain,
( ! [X2: 'A_b_b_fun_fun$',X1: 'B_a_fun$'] :
( 'register$'('register_from_getter_setter$'(X1,X2))
| ~ 'valid_getter_setter$a'(X1,X2) )
| ~ spl249_227 ),
inference(avatar_component_clause,[],[f4577]) ).
tff(f17683,plain,
( spl249_1219
| ~ spl249_51
| ~ spl249_226 ),
inference(avatar_split_clause,[],[f4804,f4573,f3834,f17681]) ).
tff(f17681,plain,
( spl249_1219
<=> ! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ~ 'valid_getter_setter$'(X0,X1)
| 'preregister$b'('register_from_getter_setter$a'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1219])]) ).
tff(f3834,plain,
( spl249_51
<=> ! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( 'preregister$b'(X0)
| ~ 'register$a'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_51])]) ).
tff(f4573,plain,
( spl249_226
<=> ! [X2: 'B_c_c_fun_fun$',X1: 'C_b_fun$'] :
( 'register$a'('register_from_getter_setter$a'(X1,X2))
| ~ 'valid_getter_setter$'(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_226])]) ).
tff(f4804,plain,
( ! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ~ 'valid_getter_setter$'(X0,X1)
| 'preregister$b'('register_from_getter_setter$a'(X0,X1)) )
| ~ spl249_51
| ~ spl249_226 ),
inference(resolution,[],[f4574,f3835]) ).
tff(f3835,plain,
( ! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ~ 'register$a'(X0)
| 'preregister$b'(X0) )
| ~ spl249_51 ),
inference(avatar_component_clause,[],[f3834]) ).
tff(f4574,plain,
( ! [X2: 'B_c_c_fun_fun$',X1: 'C_b_fun$'] :
( 'register$a'('register_from_getter_setter$a'(X1,X2))
| ~ 'valid_getter_setter$'(X1,X2) )
| ~ spl249_226 ),
inference(avatar_component_clause,[],[f4573]) ).
tff(f17679,plain,
( spl249_1218
| ~ spl249_49
| ~ spl249_225 ),
inference(avatar_split_clause,[],[f4802,f4569,f3826,f17677]) ).
tff(f17677,plain,
( spl249_1218
<=> ! [X0: 'B_b_fun$',X1: 'B_b_b_fun_fun$'] :
( ~ 'valid_getter_setter$b'(X0,X1)
| 'preregister$'('register_from_getter_setter$b'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1218])]) ).
tff(f3826,plain,
( spl249_49
<=> ! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( 'preregister$'(X0)
| ~ 'register$h'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_49])]) ).
tff(f4569,plain,
( spl249_225
<=> ! [X2: 'B_b_b_fun_fun$',X1: 'B_b_fun$'] :
( 'register$h'('register_from_getter_setter$b'(X1,X2))
| ~ 'valid_getter_setter$b'(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_225])]) ).
tff(f4802,plain,
( ! [X0: 'B_b_fun$',X1: 'B_b_b_fun_fun$'] :
( ~ 'valid_getter_setter$b'(X0,X1)
| 'preregister$'('register_from_getter_setter$b'(X0,X1)) )
| ~ spl249_49
| ~ spl249_225 ),
inference(resolution,[],[f4570,f3827]) ).
tff(f3827,plain,
( ! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ~ 'register$h'(X0)
| 'preregister$'(X0) )
| ~ spl249_49 ),
inference(avatar_component_clause,[],[f3826]) ).
tff(f4570,plain,
( ! [X2: 'B_b_b_fun_fun$',X1: 'B_b_fun$'] :
( 'register$h'('register_from_getter_setter$b'(X1,X2))
| ~ 'valid_getter_setter$b'(X1,X2) )
| ~ spl249_225 ),
inference(avatar_component_clause,[],[f4569]) ).
tff(f17675,plain,
( spl249_1217
| ~ spl249_48
| ~ spl249_224 ),
inference(avatar_split_clause,[],[f4800,f4565,f3822,f17673]) ).
tff(f17673,plain,
( spl249_1217
<=> ! [X0: 'C_c_fun$',X1: 'C_c_c_fun_fun$'] :
( ~ 'valid_getter_setter$d'(X0,X1)
| 'preregister$a'('register_from_getter_setter$d'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1217])]) ).
tff(f3822,plain,
( spl249_48
<=> ! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( 'preregister$a'(X0)
| ~ 'register$f'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_48])]) ).
tff(f4565,plain,
( spl249_224
<=> ! [X2: 'C_c_c_fun_fun$',X1: 'C_c_fun$'] :
( 'register$f'('register_from_getter_setter$d'(X1,X2))
| ~ 'valid_getter_setter$d'(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_224])]) ).
tff(f4800,plain,
( ! [X0: 'C_c_fun$',X1: 'C_c_c_fun_fun$'] :
( ~ 'valid_getter_setter$d'(X0,X1)
| 'preregister$a'('register_from_getter_setter$d'(X0,X1)) )
| ~ spl249_48
| ~ spl249_224 ),
inference(resolution,[],[f4566,f3823]) ).
tff(f3823,plain,
( ! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ~ 'register$f'(X0)
| 'preregister$a'(X0) )
| ~ spl249_48 ),
inference(avatar_component_clause,[],[f3822]) ).
tff(f4566,plain,
( ! [X2: 'C_c_c_fun_fun$',X1: 'C_c_fun$'] :
( 'register$f'('register_from_getter_setter$d'(X1,X2))
| ~ 'valid_getter_setter$d'(X1,X2) )
| ~ spl249_224 ),
inference(avatar_component_clause,[],[f4565]) ).
tff(f17670,plain,
( spl249_1216
| ~ spl249_10
| ~ spl249_140
| ~ spl249_189 ),
inference(avatar_split_clause,[],[f4728,f4425,f4209,f3650,f17667]) ).
tff(f17667,plain,
( spl249_1216
<=> ( 'none$a' = sK109('is_none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1216])]) ).
tff(f3650,plain,
( spl249_10
<=> 'fun_app$a'('is_none$','none$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_10])]) ).
tff(f4209,plain,
( spl249_140
<=> ! [X0: 'B_option$'] :
( ( 'none$a' = X0 )
| ~ 'fun_app$a'('is_none$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_140])]) ).
tff(f4425,plain,
( spl249_189
<=> ! [X0: 'B_option_bool_fun$'] :
( 'fun_app$a'(X0,sK109(X0))
| ~ 'fun_app$a'(X0,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_189])]) ).
tff(f4728,plain,
( ~ 'fun_app$a'('is_none$','none$a')
| ( 'none$a' = sK109('is_none$') )
| ~ spl249_140
| ~ spl249_189 ),
inference(resolution,[],[f4426,f4210]) ).
tff(f4210,plain,
( ! [X0: 'B_option$'] :
( ~ 'fun_app$a'('is_none$',X0)
| ( 'none$a' = X0 ) )
| ~ spl249_140 ),
inference(avatar_component_clause,[],[f4209]) ).
tff(f4426,plain,
( ! [X0: 'B_option_bool_fun$'] :
( 'fun_app$a'(X0,sK109(X0))
| ~ 'fun_app$a'(X0,'none$a') )
| ~ spl249_189 ),
inference(avatar_component_clause,[],[f4425]) ).
tff(f17664,plain,
( spl249_1215
| ~ spl249_9
| ~ spl249_138
| ~ spl249_188 ),
inference(avatar_split_clause,[],[f4726,f4421,f4201,f3645,f17661]) ).
tff(f17661,plain,
( spl249_1215
<=> ( 'none$' = sK107('is_none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1215])]) ).
tff(f3645,plain,
( spl249_9
<=> 'fun_app$'('is_none$a','none$') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_9])]) ).
tff(f4201,plain,
( spl249_138
<=> ! [X0: 'C_option$'] :
( ( 'none$' = X0 )
| ~ 'fun_app$'('is_none$a',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_138])]) ).
tff(f4421,plain,
( spl249_188
<=> ! [X0: 'C_option_bool_fun$'] :
( 'fun_app$'(X0,sK107(X0))
| ~ 'fun_app$'(X0,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_188])]) ).
tff(f4726,plain,
( ~ 'fun_app$'('is_none$a','none$')
| ( 'none$' = sK107('is_none$a') )
| ~ spl249_138
| ~ spl249_188 ),
inference(resolution,[],[f4422,f4202]) ).
tff(f4202,plain,
( ! [X0: 'C_option$'] :
( ~ 'fun_app$'('is_none$a',X0)
| ( 'none$' = X0 ) )
| ~ spl249_138 ),
inference(avatar_component_clause,[],[f4201]) ).
tff(f4422,plain,
( ! [X0: 'C_option_bool_fun$'] :
( 'fun_app$'(X0,sK107(X0))
| ~ 'fun_app$'(X0,'none$') )
| ~ spl249_188 ),
inference(avatar_component_clause,[],[f4421]) ).
tff(f17658,plain,
( spl249_1214
| ~ spl249_8
| ~ spl249_136
| ~ spl249_187 ),
inference(avatar_split_clause,[],[f4724,f4417,f4193,f3640,f17655]) ).
tff(f17655,plain,
( spl249_1214
<=> ( 'none$b' = sK105('is_none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1214])]) ).
tff(f3640,plain,
( spl249_8
<=> 'fun_app$aw'('is_none$b','none$b') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_8])]) ).
tff(f4193,plain,
( spl249_136
<=> ! [X0: 'A_option$'] :
( ( 'none$b' = X0 )
| ~ 'fun_app$aw'('is_none$b',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_136])]) ).
tff(f4417,plain,
( spl249_187
<=> ! [X0: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X0,sK105(X0))
| ~ 'fun_app$aw'(X0,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_187])]) ).
tff(f4724,plain,
( ~ 'fun_app$aw'('is_none$b','none$b')
| ( 'none$b' = sK105('is_none$b') )
| ~ spl249_136
| ~ spl249_187 ),
inference(resolution,[],[f4418,f4194]) ).
tff(f4194,plain,
( ! [X0: 'A_option$'] :
( ~ 'fun_app$aw'('is_none$b',X0)
| ( 'none$b' = X0 ) )
| ~ spl249_136 ),
inference(avatar_component_clause,[],[f4193]) ).
tff(f4418,plain,
( ! [X0: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X0,sK105(X0))
| ~ 'fun_app$aw'(X0,'none$b') )
| ~ spl249_187 ),
inference(avatar_component_clause,[],[f4417]) ).
tff(f17653,plain,
( spl249_1213
| ~ spl249_82
| ~ spl249_172 ),
inference(avatar_split_clause,[],[f4702,f4357,f3970,f17651]) ).
tff(f3970,plain,
( spl249_82
<=> ! [X0: 'B_option_set$'] : ( 'collect$b'('uvk$'(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_82])]) ).
tff(f4357,plain,
( spl249_172
<=> ! [X2: 'B_option$',X0: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X0,X2)
| ( 'bot$a' != 'collect$b'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_172])]) ).
tff(f4702,plain,
( ! [X0: 'B_option_set$',X1: 'B_option$'] :
( ( 'bot$a' != X0 )
| ~ 'fun_app$a'('uvk$'(X0),X1) )
| ~ spl249_82
| ~ spl249_172 ),
inference(superposition,[],[f4358,f3971]) ).
tff(f3971,plain,
( ! [X0: 'B_option_set$'] : ( 'collect$b'('uvk$'(X0)) = X0 )
| ~ spl249_82 ),
inference(avatar_component_clause,[],[f3970]) ).
tff(f4358,plain,
( ! [X2: 'B_option$',X0: 'B_option_bool_fun$'] :
( ( 'bot$a' != 'collect$b'(X0) )
| ~ 'fun_app$a'(X0,X2) )
| ~ spl249_172 ),
inference(avatar_component_clause,[],[f4357]) ).
tff(f17649,plain,
( spl249_1212
| ~ spl249_81
| ~ spl249_171 ),
inference(avatar_split_clause,[],[f4697,f4353,f3966,f17647]) ).
tff(f3966,plain,
( spl249_81
<=> ! [X0: 'C_option_set$'] : ( 'collect$c'('uvl$'(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_81])]) ).
tff(f4353,plain,
( spl249_171
<=> ! [X2: 'C_option$',X0: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X0,X2)
| ( 'bot$b' != 'collect$c'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_171])]) ).
tff(f4697,plain,
( ! [X0: 'C_option_set$',X1: 'C_option$'] :
( ( 'bot$b' != X0 )
| ~ 'fun_app$'('uvl$'(X0),X1) )
| ~ spl249_81
| ~ spl249_171 ),
inference(superposition,[],[f4354,f3967]) ).
tff(f3967,plain,
( ! [X0: 'C_option_set$'] : ( 'collect$c'('uvl$'(X0)) = X0 )
| ~ spl249_81 ),
inference(avatar_component_clause,[],[f3966]) ).
tff(f4354,plain,
( ! [X2: 'C_option$',X0: 'C_option_bool_fun$'] :
( ( 'bot$b' != 'collect$c'(X0) )
| ~ 'fun_app$'(X0,X2) )
| ~ spl249_171 ),
inference(avatar_component_clause,[],[f4353]) ).
tff(f17645,plain,
( spl249_1211
| ~ spl249_83
| ~ spl249_170 ),
inference(avatar_split_clause,[],[f4690,f4349,f3974,f17643]) ).
tff(f3974,plain,
( spl249_83
<=> ! [X0: 'B_set$'] : ( 'collect$'('uvi$'(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_83])]) ).
tff(f4349,plain,
( spl249_170
<=> ! [X2: 'B$',X0: 'B_bool_fun$'] :
( ~ 'fun_app$c'(X0,X2)
| ( 'bot$d' != 'collect$'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_170])]) ).
tff(f4690,plain,
( ! [X0: 'B_set$',X1: 'B$'] :
( ( 'bot$d' != X0 )
| ~ 'fun_app$c'('uvi$'(X0),X1) )
| ~ spl249_83
| ~ spl249_170 ),
inference(superposition,[],[f4350,f3975]) ).
tff(f3975,plain,
( ! [X0: 'B_set$'] : ( 'collect$'('uvi$'(X0)) = X0 )
| ~ spl249_83 ),
inference(avatar_component_clause,[],[f3974]) ).
tff(f4350,plain,
( ! [X2: 'B$',X0: 'B_bool_fun$'] :
( ( 'bot$d' != 'collect$'(X0) )
| ~ 'fun_app$c'(X0,X2) )
| ~ spl249_170 ),
inference(avatar_component_clause,[],[f4349]) ).
tff(f17641,plain,
( spl249_1210
| ~ spl249_84
| ~ spl249_169 ),
inference(avatar_split_clause,[],[f4683,f4345,f3978,f17639]) ).
tff(f3978,plain,
( spl249_84
<=> ! [X0: 'C_set$'] : ( 'collect$a'('uvj$'(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_84])]) ).
tff(f4345,plain,
( spl249_169
<=> ! [X2: 'C$',X0: 'C_bool_fun$'] :
( ~ 'fun_app$b'(X0,X2)
| ( 'bot$c' != 'collect$a'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_169])]) ).
tff(f4683,plain,
( ! [X0: 'C_set$',X1: 'C$'] :
( ( 'bot$c' != X0 )
| ~ 'fun_app$b'('uvj$'(X0),X1) )
| ~ spl249_84
| ~ spl249_169 ),
inference(superposition,[],[f4346,f3979]) ).
tff(f3979,plain,
( ! [X0: 'C_set$'] : ( 'collect$a'('uvj$'(X0)) = X0 )
| ~ spl249_84 ),
inference(avatar_component_clause,[],[f3978]) ).
tff(f4346,plain,
( ! [X2: 'C$',X0: 'C_bool_fun$'] :
( ( 'bot$c' != 'collect$a'(X0) )
| ~ 'fun_app$b'(X0,X2) )
| ~ spl249_169 ),
inference(avatar_component_clause,[],[f4345]) ).
tff(f17637,plain,
( spl249_1209
| ~ spl249_59
| ~ spl249_133 ),
inference(avatar_split_clause,[],[f4242,f4181,f3868,f17635]) ).
tff(f17635,plain,
( spl249_1209
<=> ! [X0: tlbool,X1: 'B_bool_fun$'] :
( sP25('none$a',X1,X0)
| ( tlfalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1209])]) ).
tff(f3868,plain,
( spl249_59
<=> ! [X1: 'B_bool_fun$'] : sP25('none$a',X1,tltrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_59])]) ).
tff(f4181,plain,
( spl249_133
<=> ! [X0: tlbool] :
( ( tlfalse = X0 )
| ( tltrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_133])]) ).
tff(f4242,plain,
( ! [X0: tlbool,X1: 'B_bool_fun$'] :
( sP25('none$a',X1,X0)
| ( tlfalse = X0 ) )
| ~ spl249_59
| ~ spl249_133 ),
inference(superposition,[],[f3869,f4182]) ).
tff(f4182,plain,
( ! [X0: tlbool] :
( ( tltrue = X0 )
| ( tlfalse = X0 ) )
| ~ spl249_133 ),
inference(avatar_component_clause,[],[f4181]) ).
tff(f3869,plain,
( ! [X1: 'B_bool_fun$'] : sP25('none$a',X1,tltrue)
| ~ spl249_59 ),
inference(avatar_component_clause,[],[f3868]) ).
tff(f17514,plain,
( spl249_1208
| ~ spl249_119
| ~ spl249_202
| ~ spl249_928 ),
inference(avatar_split_clause,[],[f12815,f11182,f4477,f4123,f17512]) ).
tff(f17512,plain,
( spl249_1208
<=> ! [X0: 'B_option$',X1: 'C_b_option_fun$'] : ( 'case_option$h'(X0,X1,'none$') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1208])]) ).
tff(f4123,plain,
( spl249_119
<=> ! [X0: 'B_c_fun$'] : ( 'none$' = 'fun_app$an'('map_option$d'(X0),'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_119])]) ).
tff(f4477,plain,
( spl249_202
<=> ! [X0: 'B_option$',X1: 'B_b_option_fun$'] : ( 'fun_app$s'('case_option$'(X0,X1),'none$a') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_202])]) ).
tff(f11182,plain,
( spl249_928
<=> ! [X0: 'B_option$',X3: 'B_option$',X2: 'B_c_fun$',X1: 'C_b_option_fun$'] : ( 'case_option$h'(X0,X1,'fun_app$an'('map_option$d'(X2),X3)) = 'fun_app$s'('case_option$'(X0,'comp$o'(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_928])]) ).
tff(f12815,plain,
( ! [X0: 'B_option$',X1: 'C_b_option_fun$'] : ( 'case_option$h'(X0,X1,'none$') = X0 )
| ~ spl249_119
| ~ spl249_202
| ~ spl249_928 ),
inference(forward_demodulation,[],[f12803,f4124]) ).
tff(f4124,plain,
( ! [X0: 'B_c_fun$'] : ( 'none$' = 'fun_app$an'('map_option$d'(X0),'none$a') )
| ~ spl249_119 ),
inference(avatar_component_clause,[],[f4123]) ).
tff(f12803,plain,
( ! [X2: 'B_c_fun$',X0: 'B_option$',X1: 'C_b_option_fun$'] : ( 'case_option$h'(X0,X1,'fun_app$an'('map_option$d'(X2),'none$a')) = X0 )
| ~ spl249_202
| ~ spl249_928 ),
inference(superposition,[],[f11183,f4478]) ).
tff(f4478,plain,
( ! [X0: 'B_option$',X1: 'B_b_option_fun$'] : ( 'fun_app$s'('case_option$'(X0,X1),'none$a') = X0 )
| ~ spl249_202 ),
inference(avatar_component_clause,[],[f4477]) ).
tff(f11183,plain,
( ! [X2: 'B_c_fun$',X3: 'B_option$',X0: 'B_option$',X1: 'C_b_option_fun$'] : ( 'case_option$h'(X0,X1,'fun_app$an'('map_option$d'(X2),X3)) = 'fun_app$s'('case_option$'(X0,'comp$o'(X1,X2)),X3) )
| ~ spl249_928 ),
inference(avatar_component_clause,[],[f11182]) ).
tff(f17510,plain,
( spl249_1207
| ~ spl249_89
| ~ spl249_824 ),
inference(avatar_split_clause,[],[f11864,f10766,f3999,f17508]) ).
tff(f3999,plain,
( spl249_89
<=> ! [X0: 'C$'] : ( 'fun_app$k'('uvs$',X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_89])]) ).
tff(f10766,plain,
( spl249_824
<=> ! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ( 'fun_app$u'('map_option$c'(X1),X0) = X0 )
| ( sK120(X0,X1) != 'fun_app$k'(X1,sK120(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_824])]) ).
tff(f11864,plain,
( ! [X0: 'C_option$'] : ( 'fun_app$u'('map_option$c'('uvs$'),X0) = X0 )
| ~ spl249_89
| ~ spl249_824 ),
inference(trivial_inequality_removal,[],[f11861]) ).
tff(f11861,plain,
( ! [X0: 'C_option$'] :
( ( sK120(X0,'uvs$') != sK120(X0,'uvs$') )
| ( 'fun_app$u'('map_option$c'('uvs$'),X0) = X0 ) )
| ~ spl249_89
| ~ spl249_824 ),
inference(superposition,[],[f10767,f4000]) ).
tff(f4000,plain,
( ! [X0: 'C$'] : ( 'fun_app$k'('uvs$',X0) = X0 )
| ~ spl249_89 ),
inference(avatar_component_clause,[],[f3999]) ).
tff(f10767,plain,
( ! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ( sK120(X0,X1) != 'fun_app$k'(X1,sK120(X0,X1)) )
| ( 'fun_app$u'('map_option$c'(X1),X0) = X0 ) )
| ~ spl249_824 ),
inference(avatar_component_clause,[],[f10766]) ).
tff(f17506,plain,
( spl249_1206
| ~ spl249_70
| ~ spl249_621 ),
inference(avatar_split_clause,[],[f8361,f7938,f3921,f17504]) ).
tff(f17504,plain,
( spl249_1206
<=> ! [X0: 'A$',X1: 'B$'] : ~ 'fun_app$a'('is_none$','fun_app$f'('uur$'(X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1206])]) ).
tff(f7938,plain,
( spl249_621
<=> ! [X0: 'B$',X1: 'A$'] : ( 'fun_app$f'('uur$'(X0),X1) = 'fun_app$g'('some$','fun_app$h'('fun_app$i'('sF$',X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_621])]) ).
tff(f8361,plain,
( ! [X0: 'A$',X1: 'B$'] : ~ 'fun_app$a'('is_none$','fun_app$f'('uur$'(X1),X0))
| ~ spl249_70
| ~ spl249_621 ),
inference(superposition,[],[f3922,f7939]) ).
tff(f7939,plain,
( ! [X0: 'B$',X1: 'A$'] : ( 'fun_app$f'('uur$'(X0),X1) = 'fun_app$g'('some$','fun_app$h'('fun_app$i'('sF$',X1),X0)) )
| ~ spl249_621 ),
inference(avatar_component_clause,[],[f7938]) ).
tff(f17502,plain,
( spl249_1205
| ~ spl249_67
| ~ spl249_621 ),
inference(avatar_split_clause,[],[f8360,f7938,f3909,f17500]) ).
tff(f17500,plain,
( spl249_1205
<=> ! [X0: 'A$',X1: 'B$'] : ( 'none$a' != 'fun_app$f'('uur$'(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1205])]) ).
tff(f8360,plain,
( ! [X0: 'A$',X1: 'B$'] : ( 'none$a' != 'fun_app$f'('uur$'(X1),X0) )
| ~ spl249_67
| ~ spl249_621 ),
inference(superposition,[],[f3910,f7939]) ).
tff(f17498,plain,
( spl249_1204
| ~ spl249_107
| ~ spl249_582 ),
inference(avatar_split_clause,[],[f7755,f7296,f4075,f17496]) ).
tff(f17496,plain,
( spl249_1204
<=> ! [X0: 'B_bool_fun$'] : ( tltrue = def_16(tltrue,X0,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1204])]) ).
tff(f7296,plain,
( spl249_582
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ( tltrue = def_16(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_582])]) ).
tff(f7755,plain,
( ! [X0: 'B_bool_fun$'] : ( tltrue = def_16(tltrue,X0,'none$a') )
| ~ spl249_107
| ~ spl249_582 ),
inference(resolution,[],[f7297,f4076]) ).
tff(f7297,plain,
( ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ~ 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue = def_16(X0,X1,X2) ) )
| ~ spl249_582 ),
inference(avatar_component_clause,[],[f7296]) ).
tff(f17494,plain,
( spl249_1203
| ~ spl249_107
| ~ spl249_580 ),
inference(avatar_split_clause,[],[f7740,f7288,f4075,f17492]) ).
tff(f17492,plain,
( spl249_1203
<=> ! [X0: 'B_bool_fun$'] : ( tltrue = def_20(tltrue,X0,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1203])]) ).
tff(f7288,plain,
( spl249_580
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ( tltrue = def_20(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_580])]) ).
tff(f7740,plain,
( ! [X0: 'B_bool_fun$'] : ( tltrue = def_20(tltrue,X0,'none$a') )
| ~ spl249_107
| ~ spl249_580 ),
inference(resolution,[],[f7289,f4076]) ).
tff(f7289,plain,
( ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ~ 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue = def_20(X0,X1,X2) ) )
| ~ spl249_580 ),
inference(avatar_component_clause,[],[f7288]) ).
tff(f17490,plain,
( spl249_1202
| ~ spl249_107
| ~ spl249_578 ),
inference(avatar_split_clause,[],[f7725,f7280,f4075,f17488]) ).
tff(f17488,plain,
( spl249_1202
<=> ! [X0: 'B_bool_fun$'] : ( tltrue = def_12(tltrue,X0,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1202])]) ).
tff(f7280,plain,
( spl249_578
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ( tltrue = def_12(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_578])]) ).
tff(f7725,plain,
( ! [X0: 'B_bool_fun$'] : ( tltrue = def_12(tltrue,X0,'none$a') )
| ~ spl249_107
| ~ spl249_578 ),
inference(resolution,[],[f7281,f4076]) ).
tff(f7281,plain,
( ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ~ 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue = def_12(X0,X1,X2) ) )
| ~ spl249_578 ),
inference(avatar_component_clause,[],[f7280]) ).
tff(f17486,plain,
( spl249_1201
| ~ spl249_107
| ~ spl249_575 ),
inference(avatar_split_clause,[],[f7710,f7267,f4075,f17484]) ).
tff(f17484,plain,
( spl249_1201
<=> ! [X0: 'B_bool_fun$'] : ( tltrue = def_6(tltrue,X0,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1201])]) ).
tff(f7267,plain,
( spl249_575
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ( tltrue = def_6(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_575])]) ).
tff(f7710,plain,
( ! [X0: 'B_bool_fun$'] : ( tltrue = def_6(tltrue,X0,'none$a') )
| ~ spl249_107
| ~ spl249_575 ),
inference(resolution,[],[f7268,f4076]) ).
tff(f7268,plain,
( ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ~ 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue = def_6(X0,X1,X2) ) )
| ~ spl249_575 ),
inference(avatar_component_clause,[],[f7267]) ).
tff(f17482,plain,
( spl249_1200
| ~ spl249_107
| ~ spl249_573 ),
inference(avatar_split_clause,[],[f7695,f7259,f4075,f17480]) ).
tff(f17480,plain,
( spl249_1200
<=> ! [X0: 'B_bool_fun$'] : ( tltrue = def_11(tltrue,X0,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1200])]) ).
tff(f7259,plain,
( spl249_573
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ( tltrue = def_11(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_573])]) ).
tff(f7695,plain,
( ! [X0: 'B_bool_fun$'] : ( tltrue = def_11(tltrue,X0,'none$a') )
| ~ spl249_107
| ~ spl249_573 ),
inference(resolution,[],[f7260,f4076]) ).
tff(f7260,plain,
( ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ~ 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue = def_11(X0,X1,X2) ) )
| ~ spl249_573 ),
inference(avatar_component_clause,[],[f7259]) ).
tff(f17478,plain,
( spl249_1199
| ~ spl249_104
| ~ spl249_571 ),
inference(avatar_split_clause,[],[f7680,f7251,f4063,f17476]) ).
tff(f17476,plain,
( spl249_1199
<=> ! [X0: 'C_bool_fun$'] : ( tltrue = def_8(tltrue,X0,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1199])]) ).
tff(f7251,plain,
( spl249_571
<=> ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ( tltrue = def_8(X0,X1,X2) )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_571])]) ).
tff(f7680,plain,
( ! [X0: 'C_bool_fun$'] : ( tltrue = def_8(tltrue,X0,'none$') )
| ~ spl249_104
| ~ spl249_571 ),
inference(resolution,[],[f7252,f4064]) ).
tff(f7252,plain,
( ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ~ 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue = def_8(X0,X1,X2) ) )
| ~ spl249_571 ),
inference(avatar_component_clause,[],[f7251]) ).
tff(f17474,plain,
( spl249_1198
| ~ spl249_104
| ~ spl249_569 ),
inference(avatar_split_clause,[],[f7665,f7243,f4063,f17472]) ).
tff(f17472,plain,
( spl249_1198
<=> ! [X0: 'C_bool_fun$'] : ( tltrue = def_22(tltrue,X0,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1198])]) ).
tff(f7243,plain,
( spl249_569
<=> ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ( tltrue = def_22(X0,X1,X2) )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_569])]) ).
tff(f7665,plain,
( ! [X0: 'C_bool_fun$'] : ( tltrue = def_22(tltrue,X0,'none$') )
| ~ spl249_104
| ~ spl249_569 ),
inference(resolution,[],[f7244,f4064]) ).
tff(f7244,plain,
( ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ~ 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue = def_22(X0,X1,X2) ) )
| ~ spl249_569 ),
inference(avatar_component_clause,[],[f7243]) ).
tff(f17470,plain,
( spl249_1197
| ~ spl249_104
| ~ spl249_567 ),
inference(avatar_split_clause,[],[f7650,f7235,f4063,f17468]) ).
tff(f17468,plain,
( spl249_1197
<=> ! [X0: 'C_bool_fun$'] : ( tltrue = def_13(tltrue,X0,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1197])]) ).
tff(f7235,plain,
( spl249_567
<=> ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ( tltrue = def_13(X0,X1,X2) )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_567])]) ).
tff(f7650,plain,
( ! [X0: 'C_bool_fun$'] : ( tltrue = def_13(tltrue,X0,'none$') )
| ~ spl249_104
| ~ spl249_567 ),
inference(resolution,[],[f7236,f4064]) ).
tff(f7236,plain,
( ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ~ 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue = def_13(X0,X1,X2) ) )
| ~ spl249_567 ),
inference(avatar_component_clause,[],[f7235]) ).
tff(f17466,plain,
( spl249_1196
| ~ spl249_104
| ~ spl249_565 ),
inference(avatar_split_clause,[],[f7635,f7227,f4063,f17464]) ).
tff(f17464,plain,
( spl249_1196
<=> ! [X0: 'C_bool_fun$'] : ( tltrue = def_18(tltrue,X0,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1196])]) ).
tff(f7227,plain,
( spl249_565
<=> ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ( tltrue = def_18(X0,X1,X2) )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_565])]) ).
tff(f7635,plain,
( ! [X0: 'C_bool_fun$'] : ( tltrue = def_18(tltrue,X0,'none$') )
| ~ spl249_104
| ~ spl249_565 ),
inference(resolution,[],[f7228,f4064]) ).
tff(f7228,plain,
( ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ~ 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue = def_18(X0,X1,X2) ) )
| ~ spl249_565 ),
inference(avatar_component_clause,[],[f7227]) ).
tff(f17462,plain,
( spl249_1195
| ~ spl249_70
| ~ spl249_462 ),
inference(avatar_split_clause,[],[f6715,f6393,f3921,f17460]) ).
tff(f17460,plain,
( spl249_1195
<=> ! [X0: 'B_b_fun$',X1: 'B$'] : ~ 'fun_app$a'('is_none$','fun_app$g'('uve$'(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1195])]) ).
tff(f6393,plain,
( spl249_462
<=> ! [X0: 'B_b_fun$',X1: 'B$'] : ( 'fun_app$g'('uve$'(X0),X1) = 'fun_app$g'('some$','fun_app$h'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_462])]) ).
tff(f6715,plain,
( ! [X0: 'B_b_fun$',X1: 'B$'] : ~ 'fun_app$a'('is_none$','fun_app$g'('uve$'(X0),X1))
| ~ spl249_70
| ~ spl249_462 ),
inference(superposition,[],[f3922,f6394]) ).
tff(f6394,plain,
( ! [X0: 'B_b_fun$',X1: 'B$'] : ( 'fun_app$g'('uve$'(X0),X1) = 'fun_app$g'('some$','fun_app$h'(X0,X1)) )
| ~ spl249_462 ),
inference(avatar_component_clause,[],[f6393]) ).
tff(f17458,plain,
( spl249_1194
| ~ spl249_67
| ~ spl249_462 ),
inference(avatar_split_clause,[],[f6714,f6393,f3909,f17456]) ).
tff(f17456,plain,
( spl249_1194
<=> ! [X0: 'B_b_fun$',X1: 'B$'] : ( 'fun_app$g'('uve$'(X0),X1) != 'none$a' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1194])]) ).
tff(f6714,plain,
( ! [X0: 'B_b_fun$',X1: 'B$'] : ( 'fun_app$g'('uve$'(X0),X1) != 'none$a' )
| ~ spl249_67
| ~ spl249_462 ),
inference(superposition,[],[f3910,f6394]) ).
tff(f17454,plain,
( spl249_1193
| ~ spl249_69
| ~ spl249_461 ),
inference(avatar_split_clause,[],[f6705,f6389,f3917,f17452]) ).
tff(f17452,plain,
( spl249_1193
<=> ! [X0: 'C_c_fun$',X1: 'C$'] : ~ 'fun_app$'('is_none$a','fun_app$j'('uvf$'(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1193])]) ).
tff(f3917,plain,
( spl249_69
<=> ! [X0: 'C$'] : ~ 'fun_app$'('is_none$a','fun_app$j'('some$a',X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_69])]) ).
tff(f6389,plain,
( spl249_461
<=> ! [X0: 'C_c_fun$',X1: 'C$'] : ( 'fun_app$j'('uvf$'(X0),X1) = 'fun_app$j'('some$a','fun_app$k'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_461])]) ).
tff(f6705,plain,
( ! [X0: 'C_c_fun$',X1: 'C$'] : ~ 'fun_app$'('is_none$a','fun_app$j'('uvf$'(X0),X1))
| ~ spl249_69
| ~ spl249_461 ),
inference(superposition,[],[f3918,f6390]) ).
tff(f6390,plain,
( ! [X0: 'C_c_fun$',X1: 'C$'] : ( 'fun_app$j'('uvf$'(X0),X1) = 'fun_app$j'('some$a','fun_app$k'(X0,X1)) )
| ~ spl249_461 ),
inference(avatar_component_clause,[],[f6389]) ).
tff(f3918,plain,
( ! [X0: 'C$'] : ~ 'fun_app$'('is_none$a','fun_app$j'('some$a',X0))
| ~ spl249_69 ),
inference(avatar_component_clause,[],[f3917]) ).
tff(f17450,plain,
( spl249_1192
| ~ spl249_66
| ~ spl249_461 ),
inference(avatar_split_clause,[],[f6704,f6389,f3905,f17448]) ).
tff(f17448,plain,
( spl249_1192
<=> ! [X0: 'C_c_fun$',X1: 'C$'] : ( 'fun_app$j'('uvf$'(X0),X1) != 'none$' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1192])]) ).
tff(f3905,plain,
( spl249_66
<=> ! [X0: 'C$'] : ( 'none$' != 'fun_app$j'('some$a',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_66])]) ).
tff(f6704,plain,
( ! [X0: 'C_c_fun$',X1: 'C$'] : ( 'fun_app$j'('uvf$'(X0),X1) != 'none$' )
| ~ spl249_66
| ~ spl249_461 ),
inference(superposition,[],[f3906,f6390]) ).
tff(f3906,plain,
( ! [X0: 'C$'] : ( 'none$' != 'fun_app$j'('some$a',X0) )
| ~ spl249_66 ),
inference(avatar_component_clause,[],[f3905]) ).
tff(f17446,plain,
( spl249_1191
| ~ spl249_65
| ~ spl249_460 ),
inference(avatar_split_clause,[],[f6701,f6385,f3901,f17444]) ).
tff(f17444,plain,
( spl249_1191
<=> ! [X0: 'A_a_fun$',X1: 'A$'] : ( 'fun_app$q'('uvd$'(X0),X1) != 'none$b' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1191])]) ).
tff(f6385,plain,
( spl249_460
<=> ! [X0: 'A_a_fun$',X1: 'A$'] : ( 'fun_app$q'('uvd$'(X0),X1) = 'fun_app$q'('some$b','fun_app$r'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_460])]) ).
tff(f6701,plain,
( ! [X0: 'A_a_fun$',X1: 'A$'] : ( 'fun_app$q'('uvd$'(X0),X1) != 'none$b' )
| ~ spl249_65
| ~ spl249_460 ),
inference(superposition,[],[f3902,f6386]) ).
tff(f6386,plain,
( ! [X0: 'A_a_fun$',X1: 'A$'] : ( 'fun_app$q'('uvd$'(X0),X1) = 'fun_app$q'('some$b','fun_app$r'(X0,X1)) )
| ~ spl249_460 ),
inference(avatar_component_clause,[],[f6385]) ).
tff(f17442,plain,
( spl249_1190
| ~ spl249_68
| ~ spl249_460 ),
inference(avatar_split_clause,[],[f6700,f6385,f3913,f17440]) ).
tff(f17440,plain,
( spl249_1190
<=> ! [X0: 'A_a_fun$',X1: 'A$'] : ~ 'fun_app$aw'('is_none$b','fun_app$q'('uvd$'(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1190])]) ).
tff(f6700,plain,
( ! [X0: 'A_a_fun$',X1: 'A$'] : ~ 'fun_app$aw'('is_none$b','fun_app$q'('uvd$'(X0),X1))
| ~ spl249_68
| ~ spl249_460 ),
inference(superposition,[],[f3914,f6386]) ).
tff(f17425,plain,
spl249_1189,
inference(avatar_split_clause,[],[f3098,f17423]) ).
tff(f17423,plain,
( spl249_1189
<=> ! [X0: 'B_b_b_fun_fun$',X3: 'B_option$',X2: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$s'('combine_options$b'(X0,X1),'fun_app$s'('combine_options$b'(X0,X2),X3)) = 'fun_app$s'('combine_options$b'(X0,X2),'fun_app$s'('combine_options$b'(X0,X1),X3)) )
| ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,sK228(X0)),sK229(X0))),sK230(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK228(X0)),'fun_app$h'('fun_app$ai'(X0,sK229(X0)),sK230(X0))) )
| ( 'fun_app$h'('fun_app$ai'(X0,sK231(X0)),sK232(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK232(X0)),sK231(X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1189])]) ).
tff(f3098,plain,
! [X2: 'B_option$',X3: 'B_option$',X0: 'B_b_b_fun_fun$',X1: 'B_option$'] :
( ( 'fun_app$s'('combine_options$b'(X0,X1),'fun_app$s'('combine_options$b'(X0,X2),X3)) = 'fun_app$s'('combine_options$b'(X0,X2),'fun_app$s'('combine_options$b'(X0,X1),X3)) )
| ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,sK228(X0)),sK229(X0))),sK230(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK228(X0)),'fun_app$h'('fun_app$ai'(X0,sK229(X0)),sK230(X0))) )
| ( 'fun_app$h'('fun_app$ai'(X0,sK231(X0)),sK232(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK232(X0)),sK231(X0)) ) ),
inference(cnf_transformation,[],[f1846]) ).
tff(f1846,plain,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$',X2: 'B_option$',X3: 'B_option$'] :
( ( 'fun_app$s'('combine_options$b'(X0,X1),'fun_app$s'('combine_options$b'(X0,X2),X3)) = 'fun_app$s'('combine_options$b'(X0,X2),'fun_app$s'('combine_options$b'(X0,X1),X3)) )
| ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,sK228(X0)),sK229(X0))),sK230(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK228(X0)),'fun_app$h'('fun_app$ai'(X0,sK229(X0)),sK230(X0))) )
| ( 'fun_app$h'('fun_app$ai'(X0,sK231(X0)),sK232(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK232(X0)),sK231(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK228,sK229,sK230,sK231,sK232])],[f1070,f1845,f1844]) ).
tff(f1844,plain,
! [X0: 'B_b_b_fun_fun$'] :
( ? [X4: 'B$',X5: 'B$',X6: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,X4),X5)),X6) != 'fun_app$h'('fun_app$ai'(X0,X4),'fun_app$h'('fun_app$ai'(X0,X5),X6)) )
=> ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,sK228(X0)),sK229(X0))),sK230(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK228(X0)),'fun_app$h'('fun_app$ai'(X0,sK229(X0)),sK230(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f1845,plain,
! [X0: 'B_b_b_fun_fun$'] :
( ? [X7: 'B$',X8: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,X7),X8) != 'fun_app$h'('fun_app$ai'(X0,X8),X7) )
=> ( 'fun_app$h'('fun_app$ai'(X0,sK231(X0)),sK232(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK232(X0)),sK231(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1070,plain,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$',X2: 'B_option$',X3: 'B_option$'] :
( ( 'fun_app$s'('combine_options$b'(X0,X1),'fun_app$s'('combine_options$b'(X0,X2),X3)) = 'fun_app$s'('combine_options$b'(X0,X2),'fun_app$s'('combine_options$b'(X0,X1),X3)) )
| ? [X4: 'B$',X5: 'B$',X6: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,X4),X5)),X6) != 'fun_app$h'('fun_app$ai'(X0,X4),'fun_app$h'('fun_app$ai'(X0,X5),X6)) )
| ? [X7: 'B$',X8: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,X7),X8) != 'fun_app$h'('fun_app$ai'(X0,X8),X7) ) ),
inference(flattening,[],[f1069]) ).
tff(f1069,plain,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$',X2: 'B_option$',X3: 'B_option$'] :
( ( 'fun_app$s'('combine_options$b'(X0,X1),'fun_app$s'('combine_options$b'(X0,X2),X3)) = 'fun_app$s'('combine_options$b'(X0,X2),'fun_app$s'('combine_options$b'(X0,X1),X3)) )
| ? [X4: 'B$',X5: 'B$',X6: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,X4),X5)),X6) != 'fun_app$h'('fun_app$ai'(X0,X4),'fun_app$h'('fun_app$ai'(X0,X5),X6)) )
| ? [X7: 'B$',X8: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,X7),X8) != 'fun_app$h'('fun_app$ai'(X0,X8),X7) ) ),
inference(ennf_transformation,[],[f848]) ).
tff(f848,plain,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$',X2: 'B_option$',X3: 'B_option$'] :
( ( ! [X4: 'B$',X5: 'B$',X6: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,X4),X5)),X6) = 'fun_app$h'('fun_app$ai'(X0,X4),'fun_app$h'('fun_app$ai'(X0,X5),X6)) )
& ! [X7: 'B$',X8: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,X7),X8) = 'fun_app$h'('fun_app$ai'(X0,X8),X7) ) )
=> ( 'fun_app$s'('combine_options$b'(X0,X1),'fun_app$s'('combine_options$b'(X0,X2),X3)) = 'fun_app$s'('combine_options$b'(X0,X2),'fun_app$s'('combine_options$b'(X0,X1),X3)) ) ),
inference(rectify,[],[f258]) ).
tff(f258,axiom,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$',X2: 'B_option$',X3: 'B_option$'] :
( ( ! [X4: 'B$',X5: 'B$',X6: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,X4),X5)),X6) = 'fun_app$h'('fun_app$ai'(X0,X4),'fun_app$h'('fun_app$ai'(X0,X5),X6)) )
& ! [X4: 'B$',X5: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,X4),X5) = 'fun_app$h'('fun_app$ai'(X0,X5),X4) ) )
=> ( 'fun_app$s'('combine_options$b'(X0,X1),'fun_app$s'('combine_options$b'(X0,X2),X3)) = 'fun_app$s'('combine_options$b'(X0,X2),'fun_app$s'('combine_options$b'(X0,X1),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom256) ).
tff(f17421,plain,
spl249_1188,
inference(avatar_split_clause,[],[f3097,f17419]) ).
tff(f17419,plain,
( spl249_1188
<=> ! [X0: 'C_c_c_fun_fun$',X3: 'C_option$',X2: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$u'('combine_options$a'(X0,X1),'fun_app$u'('combine_options$a'(X0,X2),X3)) = 'fun_app$u'('combine_options$a'(X0,X2),'fun_app$u'('combine_options$a'(X0,X1),X3)) )
| ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,sK223(X0)),sK224(X0))),sK225(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK223(X0)),'fun_app$k'('fun_app$ah'(X0,sK224(X0)),sK225(X0))) )
| ( 'fun_app$k'('fun_app$ah'(X0,sK226(X0)),sK227(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK227(X0)),sK226(X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1188])]) ).
tff(f3097,plain,
! [X2: 'C_option$',X3: 'C_option$',X0: 'C_c_c_fun_fun$',X1: 'C_option$'] :
( ( 'fun_app$u'('combine_options$a'(X0,X1),'fun_app$u'('combine_options$a'(X0,X2),X3)) = 'fun_app$u'('combine_options$a'(X0,X2),'fun_app$u'('combine_options$a'(X0,X1),X3)) )
| ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,sK223(X0)),sK224(X0))),sK225(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK223(X0)),'fun_app$k'('fun_app$ah'(X0,sK224(X0)),sK225(X0))) )
| ( 'fun_app$k'('fun_app$ah'(X0,sK226(X0)),sK227(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK227(X0)),sK226(X0)) ) ),
inference(cnf_transformation,[],[f1843]) ).
tff(f1843,plain,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$',X2: 'C_option$',X3: 'C_option$'] :
( ( 'fun_app$u'('combine_options$a'(X0,X1),'fun_app$u'('combine_options$a'(X0,X2),X3)) = 'fun_app$u'('combine_options$a'(X0,X2),'fun_app$u'('combine_options$a'(X0,X1),X3)) )
| ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,sK223(X0)),sK224(X0))),sK225(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK223(X0)),'fun_app$k'('fun_app$ah'(X0,sK224(X0)),sK225(X0))) )
| ( 'fun_app$k'('fun_app$ah'(X0,sK226(X0)),sK227(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK227(X0)),sK226(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK223,sK224,sK225,sK226,sK227])],[f1068,f1842,f1841]) ).
tff(f1841,plain,
! [X0: 'C_c_c_fun_fun$'] :
( ? [X4: 'C$',X5: 'C$',X6: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,X4),X5)),X6) != 'fun_app$k'('fun_app$ah'(X0,X4),'fun_app$k'('fun_app$ah'(X0,X5),X6)) )
=> ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,sK223(X0)),sK224(X0))),sK225(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK223(X0)),'fun_app$k'('fun_app$ah'(X0,sK224(X0)),sK225(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f1842,plain,
! [X0: 'C_c_c_fun_fun$'] :
( ? [X7: 'C$',X8: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,X7),X8) != 'fun_app$k'('fun_app$ah'(X0,X8),X7) )
=> ( 'fun_app$k'('fun_app$ah'(X0,sK226(X0)),sK227(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK227(X0)),sK226(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1068,plain,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$',X2: 'C_option$',X3: 'C_option$'] :
( ( 'fun_app$u'('combine_options$a'(X0,X1),'fun_app$u'('combine_options$a'(X0,X2),X3)) = 'fun_app$u'('combine_options$a'(X0,X2),'fun_app$u'('combine_options$a'(X0,X1),X3)) )
| ? [X4: 'C$',X5: 'C$',X6: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,X4),X5)),X6) != 'fun_app$k'('fun_app$ah'(X0,X4),'fun_app$k'('fun_app$ah'(X0,X5),X6)) )
| ? [X7: 'C$',X8: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,X7),X8) != 'fun_app$k'('fun_app$ah'(X0,X8),X7) ) ),
inference(flattening,[],[f1067]) ).
tff(f1067,plain,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$',X2: 'C_option$',X3: 'C_option$'] :
( ( 'fun_app$u'('combine_options$a'(X0,X1),'fun_app$u'('combine_options$a'(X0,X2),X3)) = 'fun_app$u'('combine_options$a'(X0,X2),'fun_app$u'('combine_options$a'(X0,X1),X3)) )
| ? [X4: 'C$',X5: 'C$',X6: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,X4),X5)),X6) != 'fun_app$k'('fun_app$ah'(X0,X4),'fun_app$k'('fun_app$ah'(X0,X5),X6)) )
| ? [X7: 'C$',X8: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,X7),X8) != 'fun_app$k'('fun_app$ah'(X0,X8),X7) ) ),
inference(ennf_transformation,[],[f847]) ).
tff(f847,plain,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$',X2: 'C_option$',X3: 'C_option$'] :
( ( ! [X4: 'C$',X5: 'C$',X6: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,X4),X5)),X6) = 'fun_app$k'('fun_app$ah'(X0,X4),'fun_app$k'('fun_app$ah'(X0,X5),X6)) )
& ! [X7: 'C$',X8: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,X7),X8) = 'fun_app$k'('fun_app$ah'(X0,X8),X7) ) )
=> ( 'fun_app$u'('combine_options$a'(X0,X1),'fun_app$u'('combine_options$a'(X0,X2),X3)) = 'fun_app$u'('combine_options$a'(X0,X2),'fun_app$u'('combine_options$a'(X0,X1),X3)) ) ),
inference(rectify,[],[f259]) ).
tff(f259,axiom,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$',X2: 'C_option$',X3: 'C_option$'] :
( ( ! [X4: 'C$',X5: 'C$',X6: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,X4),X5)),X6) = 'fun_app$k'('fun_app$ah'(X0,X4),'fun_app$k'('fun_app$ah'(X0,X5),X6)) )
& ! [X4: 'C$',X5: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,X4),X5) = 'fun_app$k'('fun_app$ah'(X0,X5),X4) ) )
=> ( 'fun_app$u'('combine_options$a'(X0,X1),'fun_app$u'('combine_options$a'(X0,X2),X3)) = 'fun_app$u'('combine_options$a'(X0,X2),'fun_app$u'('combine_options$a'(X0,X1),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom257) ).
tff(f17417,plain,
( spl249_1187
| ~ spl249_70
| ~ spl249_455 ),
inference(avatar_split_clause,[],[f6667,f6365,f3921,f17415]) ).
tff(f17415,plain,
( spl249_1187
<=> ! [X0: 'A_b_fun$',X1: 'A$'] : ~ 'fun_app$a'('is_none$','fun_app$f'('uvh$'(X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1187])]) ).
tff(f6365,plain,
( spl249_455
<=> ! [X0: 'A_b_fun$',X1: 'A$'] : ( 'fun_app$f'('uvh$'(X0),X1) = 'fun_app$g'('some$','fun_app$p'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_455])]) ).
tff(f6667,plain,
( ! [X0: 'A_b_fun$',X1: 'A$'] : ~ 'fun_app$a'('is_none$','fun_app$f'('uvh$'(X0),X1))
| ~ spl249_70
| ~ spl249_455 ),
inference(superposition,[],[f3922,f6366]) ).
tff(f6366,plain,
( ! [X0: 'A_b_fun$',X1: 'A$'] : ( 'fun_app$f'('uvh$'(X0),X1) = 'fun_app$g'('some$','fun_app$p'(X0,X1)) )
| ~ spl249_455 ),
inference(avatar_component_clause,[],[f6365]) ).
tff(f17413,plain,
spl249_1186,
inference(avatar_split_clause,[],[f2349,f17411]) ).
tff(f17411,plain,
( spl249_1186
<=> ! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( 'valid_getter_setter$a'(X0,X1)
| ( 'fun_app$h'('fun_app$i'(X1,sK128(X1)),'fun_app$h'('fun_app$i'(X1,sK129(X1)),sK130(X1))) != 'fun_app$h'('fun_app$i'(X1,sK128(X1)),sK130(X1)) )
| ( sK131(X0,X1) != 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,sK131(X0,X1)),sK132(X0,X1))) )
| ( sK133(X0,X1) != 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,sK133(X0,X1))),sK133(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1186])]) ).
tff(f2349,plain,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( 'valid_getter_setter$a'(X0,X1)
| ( 'fun_app$h'('fun_app$i'(X1,sK128(X1)),'fun_app$h'('fun_app$i'(X1,sK129(X1)),sK130(X1))) != 'fun_app$h'('fun_app$i'(X1,sK128(X1)),sK130(X1)) )
| ( sK131(X0,X1) != 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,sK131(X0,X1)),sK132(X0,X1))) )
| ( sK133(X0,X1) != 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,sK133(X0,X1))),sK133(X0,X1)) ) ),
inference(cnf_transformation,[],[f1427]) ).
tff(f1427,plain,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ( 'valid_getter_setter$a'(X0,X1)
| ( 'fun_app$h'('fun_app$i'(X1,sK128(X1)),'fun_app$h'('fun_app$i'(X1,sK129(X1)),sK130(X1))) != 'fun_app$h'('fun_app$i'(X1,sK128(X1)),sK130(X1)) )
| ( sK131(X0,X1) != 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,sK131(X0,X1)),sK132(X0,X1))) )
| ( sK133(X0,X1) != 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,sK133(X0,X1))),sK133(X0,X1)) ) )
& ( ( ! [X8: 'A$',X9: 'A$',X10: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,X8),'fun_app$h'('fun_app$i'(X1,X9),X10)) = 'fun_app$h'('fun_app$i'(X1,X8),X10) )
& ! [X11: 'A$',X12: 'B$'] : ( 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,X11),X12)) = X11 )
& ! [X13: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,X13)),X13) = X13 ) )
| ~ 'valid_getter_setter$a'(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK128,sK129,sK130,sK131,sK132,sK133])],[f1423,f1426,f1425,f1424]) ).
tff(f1424,plain,
! [X1: 'A_b_b_fun_fun$'] :
( ? [X2: 'A$',X3: 'A$',X4: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,X2),'fun_app$h'('fun_app$i'(X1,X3),X4)) != 'fun_app$h'('fun_app$i'(X1,X2),X4) )
=> ( 'fun_app$h'('fun_app$i'(X1,sK128(X1)),'fun_app$h'('fun_app$i'(X1,sK129(X1)),sK130(X1))) != 'fun_app$h'('fun_app$i'(X1,sK128(X1)),sK130(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1425,plain,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ? [X5: 'A$',X6: 'B$'] : ( 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,X5),X6)) != X5 )
=> ( sK131(X0,X1) != 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,sK131(X0,X1)),sK132(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f1426,plain,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ? [X7: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,X7)),X7) != X7 )
=> ( sK133(X0,X1) != 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,sK133(X0,X1))),sK133(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1423,plain,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ( 'valid_getter_setter$a'(X0,X1)
| ? [X2: 'A$',X3: 'A$',X4: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,X2),'fun_app$h'('fun_app$i'(X1,X3),X4)) != 'fun_app$h'('fun_app$i'(X1,X2),X4) )
| ? [X5: 'A$',X6: 'B$'] : ( 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,X5),X6)) != X5 )
| ? [X7: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,X7)),X7) != X7 ) )
& ( ( ! [X8: 'A$',X9: 'A$',X10: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,X8),'fun_app$h'('fun_app$i'(X1,X9),X10)) = 'fun_app$h'('fun_app$i'(X1,X8),X10) )
& ! [X11: 'A$',X12: 'B$'] : ( 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,X11),X12)) = X11 )
& ! [X13: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,X13)),X13) = X13 ) )
| ~ 'valid_getter_setter$a'(X0,X1) ) ),
inference(rectify,[],[f1422]) ).
tff(f1422,plain,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ( 'valid_getter_setter$a'(X0,X1)
| ? [X2: 'A$',X3: 'A$',X4: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,X2),'fun_app$h'('fun_app$i'(X1,X3),X4)) != 'fun_app$h'('fun_app$i'(X1,X2),X4) )
| ? [X5: 'A$',X6: 'B$'] : ( 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,X5),X6)) != X5 )
| ? [X7: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,X7)),X7) != X7 ) )
& ( ( ! [X2: 'A$',X3: 'A$',X4: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,X2),'fun_app$h'('fun_app$i'(X1,X3),X4)) = 'fun_app$h'('fun_app$i'(X1,X2),X4) )
& ! [X5: 'A$',X6: 'B$'] : ( 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,X5),X6)) = X5 )
& ! [X7: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,X7)),X7) = X7 ) )
| ~ 'valid_getter_setter$a'(X0,X1) ) ),
inference(flattening,[],[f1421]) ).
tff(f1421,plain,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ( 'valid_getter_setter$a'(X0,X1)
| ? [X2: 'A$',X3: 'A$',X4: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,X2),'fun_app$h'('fun_app$i'(X1,X3),X4)) != 'fun_app$h'('fun_app$i'(X1,X2),X4) )
| ? [X5: 'A$',X6: 'B$'] : ( 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,X5),X6)) != X5 )
| ? [X7: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,X7)),X7) != X7 ) )
& ( ( ! [X2: 'A$',X3: 'A$',X4: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,X2),'fun_app$h'('fun_app$i'(X1,X3),X4)) = 'fun_app$h'('fun_app$i'(X1,X2),X4) )
& ! [X5: 'A$',X6: 'B$'] : ( 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,X5),X6)) = X5 )
& ! [X7: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,X7)),X7) = X7 ) )
| ~ 'valid_getter_setter$a'(X0,X1) ) ),
inference(nnf_transformation,[],[f821]) ).
tff(f821,plain,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( 'valid_getter_setter$a'(X0,X1)
<=> ( ! [X2: 'A$',X3: 'A$',X4: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,X2),'fun_app$h'('fun_app$i'(X1,X3),X4)) = 'fun_app$h'('fun_app$i'(X1,X2),X4) )
& ! [X5: 'A$',X6: 'B$'] : ( 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,X5),X6)) = X5 )
& ! [X7: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,X7)),X7) = X7 ) ) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( 'valid_getter_setter$a'(X0,X1)
<=> ( ! [X2: 'A$',X3: 'A$',X4: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,X2),'fun_app$h'('fun_app$i'(X1,X3),X4)) = 'fun_app$h'('fun_app$i'(X1,X2),X4) )
& ! [X2: 'A$',X3: 'B$'] : ( 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,X2),X3)) = X2 )
& ! [X2: 'B$'] : ( 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,X2)),X2) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom77) ).
tff(f17409,plain,
spl249_1185,
inference(avatar_split_clause,[],[f2345,f17407]) ).
tff(f17407,plain,
( spl249_1185
<=> ! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( 'valid_getter_setter$'(X0,X1)
| ( 'fun_app$k'('fun_app$y'(X1,sK122(X1)),'fun_app$k'('fun_app$y'(X1,sK123(X1)),sK124(X1))) != 'fun_app$k'('fun_app$y'(X1,sK122(X1)),sK124(X1)) )
| ( sK125(X0,X1) != 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,sK125(X0,X1)),sK126(X0,X1))) )
| ( sK127(X0,X1) != 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,sK127(X0,X1))),sK127(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1185])]) ).
tff(f2345,plain,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( 'valid_getter_setter$'(X0,X1)
| ( 'fun_app$k'('fun_app$y'(X1,sK122(X1)),'fun_app$k'('fun_app$y'(X1,sK123(X1)),sK124(X1))) != 'fun_app$k'('fun_app$y'(X1,sK122(X1)),sK124(X1)) )
| ( sK125(X0,X1) != 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,sK125(X0,X1)),sK126(X0,X1))) )
| ( sK127(X0,X1) != 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,sK127(X0,X1))),sK127(X0,X1)) ) ),
inference(cnf_transformation,[],[f1420]) ).
tff(f1420,plain,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ( 'valid_getter_setter$'(X0,X1)
| ( 'fun_app$k'('fun_app$y'(X1,sK122(X1)),'fun_app$k'('fun_app$y'(X1,sK123(X1)),sK124(X1))) != 'fun_app$k'('fun_app$y'(X1,sK122(X1)),sK124(X1)) )
| ( sK125(X0,X1) != 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,sK125(X0,X1)),sK126(X0,X1))) )
| ( sK127(X0,X1) != 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,sK127(X0,X1))),sK127(X0,X1)) ) )
& ( ( ! [X8: 'B$',X9: 'B$',X10: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,X8),'fun_app$k'('fun_app$y'(X1,X9),X10)) = 'fun_app$k'('fun_app$y'(X1,X8),X10) )
& ! [X11: 'B$',X12: 'C$'] : ( 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,X11),X12)) = X11 )
& ! [X13: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,X13)),X13) = X13 ) )
| ~ 'valid_getter_setter$'(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK122,sK123,sK124,sK125,sK126,sK127])],[f1416,f1419,f1418,f1417]) ).
tff(f1417,plain,
! [X1: 'B_c_c_fun_fun$'] :
( ? [X2: 'B$',X3: 'B$',X4: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,X2),'fun_app$k'('fun_app$y'(X1,X3),X4)) != 'fun_app$k'('fun_app$y'(X1,X2),X4) )
=> ( 'fun_app$k'('fun_app$y'(X1,sK122(X1)),'fun_app$k'('fun_app$y'(X1,sK123(X1)),sK124(X1))) != 'fun_app$k'('fun_app$y'(X1,sK122(X1)),sK124(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1418,plain,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ? [X5: 'B$',X6: 'C$'] : ( 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,X5),X6)) != X5 )
=> ( sK125(X0,X1) != 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,sK125(X0,X1)),sK126(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f1419,plain,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ? [X7: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,X7)),X7) != X7 )
=> ( sK127(X0,X1) != 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,sK127(X0,X1))),sK127(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1416,plain,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ( 'valid_getter_setter$'(X0,X1)
| ? [X2: 'B$',X3: 'B$',X4: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,X2),'fun_app$k'('fun_app$y'(X1,X3),X4)) != 'fun_app$k'('fun_app$y'(X1,X2),X4) )
| ? [X5: 'B$',X6: 'C$'] : ( 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,X5),X6)) != X5 )
| ? [X7: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,X7)),X7) != X7 ) )
& ( ( ! [X8: 'B$',X9: 'B$',X10: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,X8),'fun_app$k'('fun_app$y'(X1,X9),X10)) = 'fun_app$k'('fun_app$y'(X1,X8),X10) )
& ! [X11: 'B$',X12: 'C$'] : ( 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,X11),X12)) = X11 )
& ! [X13: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,X13)),X13) = X13 ) )
| ~ 'valid_getter_setter$'(X0,X1) ) ),
inference(rectify,[],[f1415]) ).
tff(f1415,plain,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ( 'valid_getter_setter$'(X0,X1)
| ? [X2: 'B$',X3: 'B$',X4: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,X2),'fun_app$k'('fun_app$y'(X1,X3),X4)) != 'fun_app$k'('fun_app$y'(X1,X2),X4) )
| ? [X5: 'B$',X6: 'C$'] : ( 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,X5),X6)) != X5 )
| ? [X7: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,X7)),X7) != X7 ) )
& ( ( ! [X2: 'B$',X3: 'B$',X4: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,X2),'fun_app$k'('fun_app$y'(X1,X3),X4)) = 'fun_app$k'('fun_app$y'(X1,X2),X4) )
& ! [X5: 'B$',X6: 'C$'] : ( 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,X5),X6)) = X5 )
& ! [X7: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,X7)),X7) = X7 ) )
| ~ 'valid_getter_setter$'(X0,X1) ) ),
inference(flattening,[],[f1414]) ).
tff(f1414,plain,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ( 'valid_getter_setter$'(X0,X1)
| ? [X2: 'B$',X3: 'B$',X4: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,X2),'fun_app$k'('fun_app$y'(X1,X3),X4)) != 'fun_app$k'('fun_app$y'(X1,X2),X4) )
| ? [X5: 'B$',X6: 'C$'] : ( 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,X5),X6)) != X5 )
| ? [X7: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,X7)),X7) != X7 ) )
& ( ( ! [X2: 'B$',X3: 'B$',X4: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,X2),'fun_app$k'('fun_app$y'(X1,X3),X4)) = 'fun_app$k'('fun_app$y'(X1,X2),X4) )
& ! [X5: 'B$',X6: 'C$'] : ( 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,X5),X6)) = X5 )
& ! [X7: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,X7)),X7) = X7 ) )
| ~ 'valid_getter_setter$'(X0,X1) ) ),
inference(nnf_transformation,[],[f820]) ).
tff(f820,plain,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( 'valid_getter_setter$'(X0,X1)
<=> ( ! [X2: 'B$',X3: 'B$',X4: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,X2),'fun_app$k'('fun_app$y'(X1,X3),X4)) = 'fun_app$k'('fun_app$y'(X1,X2),X4) )
& ! [X5: 'B$',X6: 'C$'] : ( 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,X5),X6)) = X5 )
& ! [X7: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,X7)),X7) = X7 ) ) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( 'valid_getter_setter$'(X0,X1)
<=> ( ! [X2: 'B$',X3: 'B$',X4: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,X2),'fun_app$k'('fun_app$y'(X1,X3),X4)) = 'fun_app$k'('fun_app$y'(X1,X2),X4) )
& ! [X2: 'B$',X3: 'C$'] : ( 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,X2),X3)) = X2 )
& ! [X2: 'C$'] : ( 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,X2)),X2) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom76) ).
tff(f17399,plain,
spl249_1184,
inference(avatar_split_clause,[],[f3120,f17397]) ).
tff(f17397,plain,
( spl249_1184
<=> ! [X0: 'B_b_b_fun_fun$',X3: 'B_option$',X2: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$s'('combine_options$b'(X0,'fun_app$s'('combine_options$b'(X0,X1),X2)),X3) = 'fun_app$s'('combine_options$b'(X0,X1),'fun_app$s'('combine_options$b'(X0,X2),X3)) )
| ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,sK246(X0)),sK247(X0))),sK248(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK246(X0)),'fun_app$h'('fun_app$ai'(X0,sK247(X0)),sK248(X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1184])]) ).
tff(f3120,plain,
! [X2: 'B_option$',X3: 'B_option$',X0: 'B_b_b_fun_fun$',X1: 'B_option$'] :
( ( 'fun_app$s'('combine_options$b'(X0,'fun_app$s'('combine_options$b'(X0,X1),X2)),X3) = 'fun_app$s'('combine_options$b'(X0,X1),'fun_app$s'('combine_options$b'(X0,X2),X3)) )
| ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,sK246(X0)),sK247(X0))),sK248(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK246(X0)),'fun_app$h'('fun_app$ai'(X0,sK247(X0)),sK248(X0))) ) ),
inference(cnf_transformation,[],[f1860]) ).
tff(f1860,plain,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$',X2: 'B_option$',X3: 'B_option$'] :
( ( 'fun_app$s'('combine_options$b'(X0,'fun_app$s'('combine_options$b'(X0,X1),X2)),X3) = 'fun_app$s'('combine_options$b'(X0,X1),'fun_app$s'('combine_options$b'(X0,X2),X3)) )
| ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,sK246(X0)),sK247(X0))),sK248(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK246(X0)),'fun_app$h'('fun_app$ai'(X0,sK247(X0)),sK248(X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK246,sK247,sK248])],[f1082,f1859]) ).
tff(f1859,plain,
! [X0: 'B_b_b_fun_fun$'] :
( ? [X4: 'B$',X5: 'B$',X6: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,X4),X5)),X6) != 'fun_app$h'('fun_app$ai'(X0,X4),'fun_app$h'('fun_app$ai'(X0,X5),X6)) )
=> ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,sK246(X0)),sK247(X0))),sK248(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK246(X0)),'fun_app$h'('fun_app$ai'(X0,sK247(X0)),sK248(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f1082,plain,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$',X2: 'B_option$',X3: 'B_option$'] :
( ( 'fun_app$s'('combine_options$b'(X0,'fun_app$s'('combine_options$b'(X0,X1),X2)),X3) = 'fun_app$s'('combine_options$b'(X0,X1),'fun_app$s'('combine_options$b'(X0,X2),X3)) )
| ? [X4: 'B$',X5: 'B$',X6: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,X4),X5)),X6) != 'fun_app$h'('fun_app$ai'(X0,X4),'fun_app$h'('fun_app$ai'(X0,X5),X6)) ) ),
inference(ennf_transformation,[],[f246]) ).
tff(f246,axiom,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$',X2: 'B_option$',X3: 'B_option$'] :
( ! [X4: 'B$',X5: 'B$',X6: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,'fun_app$h'('fun_app$ai'(X0,X4),X5)),X6) = 'fun_app$h'('fun_app$ai'(X0,X4),'fun_app$h'('fun_app$ai'(X0,X5),X6)) )
=> ( 'fun_app$s'('combine_options$b'(X0,'fun_app$s'('combine_options$b'(X0,X1),X2)),X3) = 'fun_app$s'('combine_options$b'(X0,X1),'fun_app$s'('combine_options$b'(X0,X2),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom244) ).
tff(f17395,plain,
spl249_1183,
inference(avatar_split_clause,[],[f3119,f17393]) ).
tff(f17393,plain,
( spl249_1183
<=> ! [X0: 'C_c_c_fun_fun$',X3: 'C_option$',X2: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$u'('combine_options$a'(X0,'fun_app$u'('combine_options$a'(X0,X1),X2)),X3) = 'fun_app$u'('combine_options$a'(X0,X1),'fun_app$u'('combine_options$a'(X0,X2),X3)) )
| ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,sK243(X0)),sK244(X0))),sK245(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK243(X0)),'fun_app$k'('fun_app$ah'(X0,sK244(X0)),sK245(X0))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1183])]) ).
tff(f3119,plain,
! [X2: 'C_option$',X3: 'C_option$',X0: 'C_c_c_fun_fun$',X1: 'C_option$'] :
( ( 'fun_app$u'('combine_options$a'(X0,'fun_app$u'('combine_options$a'(X0,X1),X2)),X3) = 'fun_app$u'('combine_options$a'(X0,X1),'fun_app$u'('combine_options$a'(X0,X2),X3)) )
| ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,sK243(X0)),sK244(X0))),sK245(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK243(X0)),'fun_app$k'('fun_app$ah'(X0,sK244(X0)),sK245(X0))) ) ),
inference(cnf_transformation,[],[f1858]) ).
tff(f1858,plain,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$',X2: 'C_option$',X3: 'C_option$'] :
( ( 'fun_app$u'('combine_options$a'(X0,'fun_app$u'('combine_options$a'(X0,X1),X2)),X3) = 'fun_app$u'('combine_options$a'(X0,X1),'fun_app$u'('combine_options$a'(X0,X2),X3)) )
| ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,sK243(X0)),sK244(X0))),sK245(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK243(X0)),'fun_app$k'('fun_app$ah'(X0,sK244(X0)),sK245(X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK243,sK244,sK245])],[f1081,f1857]) ).
tff(f1857,plain,
! [X0: 'C_c_c_fun_fun$'] :
( ? [X4: 'C$',X5: 'C$',X6: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,X4),X5)),X6) != 'fun_app$k'('fun_app$ah'(X0,X4),'fun_app$k'('fun_app$ah'(X0,X5),X6)) )
=> ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,sK243(X0)),sK244(X0))),sK245(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK243(X0)),'fun_app$k'('fun_app$ah'(X0,sK244(X0)),sK245(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f1081,plain,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$',X2: 'C_option$',X3: 'C_option$'] :
( ( 'fun_app$u'('combine_options$a'(X0,'fun_app$u'('combine_options$a'(X0,X1),X2)),X3) = 'fun_app$u'('combine_options$a'(X0,X1),'fun_app$u'('combine_options$a'(X0,X2),X3)) )
| ? [X4: 'C$',X5: 'C$',X6: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,X4),X5)),X6) != 'fun_app$k'('fun_app$ah'(X0,X4),'fun_app$k'('fun_app$ah'(X0,X5),X6)) ) ),
inference(ennf_transformation,[],[f247]) ).
tff(f247,axiom,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$',X2: 'C_option$',X3: 'C_option$'] :
( ! [X4: 'C$',X5: 'C$',X6: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,'fun_app$k'('fun_app$ah'(X0,X4),X5)),X6) = 'fun_app$k'('fun_app$ah'(X0,X4),'fun_app$k'('fun_app$ah'(X0,X5),X6)) )
=> ( 'fun_app$u'('combine_options$a'(X0,'fun_app$u'('combine_options$a'(X0,X1),X2)),X3) = 'fun_app$u'('combine_options$a'(X0,X1),'fun_app$u'('combine_options$a'(X0,X2),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom245) ).
tff(f17382,plain,
spl249_1182,
inference(avatar_split_clause,[],[f2085,f17380]) ).
tff(f17380,plain,
( spl249_1182
<=> ! [X2: 'B_b_b_option_fun_fun$',X0: 'B_b_option_fun_b_b_option_fun_fun$',X1: 'B_b_fun$'] :
( 'preregister$'(X0)
| ( 'fun_app$g'('fun_app$ad'(X0,sK67(X0,X1,X2)),sK68(X0,X1,X2)) != 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(X2),sK68(X0,X1,X2))),'fun_app$g'(sK67(X0,X1,X2),'fun_app$h'(X1,sK68(X0,X1,X2)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1182])]) ).
tff(f2085,plain,
! [X2: 'B_b_b_option_fun_fun$',X0: 'B_b_option_fun_b_b_option_fun_fun$',X1: 'B_b_fun$'] :
( 'preregister$'(X0)
| ( 'fun_app$g'('fun_app$ad'(X0,sK67(X0,X1,X2)),sK68(X0,X1,X2)) != 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(X2),sK68(X0,X1,X2))),'fun_app$g'(sK67(X0,X1,X2),'fun_app$h'(X1,sK68(X0,X1,X2)))) ) ),
inference(cnf_transformation,[],[f1230]) ).
tff(f1230,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ( 'preregister$'(X0)
| ! [X1: 'B_b_fun$',X2: 'B_b_b_option_fun_fun$'] : ( 'fun_app$g'('fun_app$ad'(X0,sK67(X0,X1,X2)),sK68(X0,X1,X2)) != 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(X2),sK68(X0,X1,X2))),'fun_app$g'(sK67(X0,X1,X2),'fun_app$h'(X1,sK68(X0,X1,X2)))) ) )
& ( ! [X7: 'B_b_option_fun$',X8: 'B$'] : ( 'fun_app$g'('fun_app$ad'(X0,X7),X8) = 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(sK70(X0)),X8)),'fun_app$g'(X7,'fun_app$h'(sK69(X0),X8))) )
| ~ 'preregister$'(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68,sK69,sK70])],[f1227,f1229,f1228]) ).
tff(f1228,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$',X1: 'B_b_fun$',X2: 'B_b_b_option_fun_fun$'] :
( ? [X3: 'B_b_option_fun$',X4: 'B$'] : ( 'fun_app$g'('fun_app$ad'(X0,X3),X4) != 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(X2),X4)),'fun_app$g'(X3,'fun_app$h'(X1,X4))) )
=> ( 'fun_app$g'('fun_app$ad'(X0,sK67(X0,X1,X2)),sK68(X0,X1,X2)) != 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(X2),sK68(X0,X1,X2))),'fun_app$g'(sK67(X0,X1,X2),'fun_app$h'(X1,sK68(X0,X1,X2)))) ) ),
introduced(choice_axiom,[]) ).
tff(f1229,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ? [X5: 'B_b_fun$',X6: 'B_b_b_option_fun_fun$'] :
! [X7: 'B_b_option_fun$',X8: 'B$'] : ( 'fun_app$g'('fun_app$ad'(X0,X7),X8) = 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(X6),X8)),'fun_app$g'(X7,'fun_app$h'(X5,X8))) )
=> ! [X8: 'B$',X7: 'B_b_option_fun$'] : ( 'fun_app$g'('fun_app$ad'(X0,X7),X8) = 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(sK70(X0)),X8)),'fun_app$g'(X7,'fun_app$h'(sK69(X0),X8))) ) ),
introduced(choice_axiom,[]) ).
tff(f1227,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ( 'preregister$'(X0)
| ! [X1: 'B_b_fun$',X2: 'B_b_b_option_fun_fun$'] :
? [X3: 'B_b_option_fun$',X4: 'B$'] : ( 'fun_app$g'('fun_app$ad'(X0,X3),X4) != 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(X2),X4)),'fun_app$g'(X3,'fun_app$h'(X1,X4))) ) )
& ( ? [X5: 'B_b_fun$',X6: 'B_b_b_option_fun_fun$'] :
! [X7: 'B_b_option_fun$',X8: 'B$'] : ( 'fun_app$g'('fun_app$ad'(X0,X7),X8) = 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(X6),X8)),'fun_app$g'(X7,'fun_app$h'(X5,X8))) )
| ~ 'preregister$'(X0) ) ),
inference(rectify,[],[f1226]) ).
tff(f1226,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ( 'preregister$'(X0)
| ! [X1: 'B_b_fun$',X2: 'B_b_b_option_fun_fun$'] :
? [X3: 'B_b_option_fun$',X4: 'B$'] : ( 'fun_app$g'('fun_app$ad'(X0,X3),X4) != 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(X2),X4)),'fun_app$g'(X3,'fun_app$h'(X1,X4))) ) )
& ( ? [X1: 'B_b_fun$',X2: 'B_b_b_option_fun_fun$'] :
! [X3: 'B_b_option_fun$',X4: 'B$'] : ( 'fun_app$g'('fun_app$ad'(X0,X3),X4) = 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(X2),X4)),'fun_app$g'(X3,'fun_app$h'(X1,X4))) )
| ~ 'preregister$'(X0) ) ),
inference(nnf_transformation,[],[f173]) ).
tff(f173,axiom,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( 'preregister$'(X0)
<=> ? [X1: 'B_b_fun$',X2: 'B_b_b_option_fun_fun$'] :
! [X3: 'B_b_option_fun$',X4: 'B$'] : ( 'fun_app$g'('fun_app$ad'(X0,X3),X4) = 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(X2),X4)),'fun_app$g'(X3,'fun_app$h'(X1,X4))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom171) ).
tff(f17378,plain,
( spl249_1181
| ~ spl249_67
| ~ spl249_455 ),
inference(avatar_split_clause,[],[f6666,f6365,f3909,f17376]) ).
tff(f17376,plain,
( spl249_1181
<=> ! [X0: 'A_b_fun$',X1: 'A$'] : ( 'fun_app$f'('uvh$'(X0),X1) != 'none$a' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1181])]) ).
tff(f6666,plain,
( ! [X0: 'A_b_fun$',X1: 'A$'] : ( 'fun_app$f'('uvh$'(X0),X1) != 'none$a' )
| ~ spl249_67
| ~ spl249_455 ),
inference(superposition,[],[f3910,f6366]) ).
tff(f17374,plain,
spl249_1180,
inference(avatar_split_clause,[],[f2071,f17372]) ).
tff(f17372,plain,
( spl249_1180
<=> ! [X2: 'C_c_c_option_fun_fun$',X0: 'C_c_option_fun_c_c_option_fun_fun$',X1: 'C_c_fun$'] :
( 'preregister$a'(X0)
| ( 'fun_app$j'('fun_app$aa'(X0,sK55(X0,X1,X2)),sK56(X0,X1,X2)) != 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(X2),sK56(X0,X1,X2))),'fun_app$j'(sK55(X0,X1,X2),'fun_app$k'(X1,sK56(X0,X1,X2)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1180])]) ).
tff(f2071,plain,
! [X2: 'C_c_c_option_fun_fun$',X0: 'C_c_option_fun_c_c_option_fun_fun$',X1: 'C_c_fun$'] :
( 'preregister$a'(X0)
| ( 'fun_app$j'('fun_app$aa'(X0,sK55(X0,X1,X2)),sK56(X0,X1,X2)) != 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(X2),sK56(X0,X1,X2))),'fun_app$j'(sK55(X0,X1,X2),'fun_app$k'(X1,sK56(X0,X1,X2)))) ) ),
inference(cnf_transformation,[],[f1209]) ).
tff(f1209,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ( 'preregister$a'(X0)
| ! [X1: 'C_c_fun$',X2: 'C_c_c_option_fun_fun$'] : ( 'fun_app$j'('fun_app$aa'(X0,sK55(X0,X1,X2)),sK56(X0,X1,X2)) != 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(X2),sK56(X0,X1,X2))),'fun_app$j'(sK55(X0,X1,X2),'fun_app$k'(X1,sK56(X0,X1,X2)))) ) )
& ( ! [X7: 'C_c_option_fun$',X8: 'C$'] : ( 'fun_app$j'('fun_app$aa'(X0,X7),X8) = 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(sK58(X0)),X8)),'fun_app$j'(X7,'fun_app$k'(sK57(X0),X8))) )
| ~ 'preregister$a'(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56,sK57,sK58])],[f1206,f1208,f1207]) ).
tff(f1207,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$',X1: 'C_c_fun$',X2: 'C_c_c_option_fun_fun$'] :
( ? [X3: 'C_c_option_fun$',X4: 'C$'] : ( 'fun_app$j'('fun_app$aa'(X0,X3),X4) != 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(X2),X4)),'fun_app$j'(X3,'fun_app$k'(X1,X4))) )
=> ( 'fun_app$j'('fun_app$aa'(X0,sK55(X0,X1,X2)),sK56(X0,X1,X2)) != 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(X2),sK56(X0,X1,X2))),'fun_app$j'(sK55(X0,X1,X2),'fun_app$k'(X1,sK56(X0,X1,X2)))) ) ),
introduced(choice_axiom,[]) ).
tff(f1208,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ? [X5: 'C_c_fun$',X6: 'C_c_c_option_fun_fun$'] :
! [X7: 'C_c_option_fun$',X8: 'C$'] : ( 'fun_app$j'('fun_app$aa'(X0,X7),X8) = 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(X6),X8)),'fun_app$j'(X7,'fun_app$k'(X5,X8))) )
=> ! [X8: 'C$',X7: 'C_c_option_fun$'] : ( 'fun_app$j'('fun_app$aa'(X0,X7),X8) = 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(sK58(X0)),X8)),'fun_app$j'(X7,'fun_app$k'(sK57(X0),X8))) ) ),
introduced(choice_axiom,[]) ).
tff(f1206,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ( 'preregister$a'(X0)
| ! [X1: 'C_c_fun$',X2: 'C_c_c_option_fun_fun$'] :
? [X3: 'C_c_option_fun$',X4: 'C$'] : ( 'fun_app$j'('fun_app$aa'(X0,X3),X4) != 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(X2),X4)),'fun_app$j'(X3,'fun_app$k'(X1,X4))) ) )
& ( ? [X5: 'C_c_fun$',X6: 'C_c_c_option_fun_fun$'] :
! [X7: 'C_c_option_fun$',X8: 'C$'] : ( 'fun_app$j'('fun_app$aa'(X0,X7),X8) = 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(X6),X8)),'fun_app$j'(X7,'fun_app$k'(X5,X8))) )
| ~ 'preregister$a'(X0) ) ),
inference(rectify,[],[f1205]) ).
tff(f1205,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ( 'preregister$a'(X0)
| ! [X1: 'C_c_fun$',X2: 'C_c_c_option_fun_fun$'] :
? [X3: 'C_c_option_fun$',X4: 'C$'] : ( 'fun_app$j'('fun_app$aa'(X0,X3),X4) != 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(X2),X4)),'fun_app$j'(X3,'fun_app$k'(X1,X4))) ) )
& ( ? [X1: 'C_c_fun$',X2: 'C_c_c_option_fun_fun$'] :
! [X3: 'C_c_option_fun$',X4: 'C$'] : ( 'fun_app$j'('fun_app$aa'(X0,X3),X4) = 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(X2),X4)),'fun_app$j'(X3,'fun_app$k'(X1,X4))) )
| ~ 'preregister$a'(X0) ) ),
inference(nnf_transformation,[],[f174]) ).
tff(f174,axiom,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( 'preregister$a'(X0)
<=> ? [X1: 'C_c_fun$',X2: 'C_c_c_option_fun_fun$'] :
! [X3: 'C_c_option_fun$',X4: 'C$'] : ( 'fun_app$j'('fun_app$aa'(X0,X3),X4) = 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(X2),X4)),'fun_app$j'(X3,'fun_app$k'(X1,X4))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom172) ).
tff(f17367,plain,
spl249_1179,
inference(avatar_split_clause,[],[f2089,f17365]) ).
tff(f17365,plain,
( spl249_1179
<=> ! [X2: 'A_b_b_option_fun_fun$',X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B_a_fun$'] :
( 'preregister$c'(X0)
| ( 'fun_app$g'('fun_app$au'(X0,sK75(X0,X1,X2)),sK76(X0,X1,X2)) != 'fun_app$av'('case_option$d'('none$a','uuv$'(X2,sK76(X0,X1,X2))),'fun_app$q'(sK75(X0,X1,X2),'fun_app$ao'(X1,sK76(X0,X1,X2)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1179])]) ).
tff(f2089,plain,
! [X2: 'A_b_b_option_fun_fun$',X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B_a_fun$'] :
( 'preregister$c'(X0)
| ( 'fun_app$g'('fun_app$au'(X0,sK75(X0,X1,X2)),sK76(X0,X1,X2)) != 'fun_app$av'('case_option$d'('none$a','uuv$'(X2,sK76(X0,X1,X2))),'fun_app$q'(sK75(X0,X1,X2),'fun_app$ao'(X1,sK76(X0,X1,X2)))) ) ),
inference(cnf_transformation,[],[f1240]) ).
tff(f1240,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( 'preregister$c'(X0)
| ! [X1: 'B_a_fun$',X2: 'A_b_b_option_fun_fun$'] : ( 'fun_app$g'('fun_app$au'(X0,sK75(X0,X1,X2)),sK76(X0,X1,X2)) != 'fun_app$av'('case_option$d'('none$a','uuv$'(X2,sK76(X0,X1,X2))),'fun_app$q'(sK75(X0,X1,X2),'fun_app$ao'(X1,sK76(X0,X1,X2)))) ) )
& ( ! [X7: 'A_a_option_fun$',X8: 'B$'] : ( 'fun_app$g'('fun_app$au'(X0,X7),X8) = 'fun_app$av'('case_option$d'('none$a','uuv$'(sK78(X0),X8)),'fun_app$q'(X7,'fun_app$ao'(sK77(X0),X8))) )
| ~ 'preregister$c'(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75,sK76,sK77,sK78])],[f1237,f1239,f1238]) ).
tff(f1238,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B_a_fun$',X2: 'A_b_b_option_fun_fun$'] :
( ? [X3: 'A_a_option_fun$',X4: 'B$'] : ( 'fun_app$g'('fun_app$au'(X0,X3),X4) != 'fun_app$av'('case_option$d'('none$a','uuv$'(X2,X4)),'fun_app$q'(X3,'fun_app$ao'(X1,X4))) )
=> ( 'fun_app$g'('fun_app$au'(X0,sK75(X0,X1,X2)),sK76(X0,X1,X2)) != 'fun_app$av'('case_option$d'('none$a','uuv$'(X2,sK76(X0,X1,X2))),'fun_app$q'(sK75(X0,X1,X2),'fun_app$ao'(X1,sK76(X0,X1,X2)))) ) ),
introduced(choice_axiom,[]) ).
tff(f1239,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ? [X5: 'B_a_fun$',X6: 'A_b_b_option_fun_fun$'] :
! [X7: 'A_a_option_fun$',X8: 'B$'] : ( 'fun_app$g'('fun_app$au'(X0,X7),X8) = 'fun_app$av'('case_option$d'('none$a','uuv$'(X6,X8)),'fun_app$q'(X7,'fun_app$ao'(X5,X8))) )
=> ! [X8: 'B$',X7: 'A_a_option_fun$'] : ( 'fun_app$g'('fun_app$au'(X0,X7),X8) = 'fun_app$av'('case_option$d'('none$a','uuv$'(sK78(X0),X8)),'fun_app$q'(X7,'fun_app$ao'(sK77(X0),X8))) ) ),
introduced(choice_axiom,[]) ).
tff(f1237,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( 'preregister$c'(X0)
| ! [X1: 'B_a_fun$',X2: 'A_b_b_option_fun_fun$'] :
? [X3: 'A_a_option_fun$',X4: 'B$'] : ( 'fun_app$g'('fun_app$au'(X0,X3),X4) != 'fun_app$av'('case_option$d'('none$a','uuv$'(X2,X4)),'fun_app$q'(X3,'fun_app$ao'(X1,X4))) ) )
& ( ? [X5: 'B_a_fun$',X6: 'A_b_b_option_fun_fun$'] :
! [X7: 'A_a_option_fun$',X8: 'B$'] : ( 'fun_app$g'('fun_app$au'(X0,X7),X8) = 'fun_app$av'('case_option$d'('none$a','uuv$'(X6,X8)),'fun_app$q'(X7,'fun_app$ao'(X5,X8))) )
| ~ 'preregister$c'(X0) ) ),
inference(rectify,[],[f1236]) ).
tff(f1236,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( 'preregister$c'(X0)
| ! [X1: 'B_a_fun$',X2: 'A_b_b_option_fun_fun$'] :
? [X3: 'A_a_option_fun$',X4: 'B$'] : ( 'fun_app$g'('fun_app$au'(X0,X3),X4) != 'fun_app$av'('case_option$d'('none$a','uuv$'(X2,X4)),'fun_app$q'(X3,'fun_app$ao'(X1,X4))) ) )
& ( ? [X1: 'B_a_fun$',X2: 'A_b_b_option_fun_fun$'] :
! [X3: 'A_a_option_fun$',X4: 'B$'] : ( 'fun_app$g'('fun_app$au'(X0,X3),X4) = 'fun_app$av'('case_option$d'('none$a','uuv$'(X2,X4)),'fun_app$q'(X3,'fun_app$ao'(X1,X4))) )
| ~ 'preregister$c'(X0) ) ),
inference(nnf_transformation,[],[f176]) ).
tff(f176,axiom,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( 'preregister$c'(X0)
<=> ? [X1: 'B_a_fun$',X2: 'A_b_b_option_fun_fun$'] :
! [X3: 'A_a_option_fun$',X4: 'B$'] : ( 'fun_app$g'('fun_app$au'(X0,X3),X4) = 'fun_app$av'('case_option$d'('none$a','uuv$'(X2,X4)),'fun_app$q'(X3,'fun_app$ao'(X1,X4))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom174) ).
tff(f17363,plain,
spl249_1178,
inference(avatar_split_clause,[],[f2087,f17361]) ).
tff(f17361,plain,
( spl249_1178
<=> ! [X2: 'B_c_c_option_fun_fun$',X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C_b_fun$'] :
( 'preregister$b'(X0)
| ( 'fun_app$j'('fun_app$am'(X0,sK71(X0,X1,X2)),sK72(X0,X1,X2)) != 'fun_app$an'('case_option$c'('none$','uuu$'(X2,sK72(X0,X1,X2))),'fun_app$g'(sK71(X0,X1,X2),'fun_app$m'(X1,sK72(X0,X1,X2)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1178])]) ).
tff(f2087,plain,
! [X2: 'B_c_c_option_fun_fun$',X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C_b_fun$'] :
( 'preregister$b'(X0)
| ( 'fun_app$j'('fun_app$am'(X0,sK71(X0,X1,X2)),sK72(X0,X1,X2)) != 'fun_app$an'('case_option$c'('none$','uuu$'(X2,sK72(X0,X1,X2))),'fun_app$g'(sK71(X0,X1,X2),'fun_app$m'(X1,sK72(X0,X1,X2)))) ) ),
inference(cnf_transformation,[],[f1235]) ).
tff(f1235,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( 'preregister$b'(X0)
| ! [X1: 'C_b_fun$',X2: 'B_c_c_option_fun_fun$'] : ( 'fun_app$j'('fun_app$am'(X0,sK71(X0,X1,X2)),sK72(X0,X1,X2)) != 'fun_app$an'('case_option$c'('none$','uuu$'(X2,sK72(X0,X1,X2))),'fun_app$g'(sK71(X0,X1,X2),'fun_app$m'(X1,sK72(X0,X1,X2)))) ) )
& ( ! [X7: 'B_b_option_fun$',X8: 'C$'] : ( 'fun_app$j'('fun_app$am'(X0,X7),X8) = 'fun_app$an'('case_option$c'('none$','uuu$'(sK74(X0),X8)),'fun_app$g'(X7,'fun_app$m'(sK73(X0),X8))) )
| ~ 'preregister$b'(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK71,sK72,sK73,sK74])],[f1232,f1234,f1233]) ).
tff(f1233,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C_b_fun$',X2: 'B_c_c_option_fun_fun$'] :
( ? [X3: 'B_b_option_fun$',X4: 'C$'] : ( 'fun_app$j'('fun_app$am'(X0,X3),X4) != 'fun_app$an'('case_option$c'('none$','uuu$'(X2,X4)),'fun_app$g'(X3,'fun_app$m'(X1,X4))) )
=> ( 'fun_app$j'('fun_app$am'(X0,sK71(X0,X1,X2)),sK72(X0,X1,X2)) != 'fun_app$an'('case_option$c'('none$','uuu$'(X2,sK72(X0,X1,X2))),'fun_app$g'(sK71(X0,X1,X2),'fun_app$m'(X1,sK72(X0,X1,X2)))) ) ),
introduced(choice_axiom,[]) ).
tff(f1234,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ? [X5: 'C_b_fun$',X6: 'B_c_c_option_fun_fun$'] :
! [X7: 'B_b_option_fun$',X8: 'C$'] : ( 'fun_app$j'('fun_app$am'(X0,X7),X8) = 'fun_app$an'('case_option$c'('none$','uuu$'(X6,X8)),'fun_app$g'(X7,'fun_app$m'(X5,X8))) )
=> ! [X8: 'C$',X7: 'B_b_option_fun$'] : ( 'fun_app$j'('fun_app$am'(X0,X7),X8) = 'fun_app$an'('case_option$c'('none$','uuu$'(sK74(X0),X8)),'fun_app$g'(X7,'fun_app$m'(sK73(X0),X8))) ) ),
introduced(choice_axiom,[]) ).
tff(f1232,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( 'preregister$b'(X0)
| ! [X1: 'C_b_fun$',X2: 'B_c_c_option_fun_fun$'] :
? [X3: 'B_b_option_fun$',X4: 'C$'] : ( 'fun_app$j'('fun_app$am'(X0,X3),X4) != 'fun_app$an'('case_option$c'('none$','uuu$'(X2,X4)),'fun_app$g'(X3,'fun_app$m'(X1,X4))) ) )
& ( ? [X5: 'C_b_fun$',X6: 'B_c_c_option_fun_fun$'] :
! [X7: 'B_b_option_fun$',X8: 'C$'] : ( 'fun_app$j'('fun_app$am'(X0,X7),X8) = 'fun_app$an'('case_option$c'('none$','uuu$'(X6,X8)),'fun_app$g'(X7,'fun_app$m'(X5,X8))) )
| ~ 'preregister$b'(X0) ) ),
inference(rectify,[],[f1231]) ).
tff(f1231,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( 'preregister$b'(X0)
| ! [X1: 'C_b_fun$',X2: 'B_c_c_option_fun_fun$'] :
? [X3: 'B_b_option_fun$',X4: 'C$'] : ( 'fun_app$j'('fun_app$am'(X0,X3),X4) != 'fun_app$an'('case_option$c'('none$','uuu$'(X2,X4)),'fun_app$g'(X3,'fun_app$m'(X1,X4))) ) )
& ( ? [X1: 'C_b_fun$',X2: 'B_c_c_option_fun_fun$'] :
! [X3: 'B_b_option_fun$',X4: 'C$'] : ( 'fun_app$j'('fun_app$am'(X0,X3),X4) = 'fun_app$an'('case_option$c'('none$','uuu$'(X2,X4)),'fun_app$g'(X3,'fun_app$m'(X1,X4))) )
| ~ 'preregister$b'(X0) ) ),
inference(nnf_transformation,[],[f175]) ).
tff(f175,axiom,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( 'preregister$b'(X0)
<=> ? [X1: 'C_b_fun$',X2: 'B_c_c_option_fun_fun$'] :
! [X3: 'B_b_option_fun$',X4: 'C$'] : ( 'fun_app$j'('fun_app$am'(X0,X3),X4) = 'fun_app$an'('case_option$c'('none$','uuu$'(X2,X4)),'fun_app$g'(X3,'fun_app$m'(X1,X4))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom173) ).
tff(f17359,plain,
( spl249_1177
| ~ spl249_1104
| ~ spl249_1176 ),
inference(avatar_split_clause,[],[f17355,f17352,f16394,f17357]) ).
tff(f16394,plain,
( spl249_1104
<=> ! [X0: 'C_b_fun$',X3: 'C$',X2: 'B_b_option_fun$',X1: 'B_c_c_fun_fun$'] : ( 'fun_app$j'('fun_app$am'('register_from_getter_setter$a'(X0,X1),X2),X3) = 'fun_app$an'('case_option$c'('none$','uu$'(X1,X3)),'fun_app$g'(X2,'fun_app$m'(X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1104])]) ).
tff(f17352,plain,
( spl249_1176
<=> ! [X0: 'B_c_c_fun_fun$',X1: 'C_b_fun$'] :
( ~ 'valid_getter_setter$'(X1,X0)
| ( 'fun_app$j'('fun_app$am'('g$',sK44(X0,X1)),sK45(X0,X1)) != 'fun_app$an'('case_option$c'('none$','uu$'(X0,sK45(X0,X1))),'fun_app$g'(sK44(X0,X1),'fun_app$m'(X1,sK45(X0,X1)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1176])]) ).
tff(f17355,plain,
( ! [X0: 'B_c_c_fun_fun$',X1: 'C_b_fun$'] :
( ( 'fun_app$j'('fun_app$am'('g$',sK44(X0,X1)),sK45(X0,X1)) != 'fun_app$j'('fun_app$am'('register_from_getter_setter$a'(X1,X0),sK44(X0,X1)),sK45(X0,X1)) )
| ~ 'valid_getter_setter$'(X1,X0) )
| ~ spl249_1104
| ~ spl249_1176 ),
inference(forward_demodulation,[],[f17353,f16395]) ).
tff(f16395,plain,
( ! [X2: 'B_b_option_fun$',X3: 'C$',X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] : ( 'fun_app$j'('fun_app$am'('register_from_getter_setter$a'(X0,X1),X2),X3) = 'fun_app$an'('case_option$c'('none$','uu$'(X1,X3)),'fun_app$g'(X2,'fun_app$m'(X0,X3))) )
| ~ spl249_1104 ),
inference(avatar_component_clause,[],[f16394]) ).
tff(f17353,plain,
( ! [X0: 'B_c_c_fun_fun$',X1: 'C_b_fun$'] :
( ~ 'valid_getter_setter$'(X1,X0)
| ( 'fun_app$j'('fun_app$am'('g$',sK44(X0,X1)),sK45(X0,X1)) != 'fun_app$an'('case_option$c'('none$','uu$'(X0,sK45(X0,X1))),'fun_app$g'(sK44(X0,X1),'fun_app$m'(X1,sK45(X0,X1)))) ) )
| ~ spl249_1176 ),
inference(avatar_component_clause,[],[f17352]) ).
tff(f17354,plain,
( spl249_1176
| spl249_1 ),
inference(avatar_split_clause,[],[f1920,f3605,f17352]) ).
tff(f3605,plain,
( spl249_1
<=> 'thesis$' ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1])]) ).
tff(f1920,plain,
! [X0: 'B_c_c_fun_fun$',X1: 'C_b_fun$'] :
( 'thesis$'
| ~ 'valid_getter_setter$'(X1,X0)
| ( 'fun_app$j'('fun_app$am'('g$',sK44(X0,X1)),sK45(X0,X1)) != 'fun_app$an'('case_option$c'('none$','uu$'(X0,sK45(X0,X1))),'fun_app$g'(sK44(X0,X1),'fun_app$m'(X1,sK45(X0,X1)))) ) ),
inference(cnf_transformation,[],[f1188]) ).
tff(f1188,plain,
! [X0: 'B_c_c_fun_fun$',X1: 'C_b_fun$'] :
( 'thesis$'
| ~ 'valid_getter_setter$'(X1,X0)
| ( 'fun_app$j'('fun_app$am'('g$',sK44(X0,X1)),sK45(X0,X1)) != 'fun_app$an'('case_option$c'('none$','uu$'(X0,sK45(X0,X1))),'fun_app$g'(sK44(X0,X1),'fun_app$m'(X1,sK45(X0,X1)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45])],[f862,f1187]) ).
tff(f1187,plain,
! [X0: 'B_c_c_fun_fun$',X1: 'C_b_fun$'] :
( ? [X2: 'B_b_option_fun$',X3: 'C$'] : ( 'fun_app$j'('fun_app$am'('g$',X2),X3) != 'fun_app$an'('case_option$c'('none$','uu$'(X0,X3)),'fun_app$g'(X2,'fun_app$m'(X1,X3))) )
=> ( 'fun_app$j'('fun_app$am'('g$',sK44(X0,X1)),sK45(X0,X1)) != 'fun_app$an'('case_option$c'('none$','uu$'(X0,sK45(X0,X1))),'fun_app$g'(sK44(X0,X1),'fun_app$m'(X1,sK45(X0,X1)))) ) ),
introduced(choice_axiom,[]) ).
tff(f862,plain,
! [X0: 'B_c_c_fun_fun$',X1: 'C_b_fun$'] :
( 'thesis$'
| ~ 'valid_getter_setter$'(X1,X0)
| ? [X2: 'B_b_option_fun$',X3: 'C$'] : ( 'fun_app$j'('fun_app$am'('g$',X2),X3) != 'fun_app$an'('case_option$c'('none$','uu$'(X0,X3)),'fun_app$g'(X2,'fun_app$m'(X1,X3))) ) ),
inference(flattening,[],[f861]) ).
tff(f861,plain,
! [X0: 'B_c_c_fun_fun$',X1: 'C_b_fun$'] :
( 'thesis$'
| ~ 'valid_getter_setter$'(X1,X0)
| ? [X2: 'B_b_option_fun$',X3: 'C$'] : ( 'fun_app$j'('fun_app$am'('g$',X2),X3) != 'fun_app$an'('case_option$c'('none$','uu$'(X0,X3)),'fun_app$g'(X2,'fun_app$m'(X1,X3))) ) ),
inference(ennf_transformation,[],[f75]) ).
tff(f75,axiom,
! [X0: 'B_c_c_fun_fun$',X1: 'C_b_fun$'] :
( ( 'valid_getter_setter$'(X1,X0)
& ! [X2: 'B_b_option_fun$',X3: 'C$'] : ( 'fun_app$j'('fun_app$am'('g$',X2),X3) = 'fun_app$an'('case_option$c'('none$','uu$'(X0,X3)),'fun_app$g'(X2,'fun_app$m'(X1,X3))) ) )
=> 'thesis$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis73) ).
tff(f17348,plain,
spl249_1175,
inference(avatar_split_clause,[],[f2311,f17346]) ).
tff(f17346,plain,
( spl249_1175
<=> ! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$am'(X0,'fun_app$t'('update1$b'(sK115(X0,X1)),sK116(X0,X1))) != 'fun_app$am'(X1,'fun_app$t'('update1$b'(sK115(X0,X1)),sK116(X0,X1))) )
| ~ 'preregister$b'(X1)
| ~ 'preregister$b'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1175])]) ).
tff(f2311,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$am'(X0,'fun_app$t'('update1$b'(sK115(X0,X1)),sK116(X0,X1))) != 'fun_app$am'(X1,'fun_app$t'('update1$b'(sK115(X0,X1)),sK116(X0,X1))) )
| ~ 'preregister$b'(X1)
| ~ 'preregister$b'(X0) ),
inference(cnf_transformation,[],[f1394]) ).
tff(f1394,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$am'(X0,'fun_app$t'('update1$b'(sK115(X0,X1)),sK116(X0,X1))) != 'fun_app$am'(X1,'fun_app$t'('update1$b'(sK115(X0,X1)),sK116(X0,X1))) )
| ~ 'preregister$b'(X1)
| ~ 'preregister$b'(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK115,sK116])],[f931,f1393]) ).
tff(f1393,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ? [X2: 'B$',X3: 'B$'] : ( 'fun_app$am'(X0,'fun_app$t'('update1$b'(X2),X3)) != 'fun_app$am'(X1,'fun_app$t'('update1$b'(X2),X3)) )
=> ( 'fun_app$am'(X0,'fun_app$t'('update1$b'(sK115(X0,X1)),sK116(X0,X1))) != 'fun_app$am'(X1,'fun_app$t'('update1$b'(sK115(X0,X1)),sK116(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f931,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( X0 = X1 )
| ? [X2: 'B$',X3: 'B$'] : ( 'fun_app$am'(X0,'fun_app$t'('update1$b'(X2),X3)) != 'fun_app$am'(X1,'fun_app$t'('update1$b'(X2),X3)) )
| ~ 'preregister$b'(X1)
| ~ 'preregister$b'(X0) ),
inference(flattening,[],[f930]) ).
tff(f930,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( X0 = X1 )
| ? [X2: 'B$',X3: 'B$'] : ( 'fun_app$am'(X0,'fun_app$t'('update1$b'(X2),X3)) != 'fun_app$am'(X1,'fun_app$t'('update1$b'(X2),X3)) )
| ~ 'preregister$b'(X1)
| ~ 'preregister$b'(X0) ),
inference(ennf_transformation,[],[f261]) ).
tff(f261,axiom,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( ! [X2: 'B$',X3: 'B$'] : ( 'fun_app$am'(X0,'fun_app$t'('update1$b'(X2),X3)) = 'fun_app$am'(X1,'fun_app$t'('update1$b'(X2),X3)) )
& 'preregister$b'(X1)
& 'preregister$b'(X0) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom259) ).
tff(f17269,plain,
spl249_1174,
inference(avatar_split_clause,[],[f3117,f17267]) ).
tff(f17267,plain,
( spl249_1174
<=> ! [X0: 'B_option$',X3: 'B_b_fun$',X2: 'B_b_fun$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$s'('map_option$b'(X2),X0) != 'fun_app$s'('map_option$b'(X3),X1) )
| ( 'fun_app$h'(X2,sK241(X0,X1,X2,X3)) = 'fun_app$h'(X3,sK242(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1174])]) ).
tff(f3117,plain,
! [X2: 'B_b_fun$',X3: 'B_b_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$s'('map_option$b'(X2),X0) != 'fun_app$s'('map_option$b'(X3),X1) )
| ( 'fun_app$h'(X2,sK241(X0,X1,X2,X3)) = 'fun_app$h'(X3,sK242(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f1856]) ).
tff(f1856,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$s'('map_option$b'(X2),X0) != 'fun_app$s'('map_option$b'(X3),X1) )
| ( ( sK241(X0,X1,X2,X3) != sK242(X0,X1,X2,X3) )
& ( 'fun_app$h'(X2,sK241(X0,X1,X2,X3)) = 'fun_app$h'(X3,sK242(X0,X1,X2,X3)) )
& 'member$c'(sK242(X0,X1,X2,X3),'set_option$d'(X1))
& 'member$c'(sK241(X0,X1,X2,X3),'set_option$d'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK241,sK242])],[f1080,f1855]) ).
tff(f1855,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ? [X4: 'B$',X5: 'B$'] :
( ( X4 != X5 )
& ( 'fun_app$h'(X2,X4) = 'fun_app$h'(X3,X5) )
& 'member$c'(X5,'set_option$d'(X1))
& 'member$c'(X4,'set_option$d'(X0)) )
=> ( ( sK241(X0,X1,X2,X3) != sK242(X0,X1,X2,X3) )
& ( 'fun_app$h'(X2,sK241(X0,X1,X2,X3)) = 'fun_app$h'(X3,sK242(X0,X1,X2,X3)) )
& 'member$c'(sK242(X0,X1,X2,X3),'set_option$d'(X1))
& 'member$c'(sK241(X0,X1,X2,X3),'set_option$d'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1080,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$s'('map_option$b'(X2),X0) != 'fun_app$s'('map_option$b'(X3),X1) )
| ? [X4: 'B$',X5: 'B$'] :
( ( X4 != X5 )
& ( 'fun_app$h'(X2,X4) = 'fun_app$h'(X3,X5) )
& 'member$c'(X5,'set_option$d'(X1))
& 'member$c'(X4,'set_option$d'(X0)) ) ),
inference(flattening,[],[f1079]) ).
tff(f1079,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$s'('map_option$b'(X2),X0) != 'fun_app$s'('map_option$b'(X3),X1) )
| ? [X4: 'B$',X5: 'B$'] :
( ( X4 != X5 )
& ( 'fun_app$h'(X2,X4) = 'fun_app$h'(X3,X5) )
& 'member$c'(X5,'set_option$d'(X1))
& 'member$c'(X4,'set_option$d'(X0)) ) ),
inference(ennf_transformation,[],[f450]) ).
tff(f450,axiom,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ( ( 'fun_app$s'('map_option$b'(X2),X0) = 'fun_app$s'('map_option$b'(X3),X1) )
& ! [X4: 'B$',X5: 'B$'] :
( ( ( 'fun_app$h'(X2,X4) = 'fun_app$h'(X3,X5) )
& 'member$c'(X5,'set_option$d'(X1))
& 'member$c'(X4,'set_option$d'(X0)) )
=> ( X4 = X5 ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom448) ).
tff(f17265,plain,
spl249_1173,
inference(avatar_split_clause,[],[f3113,f17263]) ).
tff(f17263,plain,
( spl249_1173
<=> ! [X0: 'B_option$',X3: 'B_c_fun$',X2: 'B_c_fun$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$an'('map_option$d'(X2),X0) != 'fun_app$an'('map_option$d'(X3),X1) )
| ( 'fun_app$o'(X2,sK239(X0,X1,X2,X3)) = 'fun_app$o'(X3,sK240(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1173])]) ).
tff(f3113,plain,
! [X2: 'B_c_fun$',X3: 'B_c_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$an'('map_option$d'(X2),X0) != 'fun_app$an'('map_option$d'(X3),X1) )
| ( 'fun_app$o'(X2,sK239(X0,X1,X2,X3)) = 'fun_app$o'(X3,sK240(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f1854]) ).
tff(f1854,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$an'('map_option$d'(X2),X0) != 'fun_app$an'('map_option$d'(X3),X1) )
| ( ( sK239(X0,X1,X2,X3) != sK240(X0,X1,X2,X3) )
& ( 'fun_app$o'(X2,sK239(X0,X1,X2,X3)) = 'fun_app$o'(X3,sK240(X0,X1,X2,X3)) )
& 'member$c'(sK240(X0,X1,X2,X3),'set_option$d'(X1))
& 'member$c'(sK239(X0,X1,X2,X3),'set_option$d'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK239,sK240])],[f1078,f1853]) ).
tff(f1853,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ? [X4: 'B$',X5: 'B$'] :
( ( X4 != X5 )
& ( 'fun_app$o'(X2,X4) = 'fun_app$o'(X3,X5) )
& 'member$c'(X5,'set_option$d'(X1))
& 'member$c'(X4,'set_option$d'(X0)) )
=> ( ( sK239(X0,X1,X2,X3) != sK240(X0,X1,X2,X3) )
& ( 'fun_app$o'(X2,sK239(X0,X1,X2,X3)) = 'fun_app$o'(X3,sK240(X0,X1,X2,X3)) )
& 'member$c'(sK240(X0,X1,X2,X3),'set_option$d'(X1))
& 'member$c'(sK239(X0,X1,X2,X3),'set_option$d'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1078,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$an'('map_option$d'(X2),X0) != 'fun_app$an'('map_option$d'(X3),X1) )
| ? [X4: 'B$',X5: 'B$'] :
( ( X4 != X5 )
& ( 'fun_app$o'(X2,X4) = 'fun_app$o'(X3,X5) )
& 'member$c'(X5,'set_option$d'(X1))
& 'member$c'(X4,'set_option$d'(X0)) ) ),
inference(flattening,[],[f1077]) ).
tff(f1077,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$an'('map_option$d'(X2),X0) != 'fun_app$an'('map_option$d'(X3),X1) )
| ? [X4: 'B$',X5: 'B$'] :
( ( X4 != X5 )
& ( 'fun_app$o'(X2,X4) = 'fun_app$o'(X3,X5) )
& 'member$c'(X5,'set_option$d'(X1))
& 'member$c'(X4,'set_option$d'(X0)) ) ),
inference(ennf_transformation,[],[f449]) ).
tff(f449,axiom,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ( ( 'fun_app$an'('map_option$d'(X2),X0) = 'fun_app$an'('map_option$d'(X3),X1) )
& ! [X4: 'B$',X5: 'B$'] :
( ( ( 'fun_app$o'(X2,X4) = 'fun_app$o'(X3,X5) )
& 'member$c'(X5,'set_option$d'(X1))
& 'member$c'(X4,'set_option$d'(X0)) )
=> ( X4 = X5 ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom447) ).
tff(f17261,plain,
spl249_1172,
inference(avatar_split_clause,[],[f3109,f17259]) ).
tff(f17259,plain,
( spl249_1172
<=> ! [X0: 'C_option$',X3: 'C_b_fun$',X2: 'C_b_fun$',X1: 'C_option$'] :
( ( X0 = X1 )
| ( 'fun_app$bg'('map_option$'(X2),X0) != 'fun_app$bg'('map_option$'(X3),X1) )
| ( 'fun_app$m'(X2,sK237(X0,X1,X2,X3)) = 'fun_app$m'(X3,sK238(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1172])]) ).
tff(f3109,plain,
! [X2: 'C_b_fun$',X3: 'C_b_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( X0 = X1 )
| ( 'fun_app$bg'('map_option$'(X2),X0) != 'fun_app$bg'('map_option$'(X3),X1) )
| ( 'fun_app$m'(X2,sK237(X0,X1,X2,X3)) = 'fun_app$m'(X3,sK238(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f1852]) ).
tff(f1852,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$bg'('map_option$'(X2),X0) != 'fun_app$bg'('map_option$'(X3),X1) )
| ( ( sK237(X0,X1,X2,X3) != sK238(X0,X1,X2,X3) )
& ( 'fun_app$m'(X2,sK237(X0,X1,X2,X3)) = 'fun_app$m'(X3,sK238(X0,X1,X2,X3)) )
& 'member$b'(sK238(X0,X1,X2,X3),'set_option$c'(X1))
& 'member$b'(sK237(X0,X1,X2,X3),'set_option$c'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK237,sK238])],[f1076,f1851]) ).
tff(f1851,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ? [X4: 'C$',X5: 'C$'] :
( ( X4 != X5 )
& ( 'fun_app$m'(X2,X4) = 'fun_app$m'(X3,X5) )
& 'member$b'(X5,'set_option$c'(X1))
& 'member$b'(X4,'set_option$c'(X0)) )
=> ( ( sK237(X0,X1,X2,X3) != sK238(X0,X1,X2,X3) )
& ( 'fun_app$m'(X2,sK237(X0,X1,X2,X3)) = 'fun_app$m'(X3,sK238(X0,X1,X2,X3)) )
& 'member$b'(sK238(X0,X1,X2,X3),'set_option$c'(X1))
& 'member$b'(sK237(X0,X1,X2,X3),'set_option$c'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1076,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$bg'('map_option$'(X2),X0) != 'fun_app$bg'('map_option$'(X3),X1) )
| ? [X4: 'C$',X5: 'C$'] :
( ( X4 != X5 )
& ( 'fun_app$m'(X2,X4) = 'fun_app$m'(X3,X5) )
& 'member$b'(X5,'set_option$c'(X1))
& 'member$b'(X4,'set_option$c'(X0)) ) ),
inference(flattening,[],[f1075]) ).
tff(f1075,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$bg'('map_option$'(X2),X0) != 'fun_app$bg'('map_option$'(X3),X1) )
| ? [X4: 'C$',X5: 'C$'] :
( ( X4 != X5 )
& ( 'fun_app$m'(X2,X4) = 'fun_app$m'(X3,X5) )
& 'member$b'(X5,'set_option$c'(X1))
& 'member$b'(X4,'set_option$c'(X0)) ) ),
inference(ennf_transformation,[],[f451]) ).
tff(f451,axiom,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ( ( 'fun_app$bg'('map_option$'(X2),X0) = 'fun_app$bg'('map_option$'(X3),X1) )
& ! [X4: 'C$',X5: 'C$'] :
( ( ( 'fun_app$m'(X2,X4) = 'fun_app$m'(X3,X5) )
& 'member$b'(X5,'set_option$c'(X1))
& 'member$b'(X4,'set_option$c'(X0)) )
=> ( X4 = X5 ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom449) ).
tff(f17257,plain,
spl249_1171,
inference(avatar_split_clause,[],[f3105,f17255]) ).
tff(f17255,plain,
( spl249_1171
<=> ! [X0: 'A_option$',X3: 'A_a_fun$',X2: 'A_a_fun$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$be'('map_option$a'(X2),X0) != 'fun_app$be'('map_option$a'(X3),X1) )
| ( 'fun_app$r'(X2,sK235(X0,X1,X2,X3)) = 'fun_app$r'(X3,sK236(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1171])]) ).
tff(f3105,plain,
! [X2: 'A_a_fun$',X3: 'A_a_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$be'('map_option$a'(X2),X0) != 'fun_app$be'('map_option$a'(X3),X1) )
| ( 'fun_app$r'(X2,sK235(X0,X1,X2,X3)) = 'fun_app$r'(X3,sK236(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f1850]) ).
tff(f1850,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$be'('map_option$a'(X2),X0) != 'fun_app$be'('map_option$a'(X3),X1) )
| ( ( sK235(X0,X1,X2,X3) != sK236(X0,X1,X2,X3) )
& ( 'fun_app$r'(X2,sK235(X0,X1,X2,X3)) = 'fun_app$r'(X3,sK236(X0,X1,X2,X3)) )
& 'member$d'(sK236(X0,X1,X2,X3),'set_option$b'(X1))
& 'member$d'(sK235(X0,X1,X2,X3),'set_option$b'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK235,sK236])],[f1074,f1849]) ).
tff(f1849,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ? [X4: 'A$',X5: 'A$'] :
( ( X4 != X5 )
& ( 'fun_app$r'(X2,X4) = 'fun_app$r'(X3,X5) )
& 'member$d'(X5,'set_option$b'(X1))
& 'member$d'(X4,'set_option$b'(X0)) )
=> ( ( sK235(X0,X1,X2,X3) != sK236(X0,X1,X2,X3) )
& ( 'fun_app$r'(X2,sK235(X0,X1,X2,X3)) = 'fun_app$r'(X3,sK236(X0,X1,X2,X3)) )
& 'member$d'(sK236(X0,X1,X2,X3),'set_option$b'(X1))
& 'member$d'(sK235(X0,X1,X2,X3),'set_option$b'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1074,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$be'('map_option$a'(X2),X0) != 'fun_app$be'('map_option$a'(X3),X1) )
| ? [X4: 'A$',X5: 'A$'] :
( ( X4 != X5 )
& ( 'fun_app$r'(X2,X4) = 'fun_app$r'(X3,X5) )
& 'member$d'(X5,'set_option$b'(X1))
& 'member$d'(X4,'set_option$b'(X0)) ) ),
inference(flattening,[],[f1073]) ).
tff(f1073,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$be'('map_option$a'(X2),X0) != 'fun_app$be'('map_option$a'(X3),X1) )
| ? [X4: 'A$',X5: 'A$'] :
( ( X4 != X5 )
& ( 'fun_app$r'(X2,X4) = 'fun_app$r'(X3,X5) )
& 'member$d'(X5,'set_option$b'(X1))
& 'member$d'(X4,'set_option$b'(X0)) ) ),
inference(ennf_transformation,[],[f448]) ).
tff(f448,axiom,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ( ( 'fun_app$be'('map_option$a'(X2),X0) = 'fun_app$be'('map_option$a'(X3),X1) )
& ! [X4: 'A$',X5: 'A$'] :
( ( ( 'fun_app$r'(X2,X4) = 'fun_app$r'(X3,X5) )
& 'member$d'(X5,'set_option$b'(X1))
& 'member$d'(X4,'set_option$b'(X0)) )
=> ( X4 = X5 ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom446) ).
tff(f17253,plain,
spl249_1170,
inference(avatar_split_clause,[],[f3101,f17251]) ).
tff(f17251,plain,
( spl249_1170
<=> ! [X0: 'A_option$',X3: 'A_b_fun$',X2: 'A_b_fun$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$av'('map_option$e'(X2),X0) != 'fun_app$av'('map_option$e'(X3),X1) )
| ( 'fun_app$p'(X2,sK233(X0,X1,X2,X3)) = 'fun_app$p'(X3,sK234(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1170])]) ).
tff(f3101,plain,
! [X2: 'A_b_fun$',X3: 'A_b_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$av'('map_option$e'(X2),X0) != 'fun_app$av'('map_option$e'(X3),X1) )
| ( 'fun_app$p'(X2,sK233(X0,X1,X2,X3)) = 'fun_app$p'(X3,sK234(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f1848]) ).
tff(f1848,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$av'('map_option$e'(X2),X0) != 'fun_app$av'('map_option$e'(X3),X1) )
| ( ( sK233(X0,X1,X2,X3) != sK234(X0,X1,X2,X3) )
& ( 'fun_app$p'(X2,sK233(X0,X1,X2,X3)) = 'fun_app$p'(X3,sK234(X0,X1,X2,X3)) )
& 'member$d'(sK234(X0,X1,X2,X3),'set_option$b'(X1))
& 'member$d'(sK233(X0,X1,X2,X3),'set_option$b'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK233,sK234])],[f1072,f1847]) ).
tff(f1847,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ? [X4: 'A$',X5: 'A$'] :
( ( X4 != X5 )
& ( 'fun_app$p'(X2,X4) = 'fun_app$p'(X3,X5) )
& 'member$d'(X5,'set_option$b'(X1))
& 'member$d'(X4,'set_option$b'(X0)) )
=> ( ( sK233(X0,X1,X2,X3) != sK234(X0,X1,X2,X3) )
& ( 'fun_app$p'(X2,sK233(X0,X1,X2,X3)) = 'fun_app$p'(X3,sK234(X0,X1,X2,X3)) )
& 'member$d'(sK234(X0,X1,X2,X3),'set_option$b'(X1))
& 'member$d'(sK233(X0,X1,X2,X3),'set_option$b'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1072,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$av'('map_option$e'(X2),X0) != 'fun_app$av'('map_option$e'(X3),X1) )
| ? [X4: 'A$',X5: 'A$'] :
( ( X4 != X5 )
& ( 'fun_app$p'(X2,X4) = 'fun_app$p'(X3,X5) )
& 'member$d'(X5,'set_option$b'(X1))
& 'member$d'(X4,'set_option$b'(X0)) ) ),
inference(flattening,[],[f1071]) ).
tff(f1071,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$av'('map_option$e'(X2),X0) != 'fun_app$av'('map_option$e'(X3),X1) )
| ? [X4: 'A$',X5: 'A$'] :
( ( X4 != X5 )
& ( 'fun_app$p'(X2,X4) = 'fun_app$p'(X3,X5) )
& 'member$d'(X5,'set_option$b'(X1))
& 'member$d'(X4,'set_option$b'(X0)) ) ),
inference(ennf_transformation,[],[f447]) ).
tff(f447,axiom,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ( ( 'fun_app$av'('map_option$e'(X2),X0) = 'fun_app$av'('map_option$e'(X3),X1) )
& ! [X4: 'A$',X5: 'A$'] :
( ( ( 'fun_app$p'(X2,X4) = 'fun_app$p'(X3,X5) )
& 'member$d'(X5,'set_option$b'(X1))
& 'member$d'(X4,'set_option$b'(X0)) )
=> ( X4 = X5 ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom445) ).
tff(f17243,plain,
spl249_1169,
inference(avatar_split_clause,[],[f2782,f17241]) ).
tff(f17241,plain,
( spl249_1169
<=> ! [X2: 'B_option$',X0: 'B_b_b_fun_fun$',X1: 'B_option$'] :
( ( 'fun_app$s'('combine_options$b'(X0,X1),X2) = 'fun_app$s'('combine_options$b'(X0,X2),X1) )
| ( 'fun_app$h'('fun_app$ai'(X0,sK167(X0)),sK168(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK168(X0)),sK167(X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1169])]) ).
tff(f2782,plain,
! [X2: 'B_option$',X0: 'B_b_b_fun_fun$',X1: 'B_option$'] :
( ( 'fun_app$s'('combine_options$b'(X0,X1),X2) = 'fun_app$s'('combine_options$b'(X0,X2),X1) )
| ( 'fun_app$h'('fun_app$ai'(X0,sK167(X0)),sK168(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK168(X0)),sK167(X0)) ) ),
inference(cnf_transformation,[],[f1598]) ).
tff(f1598,plain,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$',X2: 'B_option$'] :
( ( 'fun_app$s'('combine_options$b'(X0,X1),X2) = 'fun_app$s'('combine_options$b'(X0,X2),X1) )
| ( 'fun_app$h'('fun_app$ai'(X0,sK167(X0)),sK168(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK168(X0)),sK167(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK167,sK168])],[f998,f1597]) ).
tff(f1597,plain,
! [X0: 'B_b_b_fun_fun$'] :
( ? [X3: 'B$',X4: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,X3),X4) != 'fun_app$h'('fun_app$ai'(X0,X4),X3) )
=> ( 'fun_app$h'('fun_app$ai'(X0,sK167(X0)),sK168(X0)) != 'fun_app$h'('fun_app$ai'(X0,sK168(X0)),sK167(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f998,plain,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$',X2: 'B_option$'] :
( ( 'fun_app$s'('combine_options$b'(X0,X1),X2) = 'fun_app$s'('combine_options$b'(X0,X2),X1) )
| ? [X3: 'B$',X4: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,X3),X4) != 'fun_app$h'('fun_app$ai'(X0,X4),X3) ) ),
inference(ennf_transformation,[],[f248]) ).
tff(f248,axiom,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$',X2: 'B_option$'] :
( ! [X3: 'B$',X4: 'B$'] : ( 'fun_app$h'('fun_app$ai'(X0,X3),X4) = 'fun_app$h'('fun_app$ai'(X0,X4),X3) )
=> ( 'fun_app$s'('combine_options$b'(X0,X1),X2) = 'fun_app$s'('combine_options$b'(X0,X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom246) ).
tff(f17239,plain,
spl249_1168,
inference(avatar_split_clause,[],[f2781,f17237]) ).
tff(f17237,plain,
( spl249_1168
<=> ! [X2: 'C_option$',X0: 'C_c_c_fun_fun$',X1: 'C_option$'] :
( ( 'fun_app$u'('combine_options$a'(X0,X1),X2) = 'fun_app$u'('combine_options$a'(X0,X2),X1) )
| ( 'fun_app$k'('fun_app$ah'(X0,sK165(X0)),sK166(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK166(X0)),sK165(X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1168])]) ).
tff(f2781,plain,
! [X2: 'C_option$',X0: 'C_c_c_fun_fun$',X1: 'C_option$'] :
( ( 'fun_app$u'('combine_options$a'(X0,X1),X2) = 'fun_app$u'('combine_options$a'(X0,X2),X1) )
| ( 'fun_app$k'('fun_app$ah'(X0,sK165(X0)),sK166(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK166(X0)),sK165(X0)) ) ),
inference(cnf_transformation,[],[f1596]) ).
tff(f1596,plain,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$',X2: 'C_option$'] :
( ( 'fun_app$u'('combine_options$a'(X0,X1),X2) = 'fun_app$u'('combine_options$a'(X0,X2),X1) )
| ( 'fun_app$k'('fun_app$ah'(X0,sK165(X0)),sK166(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK166(X0)),sK165(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK165,sK166])],[f997,f1595]) ).
tff(f1595,plain,
! [X0: 'C_c_c_fun_fun$'] :
( ? [X3: 'C$',X4: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,X3),X4) != 'fun_app$k'('fun_app$ah'(X0,X4),X3) )
=> ( 'fun_app$k'('fun_app$ah'(X0,sK165(X0)),sK166(X0)) != 'fun_app$k'('fun_app$ah'(X0,sK166(X0)),sK165(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f997,plain,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$',X2: 'C_option$'] :
( ( 'fun_app$u'('combine_options$a'(X0,X1),X2) = 'fun_app$u'('combine_options$a'(X0,X2),X1) )
| ? [X3: 'C$',X4: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,X3),X4) != 'fun_app$k'('fun_app$ah'(X0,X4),X3) ) ),
inference(ennf_transformation,[],[f249]) ).
tff(f249,axiom,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$',X2: 'C_option$'] :
( ! [X3: 'C$',X4: 'C$'] : ( 'fun_app$k'('fun_app$ah'(X0,X3),X4) = 'fun_app$k'('fun_app$ah'(X0,X4),X3) )
=> ( 'fun_app$u'('combine_options$a'(X0,X1),X2) = 'fun_app$u'('combine_options$a'(X0,X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom247) ).
tff(f17235,plain,
spl249_1167,
inference(avatar_split_clause,[],[f2310,f17233]) ).
tff(f17233,plain,
( spl249_1167
<=> ! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$au'(X0,'update1$'(sK113(X0,X1),sK114(X0,X1))) != 'fun_app$au'(X1,'update1$'(sK113(X0,X1),sK114(X0,X1))) )
| ~ 'preregister$c'(X1)
| ~ 'preregister$c'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1167])]) ).
tff(f2310,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$au'(X0,'update1$'(sK113(X0,X1),sK114(X0,X1))) != 'fun_app$au'(X1,'update1$'(sK113(X0,X1),sK114(X0,X1))) )
| ~ 'preregister$c'(X1)
| ~ 'preregister$c'(X0) ),
inference(cnf_transformation,[],[f1392]) ).
tff(f1392,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( X0 = X1 )
| ( 'fun_app$au'(X0,'update1$'(sK113(X0,X1),sK114(X0,X1))) != 'fun_app$au'(X1,'update1$'(sK113(X0,X1),sK114(X0,X1))) )
| ~ 'preregister$c'(X1)
| ~ 'preregister$c'(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK113,sK114])],[f929,f1391]) ).
tff(f1391,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ? [X2: 'A$',X3: 'A$'] : ( 'fun_app$au'(X0,'update1$'(X2,X3)) != 'fun_app$au'(X1,'update1$'(X2,X3)) )
=> ( 'fun_app$au'(X0,'update1$'(sK113(X0,X1),sK114(X0,X1))) != 'fun_app$au'(X1,'update1$'(sK113(X0,X1),sK114(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f929,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( X0 = X1 )
| ? [X2: 'A$',X3: 'A$'] : ( 'fun_app$au'(X0,'update1$'(X2,X3)) != 'fun_app$au'(X1,'update1$'(X2,X3)) )
| ~ 'preregister$c'(X1)
| ~ 'preregister$c'(X0) ),
inference(flattening,[],[f928]) ).
tff(f928,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( X0 = X1 )
| ? [X2: 'A$',X3: 'A$'] : ( 'fun_app$au'(X0,'update1$'(X2,X3)) != 'fun_app$au'(X1,'update1$'(X2,X3)) )
| ~ 'preregister$c'(X1)
| ~ 'preregister$c'(X0) ),
inference(ennf_transformation,[],[f260]) ).
tff(f260,axiom,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( ! [X2: 'A$',X3: 'A$'] : ( 'fun_app$au'(X0,'update1$'(X2,X3)) = 'fun_app$au'(X1,'update1$'(X2,X3)) )
& 'preregister$c'(X1)
& 'preregister$c'(X0) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom258) ).
tff(f17136,plain,
spl249_1166,
inference(avatar_split_clause,[],[f3546,f17134]) ).
tff(f17134,plain,
( spl249_1166
<=> ! [X2: 'B_c_option_fun$',X1: 'B_option$',X3: 'B_c_option_fun$'] :
( ( 'bind$b'(X1,X2) = 'bind$b'(X1,X3) )
| ( 'bind$b'('fun_app$g'('some$',sK220(X1,X2,X3)),X2) != 'bind$b'('fun_app$g'('some$',sK220(X1,X2,X3)),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1166])]) ).
tff(f3546,plain,
! [X2: 'B_c_option_fun$',X3: 'B_c_option_fun$',X1: 'B_option$'] :
( ( 'bind$b'(X1,X2) = 'bind$b'(X1,X3) )
| ( 'bind$b'('fun_app$g'('some$',sK220(X1,X2,X3)),X2) != 'bind$b'('fun_app$g'('some$',sK220(X1,X2,X3)),X3) ) ),
inference(equality_resolution,[],[f3293]) ).
tff(f3293,plain,
! [X2: 'B_c_option_fun$',X3: 'B_c_option_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'bind$b'(X0,X2) = 'bind$b'(X1,X3) )
| ( 'bind$b'('fun_app$g'('some$',sK220(X1,X2,X3)),X2) != 'bind$b'('fun_app$g'('some$',sK220(X1,X2,X3)),X3) )
| ( X0 != X1 ) ),
inference(definition_unfolding,[],[f3088,f2234,f2234]) ).
tff(f2234,plain,
! [X0: 'B$',X1: 'B_c_option_fun$'] : ( 'bind$b'('fun_app$g'('some$',X0),X1) = 'fun_app$n'(X1,X0) ),
inference(cnf_transformation,[],[f426]) ).
tff(f426,axiom,
! [X0: 'B$',X1: 'B_c_option_fun$'] : ( 'bind$b'('fun_app$g'('some$',X0),X1) = 'fun_app$n'(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom424) ).
tff(f3088,plain,
! [X2: 'B_c_option_fun$',X3: 'B_c_option_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'bind$b'(X0,X2) = 'bind$b'(X1,X3) )
| ( 'fun_app$n'(X2,sK220(X1,X2,X3)) != 'fun_app$n'(X3,sK220(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1836]) ).
tff(f1836,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_option_fun$',X3: 'B_c_option_fun$'] :
( ( 'bind$b'(X0,X2) = 'bind$b'(X1,X3) )
| ( ( 'fun_app$n'(X2,sK220(X1,X2,X3)) != 'fun_app$n'(X3,sK220(X1,X2,X3)) )
& ( 'fun_app$g'('some$',sK220(X1,X2,X3)) = X1 ) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK220])],[f1058,f1835]) ).
tff(f1835,plain,
! [X1: 'B_option$',X2: 'B_c_option_fun$',X3: 'B_c_option_fun$'] :
( ? [X4: 'B$'] :
( ( 'fun_app$n'(X2,X4) != 'fun_app$n'(X3,X4) )
& ( 'fun_app$g'('some$',X4) = X1 ) )
=> ( ( 'fun_app$n'(X2,sK220(X1,X2,X3)) != 'fun_app$n'(X3,sK220(X1,X2,X3)) )
& ( 'fun_app$g'('some$',sK220(X1,X2,X3)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1058,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_option_fun$',X3: 'B_c_option_fun$'] :
( ( 'bind$b'(X0,X2) = 'bind$b'(X1,X3) )
| ? [X4: 'B$'] :
( ( 'fun_app$n'(X2,X4) != 'fun_app$n'(X3,X4) )
& ( 'fun_app$g'('some$',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1057]) ).
tff(f1057,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_option_fun$',X3: 'B_c_option_fun$'] :
( ( 'bind$b'(X0,X2) = 'bind$b'(X1,X3) )
| ? [X4: 'B$'] :
( ( 'fun_app$n'(X2,X4) != 'fun_app$n'(X3,X4) )
& ( 'fun_app$g'('some$',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f422]) ).
tff(f422,axiom,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_option_fun$',X3: 'B_c_option_fun$'] :
( ( ! [X4: 'B$'] :
( ( 'fun_app$g'('some$',X4) = X1 )
=> ( 'fun_app$n'(X2,X4) = 'fun_app$n'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'bind$b'(X0,X2) = 'bind$b'(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom420) ).
tff(f17132,plain,
spl249_1165,
inference(avatar_split_clause,[],[f3538,f17130]) ).
tff(f17130,plain,
( spl249_1165
<=> ! [X2: 'C_b_option_fun$',X1: 'C_option$',X3: 'C_b_option_fun$'] :
( ( 'bind$a'(X1,X2) = 'bind$a'(X1,X3) )
| ( 'bind$a'('fun_app$j'('some$a',sK216(X1,X2,X3)),X2) != 'bind$a'('fun_app$j'('some$a',sK216(X1,X2,X3)),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1165])]) ).
tff(f3538,plain,
! [X2: 'C_b_option_fun$',X3: 'C_b_option_fun$',X1: 'C_option$'] :
( ( 'bind$a'(X1,X2) = 'bind$a'(X1,X3) )
| ( 'bind$a'('fun_app$j'('some$a',sK216(X1,X2,X3)),X2) != 'bind$a'('fun_app$j'('some$a',sK216(X1,X2,X3)),X3) ) ),
inference(equality_resolution,[],[f3292]) ).
tff(f3292,plain,
! [X2: 'C_b_option_fun$',X3: 'C_b_option_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'bind$a'(X0,X2) = 'bind$a'(X1,X3) )
| ( 'bind$a'('fun_app$j'('some$a',sK216(X1,X2,X3)),X2) != 'bind$a'('fun_app$j'('some$a',sK216(X1,X2,X3)),X3) )
| ( X0 != X1 ) ),
inference(definition_unfolding,[],[f3080,f2233,f2233]) ).
tff(f2233,plain,
! [X0: 'C$',X1: 'C_b_option_fun$'] : ( 'bind$a'('fun_app$j'('some$a',X0),X1) = 'fun_app$l'(X1,X0) ),
inference(cnf_transformation,[],[f423]) ).
tff(f423,axiom,
! [X0: 'C$',X1: 'C_b_option_fun$'] : ( 'bind$a'('fun_app$j'('some$a',X0),X1) = 'fun_app$l'(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom421) ).
tff(f3080,plain,
! [X2: 'C_b_option_fun$',X3: 'C_b_option_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'bind$a'(X0,X2) = 'bind$a'(X1,X3) )
| ( 'fun_app$l'(X2,sK216(X1,X2,X3)) != 'fun_app$l'(X3,sK216(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1828]) ).
tff(f1828,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_option_fun$',X3: 'C_b_option_fun$'] :
( ( 'bind$a'(X0,X2) = 'bind$a'(X1,X3) )
| ( ( 'fun_app$l'(X2,sK216(X1,X2,X3)) != 'fun_app$l'(X3,sK216(X1,X2,X3)) )
& ( 'fun_app$j'('some$a',sK216(X1,X2,X3)) = X1 ) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK216])],[f1050,f1827]) ).
tff(f1827,plain,
! [X1: 'C_option$',X2: 'C_b_option_fun$',X3: 'C_b_option_fun$'] :
( ? [X4: 'C$'] :
( ( 'fun_app$l'(X2,X4) != 'fun_app$l'(X3,X4) )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
=> ( ( 'fun_app$l'(X2,sK216(X1,X2,X3)) != 'fun_app$l'(X3,sK216(X1,X2,X3)) )
& ( 'fun_app$j'('some$a',sK216(X1,X2,X3)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1050,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_option_fun$',X3: 'C_b_option_fun$'] :
( ( 'bind$a'(X0,X2) = 'bind$a'(X1,X3) )
| ? [X4: 'C$'] :
( ( 'fun_app$l'(X2,X4) != 'fun_app$l'(X3,X4) )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1049]) ).
tff(f1049,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_option_fun$',X3: 'C_b_option_fun$'] :
( ( 'bind$a'(X0,X2) = 'bind$a'(X1,X3) )
| ? [X4: 'C$'] :
( ( 'fun_app$l'(X2,X4) != 'fun_app$l'(X3,X4) )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f419]) ).
tff(f419,axiom,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_option_fun$',X3: 'C_b_option_fun$'] :
( ( ! [X4: 'C$'] :
( ( 'fun_app$j'('some$a',X4) = X1 )
=> ( 'fun_app$l'(X2,X4) = 'fun_app$l'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'bind$a'(X0,X2) = 'bind$a'(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom417) ).
tff(f17128,plain,
spl249_1164,
inference(avatar_split_clause,[],[f3528,f17126]) ).
tff(f17126,plain,
( spl249_1164
<=> ! [X2: 'B_c_option_fun$',X1: 'B_option$',X3: 'B_c_option_fun$'] :
( ( 'bind$b'(X1,X2) = 'bind$b'(X1,X3) )
| ( 'bind$b'('fun_app$g'('some$',sK211(X1,X2,X3)),X2) != 'bind$b'('fun_app$g'('some$',sK211(X1,X2,X3)),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1164])]) ).
tff(f3528,plain,
! [X2: 'B_c_option_fun$',X3: 'B_c_option_fun$',X1: 'B_option$'] :
( ( 'bind$b'(X1,X2) = 'bind$b'(X1,X3) )
| ( 'bind$b'('fun_app$g'('some$',sK211(X1,X2,X3)),X2) != 'bind$b'('fun_app$g'('some$',sK211(X1,X2,X3)),X3) ) ),
inference(equality_resolution,[],[f3291]) ).
tff(f3291,plain,
! [X2: 'B_c_option_fun$',X3: 'B_c_option_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'bind$b'(X0,X2) = 'bind$b'(X1,X3) )
| ( 'bind$b'('fun_app$g'('some$',sK211(X1,X2,X3)),X2) != 'bind$b'('fun_app$g'('some$',sK211(X1,X2,X3)),X3) )
| ( X0 != X1 ) ),
inference(definition_unfolding,[],[f3070,f2234,f2234]) ).
tff(f3070,plain,
! [X2: 'B_c_option_fun$',X3: 'B_c_option_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'bind$b'(X0,X2) = 'bind$b'(X1,X3) )
| ( 'fun_app$n'(X2,sK211(X1,X2,X3)) != 'fun_app$n'(X3,sK211(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1818]) ).
tff(f1818,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_option_fun$',X3: 'B_c_option_fun$'] :
( ( 'bind$b'(X0,X2) = 'bind$b'(X1,X3) )
| ( ( 'fun_app$n'(X2,sK211(X1,X2,X3)) != 'fun_app$n'(X3,sK211(X1,X2,X3)) )
& 'member$c'(sK211(X1,X2,X3),'set_option$d'(X1)) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK211])],[f1040,f1817]) ).
tff(f1817,plain,
! [X1: 'B_option$',X2: 'B_c_option_fun$',X3: 'B_c_option_fun$'] :
( ? [X4: 'B$'] :
( ( 'fun_app$n'(X2,X4) != 'fun_app$n'(X3,X4) )
& 'member$c'(X4,'set_option$d'(X1)) )
=> ( ( 'fun_app$n'(X2,sK211(X1,X2,X3)) != 'fun_app$n'(X3,sK211(X1,X2,X3)) )
& 'member$c'(sK211(X1,X2,X3),'set_option$d'(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1040,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_option_fun$',X3: 'B_c_option_fun$'] :
( ( 'bind$b'(X0,X2) = 'bind$b'(X1,X3) )
| ? [X4: 'B$'] :
( ( 'fun_app$n'(X2,X4) != 'fun_app$n'(X3,X4) )
& 'member$c'(X4,'set_option$d'(X1)) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1039]) ).
tff(f1039,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_option_fun$',X3: 'B_c_option_fun$'] :
( ( 'bind$b'(X0,X2) = 'bind$b'(X1,X3) )
| ? [X4: 'B$'] :
( ( 'fun_app$n'(X2,X4) != 'fun_app$n'(X3,X4) )
& 'member$c'(X4,'set_option$d'(X1)) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f392]) ).
tff(f392,axiom,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_option_fun$',X3: 'B_c_option_fun$'] :
( ( ! [X4: 'B$'] :
( 'member$c'(X4,'set_option$d'(X1))
=> ( 'fun_app$n'(X2,X4) = 'fun_app$n'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'bind$b'(X0,X2) = 'bind$b'(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom390) ).
tff(f17124,plain,
spl249_1163,
inference(avatar_split_clause,[],[f3520,f17122]) ).
tff(f17122,plain,
( spl249_1163
<=> ! [X2: 'C_b_option_fun$',X1: 'C_option$',X3: 'C_b_option_fun$'] :
( ( 'bind$a'(X1,X2) = 'bind$a'(X1,X3) )
| ( 'bind$a'('fun_app$j'('some$a',sK207(X1,X2,X3)),X2) != 'bind$a'('fun_app$j'('some$a',sK207(X1,X2,X3)),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1163])]) ).
tff(f3520,plain,
! [X2: 'C_b_option_fun$',X3: 'C_b_option_fun$',X1: 'C_option$'] :
( ( 'bind$a'(X1,X2) = 'bind$a'(X1,X3) )
| ( 'bind$a'('fun_app$j'('some$a',sK207(X1,X2,X3)),X2) != 'bind$a'('fun_app$j'('some$a',sK207(X1,X2,X3)),X3) ) ),
inference(equality_resolution,[],[f3290]) ).
tff(f3290,plain,
! [X2: 'C_b_option_fun$',X3: 'C_b_option_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'bind$a'(X0,X2) = 'bind$a'(X1,X3) )
| ( 'bind$a'('fun_app$j'('some$a',sK207(X1,X2,X3)),X2) != 'bind$a'('fun_app$j'('some$a',sK207(X1,X2,X3)),X3) )
| ( X0 != X1 ) ),
inference(definition_unfolding,[],[f3062,f2233,f2233]) ).
tff(f3062,plain,
! [X2: 'C_b_option_fun$',X3: 'C_b_option_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'bind$a'(X0,X2) = 'bind$a'(X1,X3) )
| ( 'fun_app$l'(X2,sK207(X1,X2,X3)) != 'fun_app$l'(X3,sK207(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1810]) ).
tff(f1810,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_option_fun$',X3: 'C_b_option_fun$'] :
( ( 'bind$a'(X0,X2) = 'bind$a'(X1,X3) )
| ( ( 'fun_app$l'(X2,sK207(X1,X2,X3)) != 'fun_app$l'(X3,sK207(X1,X2,X3)) )
& 'member$b'(sK207(X1,X2,X3),'set_option$c'(X1)) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK207])],[f1032,f1809]) ).
tff(f1809,plain,
! [X1: 'C_option$',X2: 'C_b_option_fun$',X3: 'C_b_option_fun$'] :
( ? [X4: 'C$'] :
( ( 'fun_app$l'(X2,X4) != 'fun_app$l'(X3,X4) )
& 'member$b'(X4,'set_option$c'(X1)) )
=> ( ( 'fun_app$l'(X2,sK207(X1,X2,X3)) != 'fun_app$l'(X3,sK207(X1,X2,X3)) )
& 'member$b'(sK207(X1,X2,X3),'set_option$c'(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1032,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_option_fun$',X3: 'C_b_option_fun$'] :
( ( 'bind$a'(X0,X2) = 'bind$a'(X1,X3) )
| ? [X4: 'C$'] :
( ( 'fun_app$l'(X2,X4) != 'fun_app$l'(X3,X4) )
& 'member$b'(X4,'set_option$c'(X1)) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1031]) ).
tff(f1031,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_option_fun$',X3: 'C_b_option_fun$'] :
( ( 'bind$a'(X0,X2) = 'bind$a'(X1,X3) )
| ? [X4: 'C$'] :
( ( 'fun_app$l'(X2,X4) != 'fun_app$l'(X3,X4) )
& 'member$b'(X4,'set_option$c'(X1)) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f393]) ).
tff(f393,axiom,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_option_fun$',X3: 'C_b_option_fun$'] :
( ( ! [X4: 'C$'] :
( 'member$b'(X4,'set_option$c'(X1))
=> ( 'fun_app$l'(X2,X4) = 'fun_app$l'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'bind$a'(X0,X2) = 'bind$a'(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom391) ).
tff(f17120,plain,
spl249_1162,
inference(avatar_split_clause,[],[f3118,f17118]) ).
tff(f17118,plain,
( spl249_1162
<=> ! [X0: 'B_option$',X3: 'B_b_fun$',X2: 'B_b_fun$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$s'('map_option$b'(X2),X0) != 'fun_app$s'('map_option$b'(X3),X1) )
| ( sK241(X0,X1,X2,X3) != sK242(X0,X1,X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1162])]) ).
tff(f3118,plain,
! [X2: 'B_b_fun$',X3: 'B_b_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$s'('map_option$b'(X2),X0) != 'fun_app$s'('map_option$b'(X3),X1) )
| ( sK241(X0,X1,X2,X3) != sK242(X0,X1,X2,X3) ) ),
inference(cnf_transformation,[],[f1856]) ).
tff(f17116,plain,
( spl249_1161
| ~ spl249_11
| ~ spl249_368 ),
inference(avatar_split_clause,[],[f5895,f5488,f3655,f17113]) ).
tff(f17113,plain,
( spl249_1161
<=> ( sK46 = 'setter$a'('register_from_getter_setter$'(sK47,sK46)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1161])]) ).
tff(f3655,plain,
( spl249_11
<=> 'valid_getter_setter$a'(sK47,sK46) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_11])]) ).
tff(f5488,plain,
( spl249_368
<=> ! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ( 'setter$a'('register_from_getter_setter$'(X0,X1)) = X1 )
| ~ 'valid_getter_setter$a'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_368])]) ).
tff(f5895,plain,
( ( sK46 = 'setter$a'('register_from_getter_setter$'(sK47,sK46)) )
| ~ spl249_11
| ~ spl249_368 ),
inference(resolution,[],[f5489,f3657]) ).
tff(f3657,plain,
( 'valid_getter_setter$a'(sK47,sK46)
| ~ spl249_11 ),
inference(avatar_component_clause,[],[f3655]) ).
tff(f5489,plain,
( ! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ~ 'valid_getter_setter$a'(X0,X1)
| ( 'setter$a'('register_from_getter_setter$'(X0,X1)) = X1 ) )
| ~ spl249_368 ),
inference(avatar_component_clause,[],[f5488]) ).
tff(f17111,plain,
spl249_1160,
inference(avatar_split_clause,[],[f3114,f17109]) ).
tff(f17109,plain,
( spl249_1160
<=> ! [X0: 'B_option$',X3: 'B_c_fun$',X2: 'B_c_fun$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$an'('map_option$d'(X2),X0) != 'fun_app$an'('map_option$d'(X3),X1) )
| ( sK239(X0,X1,X2,X3) != sK240(X0,X1,X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1160])]) ).
tff(f3114,plain,
! [X2: 'B_c_fun$',X3: 'B_c_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$an'('map_option$d'(X2),X0) != 'fun_app$an'('map_option$d'(X3),X1) )
| ( sK239(X0,X1,X2,X3) != sK240(X0,X1,X2,X3) ) ),
inference(cnf_transformation,[],[f1854]) ).
tff(f17107,plain,
spl249_1159,
inference(avatar_split_clause,[],[f3110,f17105]) ).
tff(f17105,plain,
( spl249_1159
<=> ! [X0: 'C_option$',X3: 'C_b_fun$',X2: 'C_b_fun$',X1: 'C_option$'] :
( ( X0 = X1 )
| ( 'fun_app$bg'('map_option$'(X2),X0) != 'fun_app$bg'('map_option$'(X3),X1) )
| ( sK237(X0,X1,X2,X3) != sK238(X0,X1,X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1159])]) ).
tff(f3110,plain,
! [X2: 'C_b_fun$',X3: 'C_b_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( X0 = X1 )
| ( 'fun_app$bg'('map_option$'(X2),X0) != 'fun_app$bg'('map_option$'(X3),X1) )
| ( sK237(X0,X1,X2,X3) != sK238(X0,X1,X2,X3) ) ),
inference(cnf_transformation,[],[f1852]) ).
tff(f17103,plain,
spl249_1158,
inference(avatar_split_clause,[],[f3106,f17101]) ).
tff(f17101,plain,
( spl249_1158
<=> ! [X0: 'A_option$',X3: 'A_a_fun$',X2: 'A_a_fun$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$be'('map_option$a'(X2),X0) != 'fun_app$be'('map_option$a'(X3),X1) )
| ( sK235(X0,X1,X2,X3) != sK236(X0,X1,X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1158])]) ).
tff(f3106,plain,
! [X2: 'A_a_fun$',X3: 'A_a_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$be'('map_option$a'(X2),X0) != 'fun_app$be'('map_option$a'(X3),X1) )
| ( sK235(X0,X1,X2,X3) != sK236(X0,X1,X2,X3) ) ),
inference(cnf_transformation,[],[f1850]) ).
tff(f17099,plain,
spl249_1157,
inference(avatar_split_clause,[],[f3102,f17097]) ).
tff(f17097,plain,
( spl249_1157
<=> ! [X0: 'A_option$',X3: 'A_b_fun$',X2: 'A_b_fun$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$av'('map_option$e'(X2),X0) != 'fun_app$av'('map_option$e'(X3),X1) )
| ( sK233(X0,X1,X2,X3) != sK234(X0,X1,X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1157])]) ).
tff(f3102,plain,
! [X2: 'A_b_fun$',X3: 'A_b_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$av'('map_option$e'(X2),X0) != 'fun_app$av'('map_option$e'(X3),X1) )
| ( sK233(X0,X1,X2,X3) != sK234(X0,X1,X2,X3) ) ),
inference(cnf_transformation,[],[f1848]) ).
tff(f17019,plain,
( spl249_1156
| ~ spl249_7
| ~ spl249_368 ),
inference(avatar_split_clause,[],[f5894,f5488,f3635,f17016]) ).
tff(f17016,plain,
( spl249_1156
<=> ( 'sF$' = 'setter$a'('register_from_getter_setter$'('gF$','sF$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1156])]) ).
tff(f3635,plain,
( spl249_7
<=> 'valid_getter_setter$a'('gF$','sF$') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_7])]) ).
tff(f5894,plain,
( ( 'sF$' = 'setter$a'('register_from_getter_setter$'('gF$','sF$')) )
| ~ spl249_7
| ~ spl249_368 ),
inference(resolution,[],[f5489,f3637]) ).
tff(f3637,plain,
( 'valid_getter_setter$a'('gF$','sF$')
| ~ spl249_7 ),
inference(avatar_component_clause,[],[f3635]) ).
tff(f16928,plain,
( spl249_1155
| ~ spl249_11
| ~ spl249_367 ),
inference(avatar_split_clause,[],[f5892,f5484,f3655,f16925]) ).
tff(f16925,plain,
( spl249_1155
<=> ( sK47 = 'getter$a'('register_from_getter_setter$'(sK47,sK46)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1155])]) ).
tff(f5484,plain,
( spl249_367
<=> ! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ( 'getter$a'('register_from_getter_setter$'(X0,X1)) = X0 )
| ~ 'valid_getter_setter$a'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_367])]) ).
tff(f5892,plain,
( ( sK47 = 'getter$a'('register_from_getter_setter$'(sK47,sK46)) )
| ~ spl249_11
| ~ spl249_367 ),
inference(resolution,[],[f5485,f3657]) ).
tff(f5485,plain,
( ! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ~ 'valid_getter_setter$a'(X0,X1)
| ( 'getter$a'('register_from_getter_setter$'(X0,X1)) = X0 ) )
| ~ spl249_367 ),
inference(avatar_component_clause,[],[f5484]) ).
tff(f16908,plain,
spl249_1154,
inference(avatar_split_clause,[],[f3550,f16906]) ).
tff(f16906,plain,
( spl249_1154
<=> ! [X2: 'B_b_option_fun$',X1: 'B_option$',X3: 'B_b_option_fun$'] :
( ( 'fun_app$ac'('bind$c'(X1),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ( 'fun_app$g'(X2,sK222(X1,X2,X3)) != 'fun_app$g'(X3,sK222(X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1154])]) ).
tff(f3550,plain,
! [X2: 'B_b_option_fun$',X3: 'B_b_option_fun$',X1: 'B_option$'] :
( ( 'fun_app$ac'('bind$c'(X1),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ( 'fun_app$g'(X2,sK222(X1,X2,X3)) != 'fun_app$g'(X3,sK222(X1,X2,X3)) ) ),
inference(equality_resolution,[],[f3092]) ).
tff(f3092,plain,
! [X2: 'B_b_option_fun$',X3: 'B_b_option_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$ac'('bind$c'(X0),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ( 'fun_app$g'(X2,sK222(X1,X2,X3)) != 'fun_app$g'(X3,sK222(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1840]) ).
tff(f1840,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_b_option_fun$'] :
( ( 'fun_app$ac'('bind$c'(X0),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ( ( 'fun_app$g'(X2,sK222(X1,X2,X3)) != 'fun_app$g'(X3,sK222(X1,X2,X3)) )
& ( 'fun_app$g'('some$',sK222(X1,X2,X3)) = X1 ) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK222])],[f1062,f1839]) ).
tff(f1839,plain,
! [X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_b_option_fun$'] :
( ? [X4: 'B$'] :
( ( 'fun_app$g'(X2,X4) != 'fun_app$g'(X3,X4) )
& ( 'fun_app$g'('some$',X4) = X1 ) )
=> ( ( 'fun_app$g'(X2,sK222(X1,X2,X3)) != 'fun_app$g'(X3,sK222(X1,X2,X3)) )
& ( 'fun_app$g'('some$',sK222(X1,X2,X3)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1062,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_b_option_fun$'] :
( ( 'fun_app$ac'('bind$c'(X0),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ? [X4: 'B$'] :
( ( 'fun_app$g'(X2,X4) != 'fun_app$g'(X3,X4) )
& ( 'fun_app$g'('some$',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1061]) ).
tff(f1061,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_b_option_fun$'] :
( ( 'fun_app$ac'('bind$c'(X0),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ? [X4: 'B$'] :
( ( 'fun_app$g'(X2,X4) != 'fun_app$g'(X3,X4) )
& ( 'fun_app$g'('some$',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f421]) ).
tff(f421,axiom,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_b_option_fun$'] :
( ( ! [X4: 'B$'] :
( ( 'fun_app$g'('some$',X4) = X1 )
=> ( 'fun_app$g'(X2,X4) = 'fun_app$g'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'fun_app$ac'('bind$c'(X0),X2) = 'fun_app$ac'('bind$c'(X1),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom419) ).
tff(f16904,plain,
spl249_1153,
inference(avatar_split_clause,[],[f3548,f16902]) ).
tff(f16902,plain,
( spl249_1153
<=> ! [X2: 'B_b_fun$',X1: 'B_option$',X3: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X3),X1) = 'fun_app$s'('map_option$b'(X2),X1) )
| ( 'fun_app$h'(X2,sK221(X1,X2,X3)) != 'fun_app$h'(X3,sK221(X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1153])]) ).
tff(f3548,plain,
! [X2: 'B_b_fun$',X3: 'B_b_fun$',X1: 'B_option$'] :
( ( 'fun_app$s'('map_option$b'(X3),X1) = 'fun_app$s'('map_option$b'(X2),X1) )
| ( 'fun_app$h'(X2,sK221(X1,X2,X3)) != 'fun_app$h'(X3,sK221(X1,X2,X3)) ) ),
inference(equality_resolution,[],[f3090]) ).
tff(f3090,plain,
! [X2: 'B_b_fun$',X3: 'B_b_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$s'('map_option$b'(X2),X0) = 'fun_app$s'('map_option$b'(X3),X1) )
| ( 'fun_app$h'(X2,sK221(X1,X2,X3)) != 'fun_app$h'(X3,sK221(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1838]) ).
tff(f1838,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X2),X0) = 'fun_app$s'('map_option$b'(X3),X1) )
| ( ( 'fun_app$h'(X2,sK221(X1,X2,X3)) != 'fun_app$h'(X3,sK221(X1,X2,X3)) )
& ( 'fun_app$g'('some$',sK221(X1,X2,X3)) = X1 ) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK221])],[f1060,f1837]) ).
tff(f1837,plain,
! [X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ? [X4: 'B$'] :
( ( 'fun_app$h'(X2,X4) != 'fun_app$h'(X3,X4) )
& ( 'fun_app$g'('some$',X4) = X1 ) )
=> ( ( 'fun_app$h'(X2,sK221(X1,X2,X3)) != 'fun_app$h'(X3,sK221(X1,X2,X3)) )
& ( 'fun_app$g'('some$',sK221(X1,X2,X3)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1060,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X2),X0) = 'fun_app$s'('map_option$b'(X3),X1) )
| ? [X4: 'B$'] :
( ( 'fun_app$h'(X2,X4) != 'fun_app$h'(X3,X4) )
& ( 'fun_app$g'('some$',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1059]) ).
tff(f1059,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X2),X0) = 'fun_app$s'('map_option$b'(X3),X1) )
| ? [X4: 'B$'] :
( ( 'fun_app$h'(X2,X4) != 'fun_app$h'(X3,X4) )
& ( 'fun_app$g'('some$',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f293]) ).
tff(f293,axiom,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ( ! [X4: 'B$'] :
( ( 'fun_app$g'('some$',X4) = X1 )
=> ( 'fun_app$h'(X2,X4) = 'fun_app$h'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'fun_app$s'('map_option$b'(X2),X0) = 'fun_app$s'('map_option$b'(X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom291) ).
tff(f16900,plain,
spl249_1152,
inference(avatar_split_clause,[],[f3544,f16898]) ).
tff(f16898,plain,
( spl249_1152
<=> ! [X2: 'B_c_fun$',X1: 'B_option$',X3: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X3),X1) = 'fun_app$an'('map_option$d'(X2),X1) )
| ( 'fun_app$o'(X2,sK219(X1,X2,X3)) != 'fun_app$o'(X3,sK219(X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1152])]) ).
tff(f3544,plain,
! [X2: 'B_c_fun$',X3: 'B_c_fun$',X1: 'B_option$'] :
( ( 'fun_app$an'('map_option$d'(X3),X1) = 'fun_app$an'('map_option$d'(X2),X1) )
| ( 'fun_app$o'(X2,sK219(X1,X2,X3)) != 'fun_app$o'(X3,sK219(X1,X2,X3)) ) ),
inference(equality_resolution,[],[f3086]) ).
tff(f3086,plain,
! [X2: 'B_c_fun$',X3: 'B_c_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$an'('map_option$d'(X2),X0) = 'fun_app$an'('map_option$d'(X3),X1) )
| ( 'fun_app$o'(X2,sK219(X1,X2,X3)) != 'fun_app$o'(X3,sK219(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1834]) ).
tff(f1834,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X2),X0) = 'fun_app$an'('map_option$d'(X3),X1) )
| ( ( 'fun_app$o'(X2,sK219(X1,X2,X3)) != 'fun_app$o'(X3,sK219(X1,X2,X3)) )
& ( 'fun_app$g'('some$',sK219(X1,X2,X3)) = X1 ) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK219])],[f1056,f1833]) ).
tff(f1833,plain,
! [X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ? [X4: 'B$'] :
( ( 'fun_app$o'(X2,X4) != 'fun_app$o'(X3,X4) )
& ( 'fun_app$g'('some$',X4) = X1 ) )
=> ( ( 'fun_app$o'(X2,sK219(X1,X2,X3)) != 'fun_app$o'(X3,sK219(X1,X2,X3)) )
& ( 'fun_app$g'('some$',sK219(X1,X2,X3)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1056,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X2),X0) = 'fun_app$an'('map_option$d'(X3),X1) )
| ? [X4: 'B$'] :
( ( 'fun_app$o'(X2,X4) != 'fun_app$o'(X3,X4) )
& ( 'fun_app$g'('some$',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1055]) ).
tff(f1055,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X2),X0) = 'fun_app$an'('map_option$d'(X3),X1) )
| ? [X4: 'B$'] :
( ( 'fun_app$o'(X2,X4) != 'fun_app$o'(X3,X4) )
& ( 'fun_app$g'('some$',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f292]) ).
tff(f292,axiom,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ( ! [X4: 'B$'] :
( ( 'fun_app$g'('some$',X4) = X1 )
=> ( 'fun_app$o'(X2,X4) = 'fun_app$o'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'fun_app$an'('map_option$d'(X2),X0) = 'fun_app$an'('map_option$d'(X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom290) ).
tff(f16896,plain,
spl249_1151,
inference(avatar_split_clause,[],[f3542,f16894]) ).
tff(f16894,plain,
( spl249_1151
<=> ! [X2: 'C_c_option_fun$',X1: 'C_option$',X3: 'C_c_option_fun$'] :
( ( 'fun_app$ab'('bind$'(X1),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ( 'fun_app$j'(X2,sK218(X1,X2,X3)) != 'fun_app$j'(X3,sK218(X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1151])]) ).
tff(f3542,plain,
! [X2: 'C_c_option_fun$',X3: 'C_c_option_fun$',X1: 'C_option$'] :
( ( 'fun_app$ab'('bind$'(X1),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ( 'fun_app$j'(X2,sK218(X1,X2,X3)) != 'fun_app$j'(X3,sK218(X1,X2,X3)) ) ),
inference(equality_resolution,[],[f3084]) ).
tff(f3084,plain,
! [X2: 'C_c_option_fun$',X3: 'C_c_option_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$ab'('bind$'(X0),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ( 'fun_app$j'(X2,sK218(X1,X2,X3)) != 'fun_app$j'(X3,sK218(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1832]) ).
tff(f1832,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_c_option_fun$'] :
( ( 'fun_app$ab'('bind$'(X0),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ( ( 'fun_app$j'(X2,sK218(X1,X2,X3)) != 'fun_app$j'(X3,sK218(X1,X2,X3)) )
& ( 'fun_app$j'('some$a',sK218(X1,X2,X3)) = X1 ) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK218])],[f1054,f1831]) ).
tff(f1831,plain,
! [X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_c_option_fun$'] :
( ? [X4: 'C$'] :
( ( 'fun_app$j'(X2,X4) != 'fun_app$j'(X3,X4) )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
=> ( ( 'fun_app$j'(X2,sK218(X1,X2,X3)) != 'fun_app$j'(X3,sK218(X1,X2,X3)) )
& ( 'fun_app$j'('some$a',sK218(X1,X2,X3)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1054,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_c_option_fun$'] :
( ( 'fun_app$ab'('bind$'(X0),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ? [X4: 'C$'] :
( ( 'fun_app$j'(X2,X4) != 'fun_app$j'(X3,X4) )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1053]) ).
tff(f1053,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_c_option_fun$'] :
( ( 'fun_app$ab'('bind$'(X0),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ? [X4: 'C$'] :
( ( 'fun_app$j'(X2,X4) != 'fun_app$j'(X3,X4) )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f420]) ).
tff(f420,axiom,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_c_option_fun$'] :
( ( ! [X4: 'C$'] :
( ( 'fun_app$j'('some$a',X4) = X1 )
=> ( 'fun_app$j'(X2,X4) = 'fun_app$j'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'fun_app$ab'('bind$'(X0),X2) = 'fun_app$ab'('bind$'(X1),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom418) ).
tff(f16892,plain,
spl249_1150,
inference(avatar_split_clause,[],[f3540,f16890]) ).
tff(f16890,plain,
( spl249_1150
<=> ! [X2: 'C_b_fun$',X1: 'C_option$',X3: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X3),X1) = 'fun_app$bg'('map_option$'(X2),X1) )
| ( 'fun_app$m'(X2,sK217(X1,X2,X3)) != 'fun_app$m'(X3,sK217(X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1150])]) ).
tff(f3540,plain,
! [X2: 'C_b_fun$',X3: 'C_b_fun$',X1: 'C_option$'] :
( ( 'fun_app$bg'('map_option$'(X3),X1) = 'fun_app$bg'('map_option$'(X2),X1) )
| ( 'fun_app$m'(X2,sK217(X1,X2,X3)) != 'fun_app$m'(X3,sK217(X1,X2,X3)) ) ),
inference(equality_resolution,[],[f3082]) ).
tff(f3082,plain,
! [X2: 'C_b_fun$',X3: 'C_b_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$bg'('map_option$'(X2),X0) = 'fun_app$bg'('map_option$'(X3),X1) )
| ( 'fun_app$m'(X2,sK217(X1,X2,X3)) != 'fun_app$m'(X3,sK217(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1830]) ).
tff(f1830,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X2),X0) = 'fun_app$bg'('map_option$'(X3),X1) )
| ( ( 'fun_app$m'(X2,sK217(X1,X2,X3)) != 'fun_app$m'(X3,sK217(X1,X2,X3)) )
& ( 'fun_app$j'('some$a',sK217(X1,X2,X3)) = X1 ) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK217])],[f1052,f1829]) ).
tff(f1829,plain,
! [X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ? [X4: 'C$'] :
( ( 'fun_app$m'(X2,X4) != 'fun_app$m'(X3,X4) )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
=> ( ( 'fun_app$m'(X2,sK217(X1,X2,X3)) != 'fun_app$m'(X3,sK217(X1,X2,X3)) )
& ( 'fun_app$j'('some$a',sK217(X1,X2,X3)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1052,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X2),X0) = 'fun_app$bg'('map_option$'(X3),X1) )
| ? [X4: 'C$'] :
( ( 'fun_app$m'(X2,X4) != 'fun_app$m'(X3,X4) )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1051]) ).
tff(f1051,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X2),X0) = 'fun_app$bg'('map_option$'(X3),X1) )
| ? [X4: 'C$'] :
( ( 'fun_app$m'(X2,X4) != 'fun_app$m'(X3,X4) )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f291]) ).
tff(f291,axiom,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ( ! [X4: 'C$'] :
( ( 'fun_app$j'('some$a',X4) = X1 )
=> ( 'fun_app$m'(X2,X4) = 'fun_app$m'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'fun_app$bg'('map_option$'(X2),X0) = 'fun_app$bg'('map_option$'(X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom289) ).
tff(f16888,plain,
( spl249_1149
| ~ spl249_7
| ~ spl249_367 ),
inference(avatar_split_clause,[],[f5891,f5484,f3635,f16885]) ).
tff(f16885,plain,
( spl249_1149
<=> ( 'gF$' = 'getter$a'('register_from_getter_setter$'('gF$','sF$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1149])]) ).
tff(f5891,plain,
( ( 'gF$' = 'getter$a'('register_from_getter_setter$'('gF$','sF$')) )
| ~ spl249_7
| ~ spl249_367 ),
inference(resolution,[],[f5485,f3637]) ).
tff(f16883,plain,
spl249_1148,
inference(avatar_split_clause,[],[f3536,f16881]) ).
tff(f16881,plain,
( spl249_1148
<=> ! [X2: 'A_a_fun$',X1: 'A_option$',X3: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X3),X1) = 'fun_app$be'('map_option$a'(X2),X1) )
| ( 'fun_app$r'(X2,sK215(X1,X2,X3)) != 'fun_app$r'(X3,sK215(X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1148])]) ).
tff(f3536,plain,
! [X2: 'A_a_fun$',X3: 'A_a_fun$',X1: 'A_option$'] :
( ( 'fun_app$be'('map_option$a'(X3),X1) = 'fun_app$be'('map_option$a'(X2),X1) )
| ( 'fun_app$r'(X2,sK215(X1,X2,X3)) != 'fun_app$r'(X3,sK215(X1,X2,X3)) ) ),
inference(equality_resolution,[],[f3078]) ).
tff(f3078,plain,
! [X2: 'A_a_fun$',X3: 'A_a_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$be'('map_option$a'(X2),X0) = 'fun_app$be'('map_option$a'(X3),X1) )
| ( 'fun_app$r'(X2,sK215(X1,X2,X3)) != 'fun_app$r'(X3,sK215(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1826]) ).
tff(f1826,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X2),X0) = 'fun_app$be'('map_option$a'(X3),X1) )
| ( ( 'fun_app$r'(X2,sK215(X1,X2,X3)) != 'fun_app$r'(X3,sK215(X1,X2,X3)) )
& ( 'fun_app$q'('some$b',sK215(X1,X2,X3)) = X1 ) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK215])],[f1048,f1825]) ).
tff(f1825,plain,
! [X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ? [X4: 'A$'] :
( ( 'fun_app$r'(X2,X4) != 'fun_app$r'(X3,X4) )
& ( 'fun_app$q'('some$b',X4) = X1 ) )
=> ( ( 'fun_app$r'(X2,sK215(X1,X2,X3)) != 'fun_app$r'(X3,sK215(X1,X2,X3)) )
& ( 'fun_app$q'('some$b',sK215(X1,X2,X3)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1048,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X2),X0) = 'fun_app$be'('map_option$a'(X3),X1) )
| ? [X4: 'A$'] :
( ( 'fun_app$r'(X2,X4) != 'fun_app$r'(X3,X4) )
& ( 'fun_app$q'('some$b',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1047]) ).
tff(f1047,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X2),X0) = 'fun_app$be'('map_option$a'(X3),X1) )
| ? [X4: 'A$'] :
( ( 'fun_app$r'(X2,X4) != 'fun_app$r'(X3,X4) )
& ( 'fun_app$q'('some$b',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f295]) ).
tff(f295,axiom,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ( ! [X4: 'A$'] :
( ( 'fun_app$q'('some$b',X4) = X1 )
=> ( 'fun_app$r'(X2,X4) = 'fun_app$r'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'fun_app$be'('map_option$a'(X2),X0) = 'fun_app$be'('map_option$a'(X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom293) ).
tff(f16879,plain,
spl249_1147,
inference(avatar_split_clause,[],[f3534,f16877]) ).
tff(f16877,plain,
( spl249_1147
<=> ! [X2: 'A_b_fun$',X1: 'A_option$',X3: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X3),X1) = 'fun_app$av'('map_option$e'(X2),X1) )
| ( 'fun_app$p'(X2,sK214(X1,X2,X3)) != 'fun_app$p'(X3,sK214(X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1147])]) ).
tff(f3534,plain,
! [X2: 'A_b_fun$',X3: 'A_b_fun$',X1: 'A_option$'] :
( ( 'fun_app$av'('map_option$e'(X3),X1) = 'fun_app$av'('map_option$e'(X2),X1) )
| ( 'fun_app$p'(X2,sK214(X1,X2,X3)) != 'fun_app$p'(X3,sK214(X1,X2,X3)) ) ),
inference(equality_resolution,[],[f3076]) ).
tff(f3076,plain,
! [X2: 'A_b_fun$',X3: 'A_b_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$av'('map_option$e'(X2),X0) = 'fun_app$av'('map_option$e'(X3),X1) )
| ( 'fun_app$p'(X2,sK214(X1,X2,X3)) != 'fun_app$p'(X3,sK214(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1824]) ).
tff(f1824,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X2),X0) = 'fun_app$av'('map_option$e'(X3),X1) )
| ( ( 'fun_app$p'(X2,sK214(X1,X2,X3)) != 'fun_app$p'(X3,sK214(X1,X2,X3)) )
& ( 'fun_app$q'('some$b',sK214(X1,X2,X3)) = X1 ) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK214])],[f1046,f1823]) ).
tff(f1823,plain,
! [X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ? [X4: 'A$'] :
( ( 'fun_app$p'(X2,X4) != 'fun_app$p'(X3,X4) )
& ( 'fun_app$q'('some$b',X4) = X1 ) )
=> ( ( 'fun_app$p'(X2,sK214(X1,X2,X3)) != 'fun_app$p'(X3,sK214(X1,X2,X3)) )
& ( 'fun_app$q'('some$b',sK214(X1,X2,X3)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1046,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X2),X0) = 'fun_app$av'('map_option$e'(X3),X1) )
| ? [X4: 'A$'] :
( ( 'fun_app$p'(X2,X4) != 'fun_app$p'(X3,X4) )
& ( 'fun_app$q'('some$b',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1045]) ).
tff(f1045,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X2),X0) = 'fun_app$av'('map_option$e'(X3),X1) )
| ? [X4: 'A$'] :
( ( 'fun_app$p'(X2,X4) != 'fun_app$p'(X3,X4) )
& ( 'fun_app$q'('some$b',X4) = X1 ) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f294]) ).
tff(f294,axiom,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ( ! [X4: 'A$'] :
( ( 'fun_app$q'('some$b',X4) = X1 )
=> ( 'fun_app$p'(X2,X4) = 'fun_app$p'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'fun_app$av'('map_option$e'(X2),X0) = 'fun_app$av'('map_option$e'(X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom292) ).
tff(f16875,plain,
spl249_1146,
inference(avatar_split_clause,[],[f3532,f16873]) ).
tff(f16873,plain,
( spl249_1146
<=> ! [X2: 'B_b_option_fun$',X1: 'B_option$',X3: 'B_b_option_fun$'] :
( ( 'fun_app$ac'('bind$c'(X1),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ( 'fun_app$g'(X2,sK213(X1,X2,X3)) != 'fun_app$g'(X3,sK213(X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1146])]) ).
tff(f3532,plain,
! [X2: 'B_b_option_fun$',X3: 'B_b_option_fun$',X1: 'B_option$'] :
( ( 'fun_app$ac'('bind$c'(X1),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ( 'fun_app$g'(X2,sK213(X1,X2,X3)) != 'fun_app$g'(X3,sK213(X1,X2,X3)) ) ),
inference(equality_resolution,[],[f3074]) ).
tff(f3074,plain,
! [X2: 'B_b_option_fun$',X3: 'B_b_option_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$ac'('bind$c'(X0),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ( 'fun_app$g'(X2,sK213(X1,X2,X3)) != 'fun_app$g'(X3,sK213(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1822]) ).
tff(f1822,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_b_option_fun$'] :
( ( 'fun_app$ac'('bind$c'(X0),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ( ( 'fun_app$g'(X2,sK213(X1,X2,X3)) != 'fun_app$g'(X3,sK213(X1,X2,X3)) )
& 'member$c'(sK213(X1,X2,X3),'set_option$d'(X1)) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK213])],[f1044,f1821]) ).
tff(f1821,plain,
! [X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_b_option_fun$'] :
( ? [X4: 'B$'] :
( ( 'fun_app$g'(X2,X4) != 'fun_app$g'(X3,X4) )
& 'member$c'(X4,'set_option$d'(X1)) )
=> ( ( 'fun_app$g'(X2,sK213(X1,X2,X3)) != 'fun_app$g'(X3,sK213(X1,X2,X3)) )
& 'member$c'(sK213(X1,X2,X3),'set_option$d'(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1044,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_b_option_fun$'] :
( ( 'fun_app$ac'('bind$c'(X0),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ? [X4: 'B$'] :
( ( 'fun_app$g'(X2,X4) != 'fun_app$g'(X3,X4) )
& 'member$c'(X4,'set_option$d'(X1)) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1043]) ).
tff(f1043,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_b_option_fun$'] :
( ( 'fun_app$ac'('bind$c'(X0),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ? [X4: 'B$'] :
( ( 'fun_app$g'(X2,X4) != 'fun_app$g'(X3,X4) )
& 'member$c'(X4,'set_option$d'(X1)) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f391]) ).
tff(f391,axiom,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_b_option_fun$'] :
( ( ! [X4: 'B$'] :
( 'member$c'(X4,'set_option$d'(X1))
=> ( 'fun_app$g'(X2,X4) = 'fun_app$g'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'fun_app$ac'('bind$c'(X0),X2) = 'fun_app$ac'('bind$c'(X1),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom389) ).
tff(f16871,plain,
spl249_1145,
inference(avatar_split_clause,[],[f3530,f16869]) ).
tff(f16869,plain,
( spl249_1145
<=> ! [X2: 'B_b_fun$',X1: 'B_option$',X3: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X3),X1) = 'fun_app$s'('map_option$b'(X2),X1) )
| ( 'fun_app$h'(X2,sK212(X1,X2,X3)) != 'fun_app$h'(X3,sK212(X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1145])]) ).
tff(f3530,plain,
! [X2: 'B_b_fun$',X3: 'B_b_fun$',X1: 'B_option$'] :
( ( 'fun_app$s'('map_option$b'(X3),X1) = 'fun_app$s'('map_option$b'(X2),X1) )
| ( 'fun_app$h'(X2,sK212(X1,X2,X3)) != 'fun_app$h'(X3,sK212(X1,X2,X3)) ) ),
inference(equality_resolution,[],[f3072]) ).
tff(f3072,plain,
! [X2: 'B_b_fun$',X3: 'B_b_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$s'('map_option$b'(X2),X0) = 'fun_app$s'('map_option$b'(X3),X1) )
| ( 'fun_app$h'(X2,sK212(X1,X2,X3)) != 'fun_app$h'(X3,sK212(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1820]) ).
tff(f1820,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X2),X0) = 'fun_app$s'('map_option$b'(X3),X1) )
| ( ( 'fun_app$h'(X2,sK212(X1,X2,X3)) != 'fun_app$h'(X3,sK212(X1,X2,X3)) )
& 'member$c'(sK212(X1,X2,X3),'set_option$d'(X1)) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK212])],[f1042,f1819]) ).
tff(f1819,plain,
! [X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ? [X4: 'B$'] :
( ( 'fun_app$h'(X2,X4) != 'fun_app$h'(X3,X4) )
& 'member$c'(X4,'set_option$d'(X1)) )
=> ( ( 'fun_app$h'(X2,sK212(X1,X2,X3)) != 'fun_app$h'(X3,sK212(X1,X2,X3)) )
& 'member$c'(sK212(X1,X2,X3),'set_option$d'(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1042,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X2),X0) = 'fun_app$s'('map_option$b'(X3),X1) )
| ? [X4: 'B$'] :
( ( 'fun_app$h'(X2,X4) != 'fun_app$h'(X3,X4) )
& 'member$c'(X4,'set_option$d'(X1)) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1041]) ).
tff(f1041,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X2),X0) = 'fun_app$s'('map_option$b'(X3),X1) )
| ? [X4: 'B$'] :
( ( 'fun_app$h'(X2,X4) != 'fun_app$h'(X3,X4) )
& 'member$c'(X4,'set_option$d'(X1)) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f460]) ).
tff(f460,axiom,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_b_fun$',X3: 'B_b_fun$'] :
( ( ! [X4: 'B$'] :
( 'member$c'(X4,'set_option$d'(X1))
=> ( 'fun_app$h'(X2,X4) = 'fun_app$h'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'fun_app$s'('map_option$b'(X2),X0) = 'fun_app$s'('map_option$b'(X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom458) ).
tff(f16867,plain,
spl249_1144,
inference(avatar_split_clause,[],[f3526,f16865]) ).
tff(f16865,plain,
( spl249_1144
<=> ! [X2: 'B_c_fun$',X1: 'B_option$',X3: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X3),X1) = 'fun_app$an'('map_option$d'(X2),X1) )
| ( 'fun_app$o'(X2,sK210(X1,X2,X3)) != 'fun_app$o'(X3,sK210(X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1144])]) ).
tff(f3526,plain,
! [X2: 'B_c_fun$',X3: 'B_c_fun$',X1: 'B_option$'] :
( ( 'fun_app$an'('map_option$d'(X3),X1) = 'fun_app$an'('map_option$d'(X2),X1) )
| ( 'fun_app$o'(X2,sK210(X1,X2,X3)) != 'fun_app$o'(X3,sK210(X1,X2,X3)) ) ),
inference(equality_resolution,[],[f3068]) ).
tff(f3068,plain,
! [X2: 'B_c_fun$',X3: 'B_c_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$an'('map_option$d'(X2),X0) = 'fun_app$an'('map_option$d'(X3),X1) )
| ( 'fun_app$o'(X2,sK210(X1,X2,X3)) != 'fun_app$o'(X3,sK210(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1816]) ).
tff(f1816,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X2),X0) = 'fun_app$an'('map_option$d'(X3),X1) )
| ( ( 'fun_app$o'(X2,sK210(X1,X2,X3)) != 'fun_app$o'(X3,sK210(X1,X2,X3)) )
& 'member$c'(sK210(X1,X2,X3),'set_option$d'(X1)) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK210])],[f1038,f1815]) ).
tff(f1815,plain,
! [X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ? [X4: 'B$'] :
( ( 'fun_app$o'(X2,X4) != 'fun_app$o'(X3,X4) )
& 'member$c'(X4,'set_option$d'(X1)) )
=> ( ( 'fun_app$o'(X2,sK210(X1,X2,X3)) != 'fun_app$o'(X3,sK210(X1,X2,X3)) )
& 'member$c'(sK210(X1,X2,X3),'set_option$d'(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1038,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X2),X0) = 'fun_app$an'('map_option$d'(X3),X1) )
| ? [X4: 'B$'] :
( ( 'fun_app$o'(X2,X4) != 'fun_app$o'(X3,X4) )
& 'member$c'(X4,'set_option$d'(X1)) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1037]) ).
tff(f1037,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X2),X0) = 'fun_app$an'('map_option$d'(X3),X1) )
| ? [X4: 'B$'] :
( ( 'fun_app$o'(X2,X4) != 'fun_app$o'(X3,X4) )
& 'member$c'(X4,'set_option$d'(X1)) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f459]) ).
tff(f459,axiom,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_c_fun$',X3: 'B_c_fun$'] :
( ( ! [X4: 'B$'] :
( 'member$c'(X4,'set_option$d'(X1))
=> ( 'fun_app$o'(X2,X4) = 'fun_app$o'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'fun_app$an'('map_option$d'(X2),X0) = 'fun_app$an'('map_option$d'(X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom457) ).
tff(f16863,plain,
spl249_1143,
inference(avatar_split_clause,[],[f3524,f16861]) ).
tff(f16861,plain,
( spl249_1143
<=> ! [X2: 'C_c_option_fun$',X1: 'C_option$',X3: 'C_c_option_fun$'] :
( ( 'fun_app$ab'('bind$'(X1),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ( 'fun_app$j'(X2,sK209(X1,X2,X3)) != 'fun_app$j'(X3,sK209(X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1143])]) ).
tff(f3524,plain,
! [X2: 'C_c_option_fun$',X3: 'C_c_option_fun$',X1: 'C_option$'] :
( ( 'fun_app$ab'('bind$'(X1),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ( 'fun_app$j'(X2,sK209(X1,X2,X3)) != 'fun_app$j'(X3,sK209(X1,X2,X3)) ) ),
inference(equality_resolution,[],[f3066]) ).
tff(f3066,plain,
! [X2: 'C_c_option_fun$',X3: 'C_c_option_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$ab'('bind$'(X0),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ( 'fun_app$j'(X2,sK209(X1,X2,X3)) != 'fun_app$j'(X3,sK209(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1814]) ).
tff(f1814,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_c_option_fun$'] :
( ( 'fun_app$ab'('bind$'(X0),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ( ( 'fun_app$j'(X2,sK209(X1,X2,X3)) != 'fun_app$j'(X3,sK209(X1,X2,X3)) )
& 'member$b'(sK209(X1,X2,X3),'set_option$c'(X1)) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK209])],[f1036,f1813]) ).
tff(f1813,plain,
! [X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_c_option_fun$'] :
( ? [X4: 'C$'] :
( ( 'fun_app$j'(X2,X4) != 'fun_app$j'(X3,X4) )
& 'member$b'(X4,'set_option$c'(X1)) )
=> ( ( 'fun_app$j'(X2,sK209(X1,X2,X3)) != 'fun_app$j'(X3,sK209(X1,X2,X3)) )
& 'member$b'(sK209(X1,X2,X3),'set_option$c'(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1036,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_c_option_fun$'] :
( ( 'fun_app$ab'('bind$'(X0),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ? [X4: 'C$'] :
( ( 'fun_app$j'(X2,X4) != 'fun_app$j'(X3,X4) )
& 'member$b'(X4,'set_option$c'(X1)) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1035]) ).
tff(f1035,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_c_option_fun$'] :
( ( 'fun_app$ab'('bind$'(X0),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ? [X4: 'C$'] :
( ( 'fun_app$j'(X2,X4) != 'fun_app$j'(X3,X4) )
& 'member$b'(X4,'set_option$c'(X1)) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f394]) ).
tff(f394,axiom,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_c_option_fun$'] :
( ( ! [X4: 'C$'] :
( 'member$b'(X4,'set_option$c'(X1))
=> ( 'fun_app$j'(X2,X4) = 'fun_app$j'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'fun_app$ab'('bind$'(X0),X2) = 'fun_app$ab'('bind$'(X1),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom392) ).
tff(f16859,plain,
spl249_1142,
inference(avatar_split_clause,[],[f3522,f16857]) ).
tff(f16857,plain,
( spl249_1142
<=> ! [X2: 'C_b_fun$',X1: 'C_option$',X3: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X3),X1) = 'fun_app$bg'('map_option$'(X2),X1) )
| ( 'fun_app$m'(X2,sK208(X1,X2,X3)) != 'fun_app$m'(X3,sK208(X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1142])]) ).
tff(f3522,plain,
! [X2: 'C_b_fun$',X3: 'C_b_fun$',X1: 'C_option$'] :
( ( 'fun_app$bg'('map_option$'(X3),X1) = 'fun_app$bg'('map_option$'(X2),X1) )
| ( 'fun_app$m'(X2,sK208(X1,X2,X3)) != 'fun_app$m'(X3,sK208(X1,X2,X3)) ) ),
inference(equality_resolution,[],[f3064]) ).
tff(f3064,plain,
! [X2: 'C_b_fun$',X3: 'C_b_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$bg'('map_option$'(X2),X0) = 'fun_app$bg'('map_option$'(X3),X1) )
| ( 'fun_app$m'(X2,sK208(X1,X2,X3)) != 'fun_app$m'(X3,sK208(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1812]) ).
tff(f1812,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X2),X0) = 'fun_app$bg'('map_option$'(X3),X1) )
| ( ( 'fun_app$m'(X2,sK208(X1,X2,X3)) != 'fun_app$m'(X3,sK208(X1,X2,X3)) )
& 'member$b'(sK208(X1,X2,X3),'set_option$c'(X1)) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK208])],[f1034,f1811]) ).
tff(f1811,plain,
! [X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ? [X4: 'C$'] :
( ( 'fun_app$m'(X2,X4) != 'fun_app$m'(X3,X4) )
& 'member$b'(X4,'set_option$c'(X1)) )
=> ( ( 'fun_app$m'(X2,sK208(X1,X2,X3)) != 'fun_app$m'(X3,sK208(X1,X2,X3)) )
& 'member$b'(sK208(X1,X2,X3),'set_option$c'(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1034,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X2),X0) = 'fun_app$bg'('map_option$'(X3),X1) )
| ? [X4: 'C$'] :
( ( 'fun_app$m'(X2,X4) != 'fun_app$m'(X3,X4) )
& 'member$b'(X4,'set_option$c'(X1)) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1033]) ).
tff(f1033,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X2),X0) = 'fun_app$bg'('map_option$'(X3),X1) )
| ? [X4: 'C$'] :
( ( 'fun_app$m'(X2,X4) != 'fun_app$m'(X3,X4) )
& 'member$b'(X4,'set_option$c'(X1)) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f461]) ).
tff(f461,axiom,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_b_fun$',X3: 'C_b_fun$'] :
( ( ! [X4: 'C$'] :
( 'member$b'(X4,'set_option$c'(X1))
=> ( 'fun_app$m'(X2,X4) = 'fun_app$m'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'fun_app$bg'('map_option$'(X2),X0) = 'fun_app$bg'('map_option$'(X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom459) ).
tff(f16855,plain,
spl249_1141,
inference(avatar_split_clause,[],[f3518,f16853]) ).
tff(f16853,plain,
( spl249_1141
<=> ! [X2: 'A_a_fun$',X1: 'A_option$',X3: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X3),X1) = 'fun_app$be'('map_option$a'(X2),X1) )
| ( 'fun_app$r'(X2,sK206(X1,X2,X3)) != 'fun_app$r'(X3,sK206(X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1141])]) ).
tff(f3518,plain,
! [X2: 'A_a_fun$',X3: 'A_a_fun$',X1: 'A_option$'] :
( ( 'fun_app$be'('map_option$a'(X3),X1) = 'fun_app$be'('map_option$a'(X2),X1) )
| ( 'fun_app$r'(X2,sK206(X1,X2,X3)) != 'fun_app$r'(X3,sK206(X1,X2,X3)) ) ),
inference(equality_resolution,[],[f3060]) ).
tff(f3060,plain,
! [X2: 'A_a_fun$',X3: 'A_a_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$be'('map_option$a'(X2),X0) = 'fun_app$be'('map_option$a'(X3),X1) )
| ( 'fun_app$r'(X2,sK206(X1,X2,X3)) != 'fun_app$r'(X3,sK206(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1808]) ).
tff(f1808,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X2),X0) = 'fun_app$be'('map_option$a'(X3),X1) )
| ( ( 'fun_app$r'(X2,sK206(X1,X2,X3)) != 'fun_app$r'(X3,sK206(X1,X2,X3)) )
& 'member$d'(sK206(X1,X2,X3),'set_option$b'(X1)) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK206])],[f1030,f1807]) ).
tff(f1807,plain,
! [X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ? [X4: 'A$'] :
( ( 'fun_app$r'(X2,X4) != 'fun_app$r'(X3,X4) )
& 'member$d'(X4,'set_option$b'(X1)) )
=> ( ( 'fun_app$r'(X2,sK206(X1,X2,X3)) != 'fun_app$r'(X3,sK206(X1,X2,X3)) )
& 'member$d'(sK206(X1,X2,X3),'set_option$b'(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1030,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X2),X0) = 'fun_app$be'('map_option$a'(X3),X1) )
| ? [X4: 'A$'] :
( ( 'fun_app$r'(X2,X4) != 'fun_app$r'(X3,X4) )
& 'member$d'(X4,'set_option$b'(X1)) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1029]) ).
tff(f1029,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X2),X0) = 'fun_app$be'('map_option$a'(X3),X1) )
| ? [X4: 'A$'] :
( ( 'fun_app$r'(X2,X4) != 'fun_app$r'(X3,X4) )
& 'member$d'(X4,'set_option$b'(X1)) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f458]) ).
tff(f458,axiom,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_a_fun$',X3: 'A_a_fun$'] :
( ( ! [X4: 'A$'] :
( 'member$d'(X4,'set_option$b'(X1))
=> ( 'fun_app$r'(X2,X4) = 'fun_app$r'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'fun_app$be'('map_option$a'(X2),X0) = 'fun_app$be'('map_option$a'(X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom456) ).
tff(f16851,plain,
spl249_1140,
inference(avatar_split_clause,[],[f3516,f16849]) ).
tff(f16849,plain,
( spl249_1140
<=> ! [X2: 'A_b_fun$',X1: 'A_option$',X3: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X3),X1) = 'fun_app$av'('map_option$e'(X2),X1) )
| ( 'fun_app$p'(X2,sK205(X1,X2,X3)) != 'fun_app$p'(X3,sK205(X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1140])]) ).
tff(f3516,plain,
! [X2: 'A_b_fun$',X3: 'A_b_fun$',X1: 'A_option$'] :
( ( 'fun_app$av'('map_option$e'(X3),X1) = 'fun_app$av'('map_option$e'(X2),X1) )
| ( 'fun_app$p'(X2,sK205(X1,X2,X3)) != 'fun_app$p'(X3,sK205(X1,X2,X3)) ) ),
inference(equality_resolution,[],[f3058]) ).
tff(f3058,plain,
! [X2: 'A_b_fun$',X3: 'A_b_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$av'('map_option$e'(X2),X0) = 'fun_app$av'('map_option$e'(X3),X1) )
| ( 'fun_app$p'(X2,sK205(X1,X2,X3)) != 'fun_app$p'(X3,sK205(X1,X2,X3)) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1806]) ).
tff(f1806,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X2),X0) = 'fun_app$av'('map_option$e'(X3),X1) )
| ( ( 'fun_app$p'(X2,sK205(X1,X2,X3)) != 'fun_app$p'(X3,sK205(X1,X2,X3)) )
& 'member$d'(sK205(X1,X2,X3),'set_option$b'(X1)) )
| ( X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK205])],[f1028,f1805]) ).
tff(f1805,plain,
! [X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ? [X4: 'A$'] :
( ( 'fun_app$p'(X2,X4) != 'fun_app$p'(X3,X4) )
& 'member$d'(X4,'set_option$b'(X1)) )
=> ( ( 'fun_app$p'(X2,sK205(X1,X2,X3)) != 'fun_app$p'(X3,sK205(X1,X2,X3)) )
& 'member$d'(sK205(X1,X2,X3),'set_option$b'(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1028,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X2),X0) = 'fun_app$av'('map_option$e'(X3),X1) )
| ? [X4: 'A$'] :
( ( 'fun_app$p'(X2,X4) != 'fun_app$p'(X3,X4) )
& 'member$d'(X4,'set_option$b'(X1)) )
| ( X0 != X1 ) ),
inference(flattening,[],[f1027]) ).
tff(f1027,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X2),X0) = 'fun_app$av'('map_option$e'(X3),X1) )
| ? [X4: 'A$'] :
( ( 'fun_app$p'(X2,X4) != 'fun_app$p'(X3,X4) )
& 'member$d'(X4,'set_option$b'(X1)) )
| ( X0 != X1 ) ),
inference(ennf_transformation,[],[f457]) ).
tff(f457,axiom,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_b_fun$',X3: 'A_b_fun$'] :
( ( ! [X4: 'A$'] :
( 'member$d'(X4,'set_option$b'(X1))
=> ( 'fun_app$p'(X2,X4) = 'fun_app$p'(X3,X4) ) )
& ( X0 = X1 ) )
=> ( 'fun_app$av'('map_option$e'(X2),X0) = 'fun_app$av'('map_option$e'(X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom455) ).
tff(f16847,plain,
spl249_1139,
inference(avatar_split_clause,[],[f2780,f16845]) ).
tff(f16845,plain,
( spl249_1139
<=> ! [X2: 'B_b_fun$',X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X1),X0) = 'fun_app$s'('map_option$b'(X2),X0) )
| ( 'fun_app$h'(X1,sK164(X0,X1,X2)) != 'fun_app$h'(X2,sK164(X0,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1139])]) ).
tff(f2780,plain,
! [X2: 'B_b_fun$',X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X1),X0) = 'fun_app$s'('map_option$b'(X2),X0) )
| ( 'fun_app$h'(X1,sK164(X0,X1,X2)) != 'fun_app$h'(X2,sK164(X0,X1,X2)) ) ),
inference(cnf_transformation,[],[f1594]) ).
tff(f1594,plain,
! [X0: 'B_option$',X1: 'B_b_fun$',X2: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X1),X0) = 'fun_app$s'('map_option$b'(X2),X0) )
| ( ( 'fun_app$h'(X1,sK164(X0,X1,X2)) != 'fun_app$h'(X2,sK164(X0,X1,X2)) )
& 'member$c'(sK164(X0,X1,X2),'set_option$d'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK164])],[f996,f1593]) ).
tff(f1593,plain,
! [X0: 'B_option$',X1: 'B_b_fun$',X2: 'B_b_fun$'] :
( ? [X3: 'B$'] :
( ( 'fun_app$h'(X1,X3) != 'fun_app$h'(X2,X3) )
& 'member$c'(X3,'set_option$d'(X0)) )
=> ( ( 'fun_app$h'(X1,sK164(X0,X1,X2)) != 'fun_app$h'(X2,sK164(X0,X1,X2)) )
& 'member$c'(sK164(X0,X1,X2),'set_option$d'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f996,plain,
! [X0: 'B_option$',X1: 'B_b_fun$',X2: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X1),X0) = 'fun_app$s'('map_option$b'(X2),X0) )
| ? [X3: 'B$'] :
( ( 'fun_app$h'(X1,X3) != 'fun_app$h'(X2,X3) )
& 'member$c'(X3,'set_option$d'(X0)) ) ),
inference(ennf_transformation,[],[f455]) ).
tff(f455,axiom,
! [X0: 'B_option$',X1: 'B_b_fun$',X2: 'B_b_fun$'] :
( ! [X3: 'B$'] :
( 'member$c'(X3,'set_option$d'(X0))
=> ( 'fun_app$h'(X1,X3) = 'fun_app$h'(X2,X3) ) )
=> ( 'fun_app$s'('map_option$b'(X1),X0) = 'fun_app$s'('map_option$b'(X2),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom453) ).
tff(f16840,plain,
spl249_1138,
inference(avatar_split_clause,[],[f2778,f16838]) ).
tff(f16838,plain,
( spl249_1138
<=> ! [X2: 'B_c_fun$',X0: 'B_option$',X1: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X1),X0) = 'fun_app$an'('map_option$d'(X2),X0) )
| ( 'fun_app$o'(X1,sK163(X0,X1,X2)) != 'fun_app$o'(X2,sK163(X0,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1138])]) ).
tff(f2778,plain,
! [X2: 'B_c_fun$',X0: 'B_option$',X1: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X1),X0) = 'fun_app$an'('map_option$d'(X2),X0) )
| ( 'fun_app$o'(X1,sK163(X0,X1,X2)) != 'fun_app$o'(X2,sK163(X0,X1,X2)) ) ),
inference(cnf_transformation,[],[f1592]) ).
tff(f1592,plain,
! [X0: 'B_option$',X1: 'B_c_fun$',X2: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X1),X0) = 'fun_app$an'('map_option$d'(X2),X0) )
| ( ( 'fun_app$o'(X1,sK163(X0,X1,X2)) != 'fun_app$o'(X2,sK163(X0,X1,X2)) )
& 'member$c'(sK163(X0,X1,X2),'set_option$d'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK163])],[f995,f1591]) ).
tff(f1591,plain,
! [X0: 'B_option$',X1: 'B_c_fun$',X2: 'B_c_fun$'] :
( ? [X3: 'B$'] :
( ( 'fun_app$o'(X1,X3) != 'fun_app$o'(X2,X3) )
& 'member$c'(X3,'set_option$d'(X0)) )
=> ( ( 'fun_app$o'(X1,sK163(X0,X1,X2)) != 'fun_app$o'(X2,sK163(X0,X1,X2)) )
& 'member$c'(sK163(X0,X1,X2),'set_option$d'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f995,plain,
! [X0: 'B_option$',X1: 'B_c_fun$',X2: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X1),X0) = 'fun_app$an'('map_option$d'(X2),X0) )
| ? [X3: 'B$'] :
( ( 'fun_app$o'(X1,X3) != 'fun_app$o'(X2,X3) )
& 'member$c'(X3,'set_option$d'(X0)) ) ),
inference(ennf_transformation,[],[f454]) ).
tff(f454,axiom,
! [X0: 'B_option$',X1: 'B_c_fun$',X2: 'B_c_fun$'] :
( ! [X3: 'B$'] :
( 'member$c'(X3,'set_option$d'(X0))
=> ( 'fun_app$o'(X1,X3) = 'fun_app$o'(X2,X3) ) )
=> ( 'fun_app$an'('map_option$d'(X1),X0) = 'fun_app$an'('map_option$d'(X2),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom452) ).
tff(f16836,plain,
spl249_1137,
inference(avatar_split_clause,[],[f2776,f16834]) ).
tff(f16834,plain,
( spl249_1137
<=> ! [X2: 'C_b_fun$',X0: 'C_option$',X1: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X1),X0) = 'fun_app$bg'('map_option$'(X2),X0) )
| ( 'fun_app$m'(X1,sK162(X0,X1,X2)) != 'fun_app$m'(X2,sK162(X0,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1137])]) ).
tff(f2776,plain,
! [X2: 'C_b_fun$',X0: 'C_option$',X1: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X1),X0) = 'fun_app$bg'('map_option$'(X2),X0) )
| ( 'fun_app$m'(X1,sK162(X0,X1,X2)) != 'fun_app$m'(X2,sK162(X0,X1,X2)) ) ),
inference(cnf_transformation,[],[f1590]) ).
tff(f1590,plain,
! [X0: 'C_option$',X1: 'C_b_fun$',X2: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X1),X0) = 'fun_app$bg'('map_option$'(X2),X0) )
| ( ( 'fun_app$m'(X1,sK162(X0,X1,X2)) != 'fun_app$m'(X2,sK162(X0,X1,X2)) )
& 'member$b'(sK162(X0,X1,X2),'set_option$c'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK162])],[f994,f1589]) ).
tff(f1589,plain,
! [X0: 'C_option$',X1: 'C_b_fun$',X2: 'C_b_fun$'] :
( ? [X3: 'C$'] :
( ( 'fun_app$m'(X1,X3) != 'fun_app$m'(X2,X3) )
& 'member$b'(X3,'set_option$c'(X0)) )
=> ( ( 'fun_app$m'(X1,sK162(X0,X1,X2)) != 'fun_app$m'(X2,sK162(X0,X1,X2)) )
& 'member$b'(sK162(X0,X1,X2),'set_option$c'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f994,plain,
! [X0: 'C_option$',X1: 'C_b_fun$',X2: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X1),X0) = 'fun_app$bg'('map_option$'(X2),X0) )
| ? [X3: 'C$'] :
( ( 'fun_app$m'(X1,X3) != 'fun_app$m'(X2,X3) )
& 'member$b'(X3,'set_option$c'(X0)) ) ),
inference(ennf_transformation,[],[f456]) ).
tff(f456,axiom,
! [X0: 'C_option$',X1: 'C_b_fun$',X2: 'C_b_fun$'] :
( ! [X3: 'C$'] :
( 'member$b'(X3,'set_option$c'(X0))
=> ( 'fun_app$m'(X1,X3) = 'fun_app$m'(X2,X3) ) )
=> ( 'fun_app$bg'('map_option$'(X1),X0) = 'fun_app$bg'('map_option$'(X2),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom454) ).
tff(f16832,plain,
spl249_1136,
inference(avatar_split_clause,[],[f2774,f16830]) ).
tff(f16830,plain,
( spl249_1136
<=> ! [X2: 'A_a_fun$',X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X1),X0) = 'fun_app$be'('map_option$a'(X2),X0) )
| ( 'fun_app$r'(X1,sK161(X0,X1,X2)) != 'fun_app$r'(X2,sK161(X0,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1136])]) ).
tff(f2774,plain,
! [X2: 'A_a_fun$',X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X1),X0) = 'fun_app$be'('map_option$a'(X2),X0) )
| ( 'fun_app$r'(X1,sK161(X0,X1,X2)) != 'fun_app$r'(X2,sK161(X0,X1,X2)) ) ),
inference(cnf_transformation,[],[f1588]) ).
tff(f1588,plain,
! [X0: 'A_option$',X1: 'A_a_fun$',X2: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X1),X0) = 'fun_app$be'('map_option$a'(X2),X0) )
| ( ( 'fun_app$r'(X1,sK161(X0,X1,X2)) != 'fun_app$r'(X2,sK161(X0,X1,X2)) )
& 'member$d'(sK161(X0,X1,X2),'set_option$b'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK161])],[f993,f1587]) ).
tff(f1587,plain,
! [X0: 'A_option$',X1: 'A_a_fun$',X2: 'A_a_fun$'] :
( ? [X3: 'A$'] :
( ( 'fun_app$r'(X1,X3) != 'fun_app$r'(X2,X3) )
& 'member$d'(X3,'set_option$b'(X0)) )
=> ( ( 'fun_app$r'(X1,sK161(X0,X1,X2)) != 'fun_app$r'(X2,sK161(X0,X1,X2)) )
& 'member$d'(sK161(X0,X1,X2),'set_option$b'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f993,plain,
! [X0: 'A_option$',X1: 'A_a_fun$',X2: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X1),X0) = 'fun_app$be'('map_option$a'(X2),X0) )
| ? [X3: 'A$'] :
( ( 'fun_app$r'(X1,X3) != 'fun_app$r'(X2,X3) )
& 'member$d'(X3,'set_option$b'(X0)) ) ),
inference(ennf_transformation,[],[f453]) ).
tff(f453,axiom,
! [X0: 'A_option$',X1: 'A_a_fun$',X2: 'A_a_fun$'] :
( ! [X3: 'A$'] :
( 'member$d'(X3,'set_option$b'(X0))
=> ( 'fun_app$r'(X1,X3) = 'fun_app$r'(X2,X3) ) )
=> ( 'fun_app$be'('map_option$a'(X1),X0) = 'fun_app$be'('map_option$a'(X2),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom451) ).
tff(f16828,plain,
spl249_1135,
inference(avatar_split_clause,[],[f2772,f16826]) ).
tff(f16826,plain,
( spl249_1135
<=> ! [X2: 'A_b_fun$',X0: 'A_option$',X1: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X1),X0) = 'fun_app$av'('map_option$e'(X2),X0) )
| ( 'fun_app$p'(X1,sK160(X0,X1,X2)) != 'fun_app$p'(X2,sK160(X0,X1,X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1135])]) ).
tff(f2772,plain,
! [X2: 'A_b_fun$',X0: 'A_option$',X1: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X1),X0) = 'fun_app$av'('map_option$e'(X2),X0) )
| ( 'fun_app$p'(X1,sK160(X0,X1,X2)) != 'fun_app$p'(X2,sK160(X0,X1,X2)) ) ),
inference(cnf_transformation,[],[f1586]) ).
tff(f1586,plain,
! [X0: 'A_option$',X1: 'A_b_fun$',X2: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X1),X0) = 'fun_app$av'('map_option$e'(X2),X0) )
| ( ( 'fun_app$p'(X1,sK160(X0,X1,X2)) != 'fun_app$p'(X2,sK160(X0,X1,X2)) )
& 'member$d'(sK160(X0,X1,X2),'set_option$b'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK160])],[f992,f1585]) ).
tff(f1585,plain,
! [X0: 'A_option$',X1: 'A_b_fun$',X2: 'A_b_fun$'] :
( ? [X3: 'A$'] :
( ( 'fun_app$p'(X1,X3) != 'fun_app$p'(X2,X3) )
& 'member$d'(X3,'set_option$b'(X0)) )
=> ( ( 'fun_app$p'(X1,sK160(X0,X1,X2)) != 'fun_app$p'(X2,sK160(X0,X1,X2)) )
& 'member$d'(sK160(X0,X1,X2),'set_option$b'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f992,plain,
! [X0: 'A_option$',X1: 'A_b_fun$',X2: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X1),X0) = 'fun_app$av'('map_option$e'(X2),X0) )
| ? [X3: 'A$'] :
( ( 'fun_app$p'(X1,X3) != 'fun_app$p'(X2,X3) )
& 'member$d'(X3,'set_option$b'(X0)) ) ),
inference(ennf_transformation,[],[f452]) ).
tff(f452,axiom,
! [X0: 'A_option$',X1: 'A_b_fun$',X2: 'A_b_fun$'] :
( ! [X3: 'A$'] :
( 'member$d'(X3,'set_option$b'(X0))
=> ( 'fun_app$p'(X1,X3) = 'fun_app$p'(X2,X3) ) )
=> ( 'fun_app$av'('map_option$e'(X1),X0) = 'fun_app$av'('map_option$e'(X2),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom450) ).
tff(f16824,plain,
spl249_1134,
inference(avatar_split_clause,[],[f2084,f16822]) ).
tff(f16822,plain,
( spl249_1134
<=> ! [X0: 'B_b_option_fun_b_b_option_fun_fun$',X8: 'B$',X7: 'B_b_option_fun$'] :
( ( 'fun_app$g'('fun_app$ad'(X0,X7),X8) = 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(sK70(X0)),X8)),'fun_app$g'(X7,'fun_app$h'(sK69(X0),X8))) )
| ~ 'preregister$'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1134])]) ).
tff(f2084,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$',X8: 'B$',X7: 'B_b_option_fun$'] :
( ( 'fun_app$g'('fun_app$ad'(X0,X7),X8) = 'fun_app$s'('case_option$'('none$a','fun_app$t'('uus$'(sK70(X0)),X8)),'fun_app$g'(X7,'fun_app$h'(sK69(X0),X8))) )
| ~ 'preregister$'(X0) ),
inference(cnf_transformation,[],[f1230]) ).
tff(f16820,plain,
spl249_1133,
inference(avatar_split_clause,[],[f2070,f16818]) ).
tff(f16818,plain,
( spl249_1133
<=> ! [X0: 'C_c_option_fun_c_c_option_fun_fun$',X8: 'C$',X7: 'C_c_option_fun$'] :
( ( 'fun_app$j'('fun_app$aa'(X0,X7),X8) = 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(sK58(X0)),X8)),'fun_app$j'(X7,'fun_app$k'(sK57(X0),X8))) )
| ~ 'preregister$a'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1133])]) ).
tff(f2070,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$',X8: 'C$',X7: 'C_c_option_fun$'] :
( ( 'fun_app$j'('fun_app$aa'(X0,X7),X8) = 'fun_app$u'('case_option$a'('none$','fun_app$v'('uut$'(sK58(X0)),X8)),'fun_app$j'(X7,'fun_app$k'(sK57(X0),X8))) )
| ~ 'preregister$a'(X0) ),
inference(cnf_transformation,[],[f1209]) ).
tff(f16811,plain,
spl249_1132,
inference(avatar_split_clause,[],[f2088,f16809]) ).
tff(f16809,plain,
( spl249_1132
<=> ! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X8: 'B$',X7: 'A_a_option_fun$'] :
( ( 'fun_app$g'('fun_app$au'(X0,X7),X8) = 'fun_app$av'('case_option$d'('none$a','uuv$'(sK78(X0),X8)),'fun_app$q'(X7,'fun_app$ao'(sK77(X0),X8))) )
| ~ 'preregister$c'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1132])]) ).
tff(f2088,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X8: 'B$',X7: 'A_a_option_fun$'] :
( ( 'fun_app$g'('fun_app$au'(X0,X7),X8) = 'fun_app$av'('case_option$d'('none$a','uuv$'(sK78(X0),X8)),'fun_app$q'(X7,'fun_app$ao'(sK77(X0),X8))) )
| ~ 'preregister$c'(X0) ),
inference(cnf_transformation,[],[f1240]) ).
tff(f16807,plain,
spl249_1131,
inference(avatar_split_clause,[],[f2086,f16805]) ).
tff(f16805,plain,
( spl249_1131
<=> ! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X8: 'C$',X7: 'B_b_option_fun$'] :
( ( 'fun_app$j'('fun_app$am'(X0,X7),X8) = 'fun_app$an'('case_option$c'('none$','uuu$'(sK74(X0),X8)),'fun_app$g'(X7,'fun_app$m'(sK73(X0),X8))) )
| ~ 'preregister$b'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1131])]) ).
tff(f2086,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X8: 'C$',X7: 'B_b_option_fun$'] :
( ( 'fun_app$j'('fun_app$am'(X0,X7),X8) = 'fun_app$an'('case_option$c'('none$','uuu$'(sK74(X0),X8)),'fun_app$g'(X7,'fun_app$m'(sK73(X0),X8))) )
| ~ 'preregister$b'(X0) ),
inference(cnf_transformation,[],[f1235]) ).
tff(f16803,plain,
( spl249_1130
| ~ spl249_57
| ~ spl249_304 ),
inference(avatar_split_clause,[],[f5305,f5020,f3860,f16801]) ).
tff(f16801,plain,
( spl249_1130
<=> ! [X0: 'B$'] : ( tltrue = def_3('uwl$'(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1130])]) ).
tff(f5020,plain,
( spl249_304
<=> ! [X0: 'B_bool_fun$',X1: 'B$'] :
( ( tltrue = def_3(X0,X1) )
| ~ 'fun_app$c'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_304])]) ).
tff(f5305,plain,
( ! [X0: 'B$'] : ( tltrue = def_3('uwl$'(X0),X0) )
| ~ spl249_57
| ~ spl249_304 ),
inference(resolution,[],[f5021,f3861]) ).
tff(f5021,plain,
( ! [X0: 'B_bool_fun$',X1: 'B$'] :
( ~ 'fun_app$c'(X0,X1)
| ( tltrue = def_3(X0,X1) ) )
| ~ spl249_304 ),
inference(avatar_component_clause,[],[f5020]) ).
tff(f16655,plain,
( spl249_1129
| ~ spl249_56
| ~ spl249_304 ),
inference(avatar_split_clause,[],[f5304,f5020,f3856,f16653]) ).
tff(f16653,plain,
( spl249_1129
<=> ! [X0: 'B$'] : ( tltrue = def_3('uwp$'(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1129])]) ).
tff(f5304,plain,
( ! [X0: 'B$'] : ( tltrue = def_3('uwp$'(X0),X0) )
| ~ spl249_56
| ~ spl249_304 ),
inference(resolution,[],[f5021,f3857]) ).
tff(f16644,plain,
spl249_1128,
inference(avatar_split_clause,[],[f3599,f16642]) ).
tff(f16642,plain,
( spl249_1128
<=> ! [X2: 'B_c_option_fun$',X4: 'B$',X0: 'B_c_option_fun$',X3: 'B_b_fun$',X1: 'B_b_fun$'] :
( ( 'bind$b'('fun_app$g'('uve$'(X3),X4),X2) = 'bind$b'('fun_app$g'('uve$'(X1),X4),X0) )
| ( 'comp$f'(X0,X1) != 'comp$f'(X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1128])]) ).
tff(f3599,plain,
! [X2: 'B_c_option_fun$',X3: 'B_b_fun$',X0: 'B_c_option_fun$',X1: 'B_b_fun$',X4: 'B$'] :
( ( 'bind$b'('fun_app$g'('uve$'(X3),X4),X2) = 'bind$b'('fun_app$g'('uve$'(X1),X4),X0) )
| ( 'comp$f'(X0,X1) != 'comp$f'(X2,X3) ) ),
inference(forward_demodulation,[],[f3598,f2245]) ).
tff(f2245,plain,
! [X0: 'B_b_fun$',X1: 'B$'] : ( 'fun_app$g'('uve$'(X0),X1) = 'fun_app$g'('some$','fun_app$h'(X0,X1)) ),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
! [X0: 'B_b_fun$',X1: 'B$'] : ( 'fun_app$g'('uve$'(X0),X1) = 'fun_app$g'('some$','fun_app$h'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom16) ).
tff(f3598,plain,
! [X2: 'B_c_option_fun$',X3: 'B_b_fun$',X0: 'B_c_option_fun$',X1: 'B_b_fun$',X4: 'B$'] :
( ( 'bind$b'('fun_app$g'('some$','fun_app$h'(X1,X4)),X0) = 'bind$b'('fun_app$g'('uve$'(X3),X4),X2) )
| ( 'comp$f'(X0,X1) != 'comp$f'(X2,X3) ) ),
inference(forward_demodulation,[],[f3294,f2245]) ).
tff(f3294,plain,
! [X2: 'B_c_option_fun$',X3: 'B_b_fun$',X0: 'B_c_option_fun$',X1: 'B_b_fun$',X4: 'B$'] :
( ( 'bind$b'('fun_app$g'('some$','fun_app$h'(X1,X4)),X0) = 'bind$b'('fun_app$g'('some$','fun_app$h'(X3,X4)),X2) )
| ( 'comp$f'(X0,X1) != 'comp$f'(X2,X3) ) ),
inference(definition_unfolding,[],[f3095,f2234,f2234]) ).
tff(f3095,plain,
! [X2: 'B_c_option_fun$',X3: 'B_b_fun$',X0: 'B_c_option_fun$',X1: 'B_b_fun$',X4: 'B$'] :
( ( 'fun_app$n'(X0,'fun_app$h'(X1,X4)) = 'fun_app$n'(X2,'fun_app$h'(X3,X4)) )
| ( 'comp$f'(X0,X1) != 'comp$f'(X2,X3) ) ),
inference(cnf_transformation,[],[f1065]) ).
tff(f1065,plain,
! [X0: 'B_c_option_fun$',X1: 'B_b_fun$',X2: 'B_c_option_fun$',X3: 'B_b_fun$'] :
( ! [X4: 'B$'] : ( 'fun_app$n'(X0,'fun_app$h'(X1,X4)) = 'fun_app$n'(X2,'fun_app$h'(X3,X4)) )
| ( 'comp$f'(X0,X1) != 'comp$f'(X2,X3) ) ),
inference(ennf_transformation,[],[f845]) ).
tff(f845,plain,
! [X0: 'B_c_option_fun$',X1: 'B_b_fun$',X2: 'B_c_option_fun$',X3: 'B_b_fun$'] :
~ ( ~ ! [X4: 'B$'] : ( 'fun_app$n'(X0,'fun_app$h'(X1,X4)) = 'fun_app$n'(X2,'fun_app$h'(X3,X4)) )
& ( 'comp$f'(X0,X1) = 'comp$f'(X2,X3) ) ),
inference(true_and_false_elimination,[],[f630]) ).
tff(f630,axiom,
! [X0: 'B_c_option_fun$',X1: 'B_b_fun$',X2: 'B_c_option_fun$',X3: 'B_b_fun$'] :
( ( ( ! [X4: 'B$'] : ( 'fun_app$n'(X0,'fun_app$h'(X1,X4)) = 'fun_app$n'(X2,'fun_app$h'(X3,X4)) )
=> $false )
& ( 'comp$f'(X0,X1) = 'comp$f'(X2,X3) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom628) ).
tff(f16640,plain,
spl249_1127,
inference(avatar_split_clause,[],[f3116,f16638]) ).
tff(f16638,plain,
( spl249_1127
<=> ! [X0: 'B_option$',X3: 'B_b_fun$',X2: 'B_b_fun$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$s'('map_option$b'(X2),X0) != 'fun_app$s'('map_option$b'(X3),X1) )
| 'member$c'(sK242(X0,X1,X2,X3),'set_option$d'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1127])]) ).
tff(f3116,plain,
! [X2: 'B_b_fun$',X3: 'B_b_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$s'('map_option$b'(X2),X0) != 'fun_app$s'('map_option$b'(X3),X1) )
| 'member$c'(sK242(X0,X1,X2,X3),'set_option$d'(X1)) ),
inference(cnf_transformation,[],[f1856]) ).
tff(f16636,plain,
spl249_1126,
inference(avatar_split_clause,[],[f3115,f16634]) ).
tff(f16634,plain,
( spl249_1126
<=> ! [X0: 'B_option$',X3: 'B_b_fun$',X2: 'B_b_fun$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$s'('map_option$b'(X2),X0) != 'fun_app$s'('map_option$b'(X3),X1) )
| 'member$c'(sK241(X0,X1,X2,X3),'set_option$d'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1126])]) ).
tff(f3115,plain,
! [X2: 'B_b_fun$',X3: 'B_b_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$s'('map_option$b'(X2),X0) != 'fun_app$s'('map_option$b'(X3),X1) )
| 'member$c'(sK241(X0,X1,X2,X3),'set_option$d'(X0)) ),
inference(cnf_transformation,[],[f1856]) ).
tff(f16632,plain,
spl249_1125,
inference(avatar_split_clause,[],[f3112,f16630]) ).
tff(f16630,plain,
( spl249_1125
<=> ! [X0: 'B_option$',X3: 'B_c_fun$',X2: 'B_c_fun$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$an'('map_option$d'(X2),X0) != 'fun_app$an'('map_option$d'(X3),X1) )
| 'member$c'(sK240(X0,X1,X2,X3),'set_option$d'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1125])]) ).
tff(f3112,plain,
! [X2: 'B_c_fun$',X3: 'B_c_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$an'('map_option$d'(X2),X0) != 'fun_app$an'('map_option$d'(X3),X1) )
| 'member$c'(sK240(X0,X1,X2,X3),'set_option$d'(X1)) ),
inference(cnf_transformation,[],[f1854]) ).
tff(f16628,plain,
spl249_1124,
inference(avatar_split_clause,[],[f3111,f16626]) ).
tff(f16626,plain,
( spl249_1124
<=> ! [X0: 'B_option$',X3: 'B_c_fun$',X2: 'B_c_fun$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$an'('map_option$d'(X2),X0) != 'fun_app$an'('map_option$d'(X3),X1) )
| 'member$c'(sK239(X0,X1,X2,X3),'set_option$d'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1124])]) ).
tff(f3111,plain,
! [X2: 'B_c_fun$',X3: 'B_c_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( 'fun_app$an'('map_option$d'(X2),X0) != 'fun_app$an'('map_option$d'(X3),X1) )
| 'member$c'(sK239(X0,X1,X2,X3),'set_option$d'(X0)) ),
inference(cnf_transformation,[],[f1854]) ).
tff(f16624,plain,
spl249_1123,
inference(avatar_split_clause,[],[f3108,f16622]) ).
tff(f16622,plain,
( spl249_1123
<=> ! [X0: 'C_option$',X3: 'C_b_fun$',X2: 'C_b_fun$',X1: 'C_option$'] :
( ( X0 = X1 )
| ( 'fun_app$bg'('map_option$'(X2),X0) != 'fun_app$bg'('map_option$'(X3),X1) )
| 'member$b'(sK238(X0,X1,X2,X3),'set_option$c'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1123])]) ).
tff(f3108,plain,
! [X2: 'C_b_fun$',X3: 'C_b_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( X0 = X1 )
| ( 'fun_app$bg'('map_option$'(X2),X0) != 'fun_app$bg'('map_option$'(X3),X1) )
| 'member$b'(sK238(X0,X1,X2,X3),'set_option$c'(X1)) ),
inference(cnf_transformation,[],[f1852]) ).
tff(f16620,plain,
spl249_1122,
inference(avatar_split_clause,[],[f3107,f16618]) ).
tff(f16618,plain,
( spl249_1122
<=> ! [X0: 'C_option$',X3: 'C_b_fun$',X2: 'C_b_fun$',X1: 'C_option$'] :
( ( X0 = X1 )
| ( 'fun_app$bg'('map_option$'(X2),X0) != 'fun_app$bg'('map_option$'(X3),X1) )
| 'member$b'(sK237(X0,X1,X2,X3),'set_option$c'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1122])]) ).
tff(f3107,plain,
! [X2: 'C_b_fun$',X3: 'C_b_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( X0 = X1 )
| ( 'fun_app$bg'('map_option$'(X2),X0) != 'fun_app$bg'('map_option$'(X3),X1) )
| 'member$b'(sK237(X0,X1,X2,X3),'set_option$c'(X0)) ),
inference(cnf_transformation,[],[f1852]) ).
tff(f16616,plain,
spl249_1121,
inference(avatar_split_clause,[],[f3104,f16614]) ).
tff(f16614,plain,
( spl249_1121
<=> ! [X0: 'A_option$',X3: 'A_a_fun$',X2: 'A_a_fun$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$be'('map_option$a'(X2),X0) != 'fun_app$be'('map_option$a'(X3),X1) )
| 'member$d'(sK236(X0,X1,X2,X3),'set_option$b'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1121])]) ).
tff(f3104,plain,
! [X2: 'A_a_fun$',X3: 'A_a_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$be'('map_option$a'(X2),X0) != 'fun_app$be'('map_option$a'(X3),X1) )
| 'member$d'(sK236(X0,X1,X2,X3),'set_option$b'(X1)) ),
inference(cnf_transformation,[],[f1850]) ).
tff(f16612,plain,
spl249_1120,
inference(avatar_split_clause,[],[f3103,f16610]) ).
tff(f16610,plain,
( spl249_1120
<=> ! [X0: 'A_option$',X3: 'A_a_fun$',X2: 'A_a_fun$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$be'('map_option$a'(X2),X0) != 'fun_app$be'('map_option$a'(X3),X1) )
| 'member$d'(sK235(X0,X1,X2,X3),'set_option$b'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1120])]) ).
tff(f3103,plain,
! [X2: 'A_a_fun$',X3: 'A_a_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$be'('map_option$a'(X2),X0) != 'fun_app$be'('map_option$a'(X3),X1) )
| 'member$d'(sK235(X0,X1,X2,X3),'set_option$b'(X0)) ),
inference(cnf_transformation,[],[f1850]) ).
tff(f16608,plain,
( spl249_1119
| ~ spl249_57
| ~ spl249_302 ),
inference(avatar_split_clause,[],[f5297,f5012,f3860,f16606]) ).
tff(f16606,plain,
( spl249_1119
<=> ! [X0: 'B$'] : ( tltrue = def_2('uwl$'(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1119])]) ).
tff(f5012,plain,
( spl249_302
<=> ! [X0: 'B_bool_fun$',X1: 'B$'] :
( ( tltrue = def_2(X0,X1) )
| ~ 'fun_app$c'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_302])]) ).
tff(f5297,plain,
( ! [X0: 'B$'] : ( tltrue = def_2('uwl$'(X0),X0) )
| ~ spl249_57
| ~ spl249_302 ),
inference(resolution,[],[f5013,f3861]) ).
tff(f5013,plain,
( ! [X0: 'B_bool_fun$',X1: 'B$'] :
( ~ 'fun_app$c'(X0,X1)
| ( tltrue = def_2(X0,X1) ) )
| ~ spl249_302 ),
inference(avatar_component_clause,[],[f5012]) ).
tff(f16604,plain,
spl249_1118,
inference(avatar_split_clause,[],[f3100,f16602]) ).
tff(f16602,plain,
( spl249_1118
<=> ! [X0: 'A_option$',X3: 'A_b_fun$',X2: 'A_b_fun$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$av'('map_option$e'(X2),X0) != 'fun_app$av'('map_option$e'(X3),X1) )
| 'member$d'(sK234(X0,X1,X2,X3),'set_option$b'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1118])]) ).
tff(f3100,plain,
! [X2: 'A_b_fun$',X3: 'A_b_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$av'('map_option$e'(X2),X0) != 'fun_app$av'('map_option$e'(X3),X1) )
| 'member$d'(sK234(X0,X1,X2,X3),'set_option$b'(X1)) ),
inference(cnf_transformation,[],[f1848]) ).
tff(f16600,plain,
spl249_1117,
inference(avatar_split_clause,[],[f3099,f16598]) ).
tff(f16598,plain,
( spl249_1117
<=> ! [X0: 'A_option$',X3: 'A_b_fun$',X2: 'A_b_fun$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$av'('map_option$e'(X2),X0) != 'fun_app$av'('map_option$e'(X3),X1) )
| 'member$d'(sK233(X0,X1,X2,X3),'set_option$b'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1117])]) ).
tff(f3099,plain,
! [X2: 'A_b_fun$',X3: 'A_b_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( 'fun_app$av'('map_option$e'(X2),X0) != 'fun_app$av'('map_option$e'(X3),X1) )
| 'member$d'(sK233(X0,X1,X2,X3),'set_option$b'(X0)) ),
inference(cnf_transformation,[],[f1848]) ).
tff(f16490,plain,
( spl249_1116
| ~ spl249_56
| ~ spl249_302 ),
inference(avatar_split_clause,[],[f5296,f5012,f3856,f16488]) ).
tff(f16488,plain,
( spl249_1116
<=> ! [X0: 'B$'] : ( tltrue = def_2('uwp$'(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1116])]) ).
tff(f5296,plain,
( ! [X0: 'B$'] : ( tltrue = def_2('uwp$'(X0),X0) )
| ~ spl249_56
| ~ spl249_302 ),
inference(resolution,[],[f5013,f3857]) ).
tff(f16440,plain,
spl249_1115,
inference(avatar_split_clause,[],[f3597,f16438]) ).
tff(f16438,plain,
( spl249_1115
<=> ! [X0: 'B_c_option_fun$',X3: 'B$',X2: 'B_c_option_fun$',X1: 'B_b_fun$'] :
( ( 'bind$b'('fun_app$g'('some$',X3),X2) = 'bind$b'('fun_app$g'('uve$'(X1),X3),X0) )
| ( 'comp$f'(X0,X1) != 'comp$ar'('id$c',X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1115])]) ).
tff(f3597,plain,
! [X2: 'B_c_option_fun$',X3: 'B$',X0: 'B_c_option_fun$',X1: 'B_b_fun$'] :
( ( 'bind$b'('fun_app$g'('some$',X3),X2) = 'bind$b'('fun_app$g'('uve$'(X1),X3),X0) )
| ( 'comp$f'(X0,X1) != 'comp$ar'('id$c',X2) ) ),
inference(forward_demodulation,[],[f3289,f2245]) ).
tff(f3289,plain,
! [X2: 'B_c_option_fun$',X3: 'B$',X0: 'B_c_option_fun$',X1: 'B_b_fun$'] :
( ( 'bind$b'('fun_app$g'('some$',X3),X2) = 'bind$b'('fun_app$g'('some$','fun_app$h'(X1,X3)),X0) )
| ( 'comp$f'(X0,X1) != 'comp$ar'('id$c',X2) ) ),
inference(definition_unfolding,[],[f3055,f2234,f2234]) ).
tff(f3055,plain,
! [X2: 'B_c_option_fun$',X3: 'B$',X0: 'B_c_option_fun$',X1: 'B_b_fun$'] :
( ( 'fun_app$n'(X2,X3) = 'fun_app$n'(X0,'fun_app$h'(X1,X3)) )
| ( 'comp$f'(X0,X1) != 'comp$ar'('id$c',X2) ) ),
inference(cnf_transformation,[],[f1025]) ).
tff(f1025,plain,
! [X0: 'B_c_option_fun$',X1: 'B_b_fun$',X2: 'B_c_option_fun$',X3: 'B$'] :
( ( 'fun_app$n'(X2,X3) = 'fun_app$n'(X0,'fun_app$h'(X1,X3)) )
| ( 'comp$f'(X0,X1) != 'comp$ar'('id$c',X2) ) ),
inference(ennf_transformation,[],[f658]) ).
tff(f658,axiom,
! [X0: 'B_c_option_fun$',X1: 'B_b_fun$',X2: 'B_c_option_fun$',X3: 'B$'] :
( ( 'comp$f'(X0,X1) = 'comp$ar'('id$c',X2) )
=> ( 'fun_app$n'(X2,X3) = 'fun_app$n'(X0,'fun_app$h'(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom656) ).
tff(f16436,plain,
spl249_1114,
inference(avatar_split_clause,[],[f3286,f16434]) ).
tff(f16434,plain,
( spl249_1114
<=> ! [X2: 'B$',X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( 'fun_app$g'('some$',X2) = 'bind$a'('fun_app$j'('some$a',sK192(X0,X1,X2)),X1) )
| ( 'fun_app$g'('some$',X2) != 'bind$a'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1114])]) ).
tff(f3286,plain,
! [X2: 'B$',X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( 'fun_app$g'('some$',X2) = 'bind$a'('fun_app$j'('some$a',sK192(X0,X1,X2)),X1) )
| ( 'fun_app$g'('some$',X2) != 'bind$a'(X0,X1) ) ),
inference(definition_unfolding,[],[f2991,f2233]) ).
tff(f2991,plain,
! [X2: 'B$',X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$l'(X1,sK192(X0,X1,X2)) )
| ( 'fun_app$g'('some$',X2) != 'bind$a'(X0,X1) ) ),
inference(cnf_transformation,[],[f1754]) ).
tff(f1754,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'bind$a'(X0,X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$g'('some$',X2) != 'fun_app$l'(X1,X3) )
| ( 'fun_app$j'('some$a',X3) != X0 ) ) )
& ( ( ( 'fun_app$g'('some$',X2) = 'fun_app$l'(X1,sK192(X0,X1,X2)) )
& ( 'fun_app$j'('some$a',sK192(X0,X1,X2)) = X0 ) )
| ( 'fun_app$g'('some$',X2) != 'bind$a'(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK192])],[f1752,f1753]) ).
tff(f1753,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$',X2: 'B$'] :
( ? [X4: 'C$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$l'(X1,X4) )
& ( 'fun_app$j'('some$a',X4) = X0 ) )
=> ( ( 'fun_app$g'('some$',X2) = 'fun_app$l'(X1,sK192(X0,X1,X2)) )
& ( 'fun_app$j'('some$a',sK192(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1752,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'bind$a'(X0,X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$g'('some$',X2) != 'fun_app$l'(X1,X3) )
| ( 'fun_app$j'('some$a',X3) != X0 ) ) )
& ( ? [X4: 'C$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$l'(X1,X4) )
& ( 'fun_app$j'('some$a',X4) = X0 ) )
| ( 'fun_app$g'('some$',X2) != 'bind$a'(X0,X1) ) ) ),
inference(rectify,[],[f1751]) ).
tff(f1751,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'bind$a'(X0,X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$g'('some$',X2) != 'fun_app$l'(X1,X3) )
| ( 'fun_app$j'('some$a',X3) != X0 ) ) )
& ( ? [X3: 'C$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$l'(X1,X3) )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ( 'fun_app$g'('some$',X2) != 'bind$a'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f417]) ).
tff(f417,axiom,
! [X0: 'C_option$',X1: 'C_b_option_fun$',X2: 'B$'] :
( ( 'fun_app$g'('some$',X2) = 'bind$a'(X0,X1) )
<=> ? [X3: 'C$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$l'(X1,X3) )
& ( 'fun_app$j'('some$a',X3) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom415) ).
tff(f16432,plain,
spl249_1113,
inference(avatar_split_clause,[],[f3284,f16430]) ).
tff(f16430,plain,
( spl249_1113
<=> ! [X2: 'C$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( 'fun_app$j'('some$a',X2) = 'bind$b'('fun_app$g'('some$',sK190(X0,X1,X2)),X1) )
| ( 'fun_app$j'('some$a',X2) != 'bind$b'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1113])]) ).
tff(f3284,plain,
! [X2: 'C$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( 'fun_app$j'('some$a',X2) = 'bind$b'('fun_app$g'('some$',sK190(X0,X1,X2)),X1) )
| ( 'fun_app$j'('some$a',X2) != 'bind$b'(X0,X1) ) ),
inference(definition_unfolding,[],[f2985,f2234]) ).
tff(f2985,plain,
! [X2: 'C$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$n'(X1,sK190(X0,X1,X2)) )
| ( 'fun_app$j'('some$a',X2) != 'bind$b'(X0,X1) ) ),
inference(cnf_transformation,[],[f1746]) ).
tff(f1746,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'bind$b'(X0,X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$j'('some$a',X2) != 'fun_app$n'(X1,X3) )
| ( 'fun_app$g'('some$',X3) != X0 ) ) )
& ( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$n'(X1,sK190(X0,X1,X2)) )
& ( 'fun_app$g'('some$',sK190(X0,X1,X2)) = X0 ) )
| ( 'fun_app$j'('some$a',X2) != 'bind$b'(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK190])],[f1744,f1745]) ).
tff(f1745,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$',X2: 'C$'] :
( ? [X4: 'B$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$n'(X1,X4) )
& ( 'fun_app$g'('some$',X4) = X0 ) )
=> ( ( 'fun_app$j'('some$a',X2) = 'fun_app$n'(X1,sK190(X0,X1,X2)) )
& ( 'fun_app$g'('some$',sK190(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1744,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'bind$b'(X0,X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$j'('some$a',X2) != 'fun_app$n'(X1,X3) )
| ( 'fun_app$g'('some$',X3) != X0 ) ) )
& ( ? [X4: 'B$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$n'(X1,X4) )
& ( 'fun_app$g'('some$',X4) = X0 ) )
| ( 'fun_app$j'('some$a',X2) != 'bind$b'(X0,X1) ) ) ),
inference(rectify,[],[f1743]) ).
tff(f1743,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'bind$b'(X0,X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$j'('some$a',X2) != 'fun_app$n'(X1,X3) )
| ( 'fun_app$g'('some$',X3) != X0 ) ) )
& ( ? [X3: 'B$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$n'(X1,X3) )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ( 'fun_app$j'('some$a',X2) != 'bind$b'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f416]) ).
tff(f416,axiom,
! [X0: 'B_option$',X1: 'B_c_option_fun$',X2: 'C$'] :
( ( 'fun_app$j'('some$a',X2) = 'bind$b'(X0,X1) )
<=> ? [X3: 'B$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$n'(X1,X3) )
& ( 'fun_app$g'('some$',X3) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom414) ).
tff(f16428,plain,
spl249_1112,
inference(avatar_split_clause,[],[f3220,f16426]) ).
tff(f16426,plain,
( spl249_1112
<=> ! [X0: 'B_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP43(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1112])]) ).
tff(f3220,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP43(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1912]) ).
tff(f1912,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$',X2: 'B_option_bool_fun$',X3: 'B_option$'] :
( ( sP43(X0,X1,X2,X3)
| ( ~ 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 ) )
| ( ~ 'fun_app$a'(X2,X3)
& ( 'none$a' = X0 ) ) )
& ( ( ( 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 ) )
& ( 'fun_app$a'(X2,X3)
| ( 'none$a' != X0 ) ) )
| ~ sP43(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1911]) ).
tff(f1911,plain,
! [X3: 'B_option$',X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( sP43(X3,X2,X0,X1)
| ( ~ 'fun_app$a'(X0,'fun_app$g'(X2,'fun_app$al'('the$',X3)))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$a'(X0,X1)
& ( 'none$a' = X3 ) ) )
& ( ( ( 'fun_app$a'(X0,'fun_app$g'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$a' != X3 ) ) )
| ~ sP43(X3,X2,X0,X1) ) ),
inference(flattening,[],[f1910]) ).
tff(f1910,plain,
! [X3: 'B_option$',X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( sP43(X3,X2,X0,X1)
| ( ~ 'fun_app$a'(X0,'fun_app$g'(X2,'fun_app$al'('the$',X3)))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$a'(X0,X1)
& ( 'none$a' = X3 ) ) )
& ( ( ( 'fun_app$a'(X0,'fun_app$g'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$a' != X3 ) ) )
| ~ sP43(X3,X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1185]) ).
tff(f1185,plain,
! [X3: 'B_option$',X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( sP43(X3,X2,X0,X1)
<=> ( ( 'fun_app$a'(X0,'fun_app$g'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$a' != X3 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP43])]) ).
tff(f16424,plain,
spl249_1111,
inference(avatar_split_clause,[],[f3212,f16422]) ).
tff(f16422,plain,
( spl249_1111
<=> ! [X0: 'B_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP42(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1111])]) ).
tff(f3212,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP42(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1908]) ).
tff(f1908,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$',X2: 'B_option_bool_fun$',X3: 'B_option$'] :
( ( sP42(X0,X1,X2,X3)
| ( ~ 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 ) )
| ( ~ 'fun_app$a'(X2,X3)
& ( 'none$a' = X0 ) ) )
& ( ( ( 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 ) )
& ( 'fun_app$a'(X2,X3)
| ( 'none$a' != X0 ) ) )
| ~ sP42(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1907]) ).
tff(f1907,plain,
! [X3: 'B_option$',X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( sP42(X3,X2,X0,X1)
| ( ~ 'fun_app$a'(X0,'fun_app$g'(X2,'fun_app$al'('the$',X3)))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$a'(X0,X1)
& ( 'none$a' = X3 ) ) )
& ( ( ( 'fun_app$a'(X0,'fun_app$g'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$a' != X3 ) ) )
| ~ sP42(X3,X2,X0,X1) ) ),
inference(flattening,[],[f1906]) ).
tff(f1906,plain,
! [X3: 'B_option$',X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( sP42(X3,X2,X0,X1)
| ( ~ 'fun_app$a'(X0,'fun_app$g'(X2,'fun_app$al'('the$',X3)))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$a'(X0,X1)
& ( 'none$a' = X3 ) ) )
& ( ( ( 'fun_app$a'(X0,'fun_app$g'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$a' != X3 ) ) )
| ~ sP42(X3,X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1183]) ).
tff(f1183,plain,
! [X3: 'B_option$',X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( sP42(X3,X2,X0,X1)
<=> ( ( 'fun_app$a'(X0,'fun_app$g'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$a' != X3 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP42])]) ).
tff(f16420,plain,
spl249_1110,
inference(avatar_split_clause,[],[f3202,f16418]) ).
tff(f16418,plain,
( spl249_1110
<=> ! [X0: 'A_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) != X0 )
| ~ sP41(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1110])]) ).
tff(f3202,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) != X0 )
| ~ sP41(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1903]) ).
tff(f1903,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$',X2: 'B_option_bool_fun$',X3: 'B_option$'] :
( ( sP41(X0,X1,X2,X3)
| ( ~ 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
& ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) = X0 ) )
| ( ~ 'fun_app$a'(X2,X3)
& ( 'none$b' = X0 ) ) )
& ( ( ( 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) != X0 ) )
& ( 'fun_app$a'(X2,X3)
| ( 'none$b' != X0 ) ) )
| ~ sP41(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1902]) ).
tff(f1902,plain,
! [X3: 'A_option$',X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( sP41(X3,X2,X0,X1)
| ( ~ 'fun_app$a'(X0,'fun_app$f'(X2,'fun_app$bf'('the$b',X3)))
& ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X3)) = X3 ) )
| ( ~ 'fun_app$a'(X0,X1)
& ( 'none$b' = X3 ) ) )
& ( ( ( 'fun_app$a'(X0,'fun_app$f'(X2,'fun_app$bf'('the$b',X3)))
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$b' != X3 ) ) )
| ~ sP41(X3,X2,X0,X1) ) ),
inference(flattening,[],[f1901]) ).
tff(f1901,plain,
! [X3: 'A_option$',X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( sP41(X3,X2,X0,X1)
| ( ~ 'fun_app$a'(X0,'fun_app$f'(X2,'fun_app$bf'('the$b',X3)))
& ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X3)) = X3 ) )
| ( ~ 'fun_app$a'(X0,X1)
& ( 'none$b' = X3 ) ) )
& ( ( ( 'fun_app$a'(X0,'fun_app$f'(X2,'fun_app$bf'('the$b',X3)))
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$b' != X3 ) ) )
| ~ sP41(X3,X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1181]) ).
tff(f1181,plain,
! [X3: 'A_option$',X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( sP41(X3,X2,X0,X1)
<=> ( ( 'fun_app$a'(X0,'fun_app$f'(X2,'fun_app$bf'('the$b',X3)))
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$b' != X3 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP41])]) ).
tff(f16416,plain,
spl249_1109,
inference(avatar_split_clause,[],[f3194,f16414]) ).
tff(f16414,plain,
( spl249_1109
<=> ! [X0: 'A_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) != X0 )
| ~ sP40(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1109])]) ).
tff(f3194,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) != X0 )
| ~ sP40(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1899]) ).
tff(f1899,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$',X2: 'B_option_bool_fun$',X3: 'B_option$'] :
( ( sP40(X0,X1,X2,X3)
| ( ~ 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
& ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) = X0 ) )
| ( ~ 'fun_app$a'(X2,X3)
& ( 'none$b' = X0 ) ) )
& ( ( ( 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) != X0 ) )
& ( 'fun_app$a'(X2,X3)
| ( 'none$b' != X0 ) ) )
| ~ sP40(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1898]) ).
tff(f1898,plain,
! [X3: 'A_option$',X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( sP40(X3,X2,X0,X1)
| ( ~ 'fun_app$a'(X0,'fun_app$f'(X2,'fun_app$bf'('the$b',X3)))
& ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X3)) = X3 ) )
| ( ~ 'fun_app$a'(X0,X1)
& ( 'none$b' = X3 ) ) )
& ( ( ( 'fun_app$a'(X0,'fun_app$f'(X2,'fun_app$bf'('the$b',X3)))
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$b' != X3 ) ) )
| ~ sP40(X3,X2,X0,X1) ) ),
inference(flattening,[],[f1897]) ).
tff(f1897,plain,
! [X3: 'A_option$',X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( sP40(X3,X2,X0,X1)
| ( ~ 'fun_app$a'(X0,'fun_app$f'(X2,'fun_app$bf'('the$b',X3)))
& ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X3)) = X3 ) )
| ( ~ 'fun_app$a'(X0,X1)
& ( 'none$b' = X3 ) ) )
& ( ( ( 'fun_app$a'(X0,'fun_app$f'(X2,'fun_app$bf'('the$b',X3)))
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$b' != X3 ) ) )
| ~ sP40(X3,X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1179]) ).
tff(f1179,plain,
! [X3: 'A_option$',X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( sP40(X3,X2,X0,X1)
<=> ( ( 'fun_app$a'(X0,'fun_app$f'(X2,'fun_app$bf'('the$b',X3)))
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$b' != X3 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP40])]) ).
tff(f16412,plain,
( spl249_1108
| ~ spl249_57
| ~ spl249_299 ),
inference(avatar_split_clause,[],[f5289,f4999,f3860,f16410]) ).
tff(f16410,plain,
( spl249_1108
<=> ! [X0: 'B$'] : ( tltrue = def_5('uwl$'(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1108])]) ).
tff(f4999,plain,
( spl249_299
<=> ! [X0: 'B_bool_fun$',X1: 'B$'] :
( ( tltrue = def_5(X0,X1) )
| ~ 'fun_app$c'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_299])]) ).
tff(f5289,plain,
( ! [X0: 'B$'] : ( tltrue = def_5('uwl$'(X0),X0) )
| ~ spl249_57
| ~ spl249_299 ),
inference(resolution,[],[f5000,f3861]) ).
tff(f5000,plain,
( ! [X0: 'B_bool_fun$',X1: 'B$'] :
( ~ 'fun_app$c'(X0,X1)
| ( tltrue = def_5(X0,X1) ) )
| ~ spl249_299 ),
inference(avatar_component_clause,[],[f4999]) ).
tff(f16408,plain,
spl249_1107,
inference(avatar_split_clause,[],[f3168,f16406]) ).
tff(f16406,plain,
( spl249_1107
<=> ! [X0: 'C_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'C_c_option_fun$'] :
( 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) != X0 )
| ~ sP37(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1107])]) ).
tff(f3168,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) != X0 )
| ~ sP37(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1886]) ).
tff(f1886,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$',X2: 'C_option_bool_fun$',X3: 'C_option$'] :
( ( sP37(X0,X1,X2,X3)
| ( ~ 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
& ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 ) )
| ( ~ 'fun_app$'(X2,X3)
& ( 'none$' = X0 ) ) )
& ( ( ( 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) != X0 ) )
& ( 'fun_app$'(X2,X3)
| ( 'none$' != X0 ) ) )
| ~ sP37(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1885]) ).
tff(f1885,plain,
! [X3: 'C_option$',X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( sP37(X3,X2,X0,X1)
| ( ~ 'fun_app$'(X0,'fun_app$j'(X2,'fun_app$ak'('the$a',X3)))
& ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) = X3 ) )
| ( ~ 'fun_app$'(X0,X1)
& ( 'none$' = X3 ) ) )
& ( ( ( 'fun_app$'(X0,'fun_app$j'(X2,'fun_app$ak'('the$a',X3)))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$' != X3 ) ) )
| ~ sP37(X3,X2,X0,X1) ) ),
inference(flattening,[],[f1884]) ).
tff(f1884,plain,
! [X3: 'C_option$',X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( sP37(X3,X2,X0,X1)
| ( ~ 'fun_app$'(X0,'fun_app$j'(X2,'fun_app$ak'('the$a',X3)))
& ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) = X3 ) )
| ( ~ 'fun_app$'(X0,X1)
& ( 'none$' = X3 ) ) )
& ( ( ( 'fun_app$'(X0,'fun_app$j'(X2,'fun_app$ak'('the$a',X3)))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$' != X3 ) ) )
| ~ sP37(X3,X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1173]) ).
tff(f1173,plain,
! [X3: 'C_option$',X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( sP37(X3,X2,X0,X1)
<=> ( ( 'fun_app$'(X0,'fun_app$j'(X2,'fun_app$ak'('the$a',X3)))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$' != X3 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP37])]) ).
tff(f16404,plain,
spl249_1106,
inference(avatar_split_clause,[],[f3160,f16402]) ).
tff(f16402,plain,
( spl249_1106
<=> ! [X0: 'C_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'C_c_option_fun$'] :
( 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) != X0 )
| ~ sP36(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1106])]) ).
tff(f3160,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) != X0 )
| ~ sP36(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1882]) ).
tff(f1882,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$',X2: 'C_option_bool_fun$',X3: 'C_option$'] :
( ( sP36(X0,X1,X2,X3)
| ( ~ 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
& ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 ) )
| ( ~ 'fun_app$'(X2,X3)
& ( 'none$' = X0 ) ) )
& ( ( ( 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) != X0 ) )
& ( 'fun_app$'(X2,X3)
| ( 'none$' != X0 ) ) )
| ~ sP36(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1881]) ).
tff(f1881,plain,
! [X3: 'C_option$',X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( sP36(X3,X2,X0,X1)
| ( ~ 'fun_app$'(X0,'fun_app$j'(X2,'fun_app$ak'('the$a',X3)))
& ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) = X3 ) )
| ( ~ 'fun_app$'(X0,X1)
& ( 'none$' = X3 ) ) )
& ( ( ( 'fun_app$'(X0,'fun_app$j'(X2,'fun_app$ak'('the$a',X3)))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$' != X3 ) ) )
| ~ sP36(X3,X2,X0,X1) ) ),
inference(flattening,[],[f1880]) ).
tff(f1880,plain,
! [X3: 'C_option$',X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( sP36(X3,X2,X0,X1)
| ( ~ 'fun_app$'(X0,'fun_app$j'(X2,'fun_app$ak'('the$a',X3)))
& ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) = X3 ) )
| ( ~ 'fun_app$'(X0,X1)
& ( 'none$' = X3 ) ) )
& ( ( ( 'fun_app$'(X0,'fun_app$j'(X2,'fun_app$ak'('the$a',X3)))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$' != X3 ) ) )
| ~ sP36(X3,X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1171]) ).
tff(f1171,plain,
! [X3: 'C_option$',X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( sP36(X3,X2,X0,X1)
<=> ( ( 'fun_app$'(X0,'fun_app$j'(X2,'fun_app$ak'('the$a',X3)))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$' != X3 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP36])]) ).
tff(f16400,plain,
spl249_1105,
inference(avatar_split_clause,[],[f3048,f16398]) ).
tff(f16398,plain,
( spl249_1105
<=> ! [X0: 'B_a_fun$',X3: 'B$',X2: 'A_a_option_fun$',X1: 'A_b_b_fun_fun$'] : ( 'fun_app$g'('fun_app$au'('register_from_getter_setter$'(X0,X1),X2),X3) = 'fun_app$av'('case_option$d'('none$a','uua$'(X1,X3)),'fun_app$q'(X2,'fun_app$ao'(X0,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1105])]) ).
tff(f3048,plain,
! [X2: 'A_a_option_fun$',X3: 'B$',X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] : ( 'fun_app$g'('fun_app$au'('register_from_getter_setter$'(X0,X1),X2),X3) = 'fun_app$av'('case_option$d'('none$a','uua$'(X1,X3)),'fun_app$q'(X2,'fun_app$ao'(X0,X3))) ),
inference(cnf_transformation,[],[f95]) ).
tff(f95,axiom,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$',X2: 'A_a_option_fun$',X3: 'B$'] : ( 'fun_app$g'('fun_app$au'('register_from_getter_setter$'(X0,X1),X2),X3) = 'fun_app$av'('case_option$d'('none$a','uua$'(X1,X3)),'fun_app$q'(X2,'fun_app$ao'(X0,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom93) ).
tff(f16396,plain,
spl249_1104,
inference(avatar_split_clause,[],[f3047,f16394]) ).
tff(f3047,plain,
! [X2: 'B_b_option_fun$',X3: 'C$',X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] : ( 'fun_app$j'('fun_app$am'('register_from_getter_setter$a'(X0,X1),X2),X3) = 'fun_app$an'('case_option$c'('none$','uu$'(X1,X3)),'fun_app$g'(X2,'fun_app$m'(X0,X3))) ),
inference(cnf_transformation,[],[f96]) ).
tff(f96,axiom,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$',X2: 'B_b_option_fun$',X3: 'C$'] : ( 'fun_app$j'('fun_app$am'('register_from_getter_setter$a'(X0,X1),X2),X3) = 'fun_app$an'('case_option$c'('none$','uu$'(X1,X3)),'fun_app$g'(X2,'fun_app$m'(X0,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom94) ).
tff(f16274,plain,
( spl249_1103
| ~ spl249_56
| ~ spl249_299 ),
inference(avatar_split_clause,[],[f5288,f4999,f3856,f16272]) ).
tff(f16272,plain,
( spl249_1103
<=> ! [X0: 'B$'] : ( tltrue = def_5('uwp$'(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1103])]) ).
tff(f5288,plain,
( ! [X0: 'B$'] : ( tltrue = def_5('uwp$'(X0),X0) )
| ~ spl249_56
| ~ spl249_299 ),
inference(resolution,[],[f5000,f3857]) ).
tff(f16255,plain,
spl249_1102,
inference(avatar_split_clause,[],[f3287,f16253]) ).
tff(f16253,plain,
( spl249_1102
<=> ! [X0: 'B_c_option_fun$',X3: 'B$',X2: 'B$',X1: 'B_b_fun$'] : ( 'comp$f'(X0,'fun_app$ai'('fun_upd$b'(X1,X2),X3)) = 'fun_upd$c'('comp$f'(X0,X1),X2,'bind$b'('fun_app$g'('some$',X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1102])]) ).
tff(f3287,plain,
! [X2: 'B$',X3: 'B$',X0: 'B_c_option_fun$',X1: 'B_b_fun$'] : ( 'comp$f'(X0,'fun_app$ai'('fun_upd$b'(X1,X2),X3)) = 'fun_upd$c'('comp$f'(X0,X1),X2,'bind$b'('fun_app$g'('some$',X3),X0)) ),
inference(definition_unfolding,[],[f3042,f2234]) ).
tff(f3042,plain,
! [X2: 'B$',X3: 'B$',X0: 'B_c_option_fun$',X1: 'B_b_fun$'] : ( 'comp$f'(X0,'fun_app$ai'('fun_upd$b'(X1,X2),X3)) = 'fun_upd$c'('comp$f'(X0,X1),X2,'fun_app$n'(X0,X3)) ),
inference(cnf_transformation,[],[f667]) ).
tff(f667,axiom,
! [X0: 'B_c_option_fun$',X1: 'B_b_fun$',X2: 'B$',X3: 'B$'] : ( 'comp$f'(X0,'fun_app$ai'('fun_upd$b'(X1,X2),X3)) = 'fun_upd$c'('comp$f'(X0,X1),X2,'fun_app$n'(X0,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom665) ).
tff(f16251,plain,
spl249_1101,
inference(avatar_split_clause,[],[f3096,f16249]) ).
tff(f16249,plain,
( spl249_1101
<=> ! [X4: 'B$',X0: 'B_option_b_fun$',X3: 'B_b_option_fun$',X2: 'B_option_b_fun$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$al'(X0,'fun_app$g'(X1,X4)) = 'fun_app$al'(X2,'fun_app$g'(X3,X4)) )
| ( 'comp$m'(X0,X1) != 'comp$m'(X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1101])]) ).
tff(f3096,plain,
! [X2: 'B_option_b_fun$',X3: 'B_b_option_fun$',X0: 'B_option_b_fun$',X1: 'B_b_option_fun$',X4: 'B$'] :
( ( 'fun_app$al'(X0,'fun_app$g'(X1,X4)) = 'fun_app$al'(X2,'fun_app$g'(X3,X4)) )
| ( 'comp$m'(X0,X1) != 'comp$m'(X2,X3) ) ),
inference(cnf_transformation,[],[f1066]) ).
tff(f1066,plain,
! [X0: 'B_option_b_fun$',X1: 'B_b_option_fun$',X2: 'B_option_b_fun$',X3: 'B_b_option_fun$'] :
( ! [X4: 'B$'] : ( 'fun_app$al'(X0,'fun_app$g'(X1,X4)) = 'fun_app$al'(X2,'fun_app$g'(X3,X4)) )
| ( 'comp$m'(X0,X1) != 'comp$m'(X2,X3) ) ),
inference(ennf_transformation,[],[f846]) ).
tff(f846,plain,
! [X0: 'B_option_b_fun$',X1: 'B_b_option_fun$',X2: 'B_option_b_fun$',X3: 'B_b_option_fun$'] :
~ ( ~ ! [X4: 'B$'] : ( 'fun_app$al'(X0,'fun_app$g'(X1,X4)) = 'fun_app$al'(X2,'fun_app$g'(X3,X4)) )
& ( 'comp$m'(X0,X1) = 'comp$m'(X2,X3) ) ),
inference(true_and_false_elimination,[],[f631]) ).
tff(f631,axiom,
! [X0: 'B_option_b_fun$',X1: 'B_b_option_fun$',X2: 'B_option_b_fun$',X3: 'B_b_option_fun$'] :
( ( ( ! [X4: 'B$'] : ( 'fun_app$al'(X0,'fun_app$g'(X1,X4)) = 'fun_app$al'(X2,'fun_app$g'(X3,X4)) )
=> $false )
& ( 'comp$m'(X0,X1) = 'comp$m'(X2,X3) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom629) ).
tff(f16247,plain,
spl249_1100,
inference(avatar_split_clause,[],[f3094,f16245]) ).
tff(f16245,plain,
( spl249_1100
<=> ! [X4: 'A$',X0: 'A_b_option_fun$',X3: 'A_a_fun$',X2: 'A_b_option_fun$',X1: 'A_a_fun$'] :
( ( 'fun_app$f'(X0,'fun_app$r'(X1,X4)) = 'fun_app$f'(X2,'fun_app$r'(X3,X4)) )
| ( 'comp$g'(X0,X1) != 'comp$g'(X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1100])]) ).
tff(f3094,plain,
! [X2: 'A_b_option_fun$',X3: 'A_a_fun$',X0: 'A_b_option_fun$',X1: 'A_a_fun$',X4: 'A$'] :
( ( 'fun_app$f'(X0,'fun_app$r'(X1,X4)) = 'fun_app$f'(X2,'fun_app$r'(X3,X4)) )
| ( 'comp$g'(X0,X1) != 'comp$g'(X2,X3) ) ),
inference(cnf_transformation,[],[f1064]) ).
tff(f1064,plain,
! [X0: 'A_b_option_fun$',X1: 'A_a_fun$',X2: 'A_b_option_fun$',X3: 'A_a_fun$'] :
( ! [X4: 'A$'] : ( 'fun_app$f'(X0,'fun_app$r'(X1,X4)) = 'fun_app$f'(X2,'fun_app$r'(X3,X4)) )
| ( 'comp$g'(X0,X1) != 'comp$g'(X2,X3) ) ),
inference(ennf_transformation,[],[f844]) ).
tff(f844,plain,
! [X0: 'A_b_option_fun$',X1: 'A_a_fun$',X2: 'A_b_option_fun$',X3: 'A_a_fun$'] :
~ ( ~ ! [X4: 'A$'] : ( 'fun_app$f'(X0,'fun_app$r'(X1,X4)) = 'fun_app$f'(X2,'fun_app$r'(X3,X4)) )
& ( 'comp$g'(X0,X1) = 'comp$g'(X2,X3) ) ),
inference(true_and_false_elimination,[],[f629]) ).
tff(f629,axiom,
! [X0: 'A_b_option_fun$',X1: 'A_a_fun$',X2: 'A_b_option_fun$',X3: 'A_a_fun$'] :
( ( ( ! [X4: 'A$'] : ( 'fun_app$f'(X0,'fun_app$r'(X1,X4)) = 'fun_app$f'(X2,'fun_app$r'(X3,X4)) )
=> $false )
& ( 'comp$g'(X0,X1) = 'comp$g'(X2,X3) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom627) ).
tff(f16243,plain,
spl249_1099,
inference(avatar_split_clause,[],[f3093,f16241]) ).
tff(f16241,plain,
( spl249_1099
<=> ! [X4: 'C$',X0: 'C_option_c_fun$',X3: 'C_c_option_fun$',X2: 'C_option_c_fun$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$ak'(X0,'fun_app$j'(X1,X4)) = 'fun_app$ak'(X2,'fun_app$j'(X3,X4)) )
| ( 'comp$n'(X0,X1) != 'comp$n'(X2,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1099])]) ).
tff(f3093,plain,
! [X2: 'C_option_c_fun$',X3: 'C_c_option_fun$',X0: 'C_option_c_fun$',X1: 'C_c_option_fun$',X4: 'C$'] :
( ( 'fun_app$ak'(X0,'fun_app$j'(X1,X4)) = 'fun_app$ak'(X2,'fun_app$j'(X3,X4)) )
| ( 'comp$n'(X0,X1) != 'comp$n'(X2,X3) ) ),
inference(cnf_transformation,[],[f1063]) ).
tff(f1063,plain,
! [X0: 'C_option_c_fun$',X1: 'C_c_option_fun$',X2: 'C_option_c_fun$',X3: 'C_c_option_fun$'] :
( ! [X4: 'C$'] : ( 'fun_app$ak'(X0,'fun_app$j'(X1,X4)) = 'fun_app$ak'(X2,'fun_app$j'(X3,X4)) )
| ( 'comp$n'(X0,X1) != 'comp$n'(X2,X3) ) ),
inference(ennf_transformation,[],[f843]) ).
tff(f843,plain,
! [X0: 'C_option_c_fun$',X1: 'C_c_option_fun$',X2: 'C_option_c_fun$',X3: 'C_c_option_fun$'] :
~ ( ~ ! [X4: 'C$'] : ( 'fun_app$ak'(X0,'fun_app$j'(X1,X4)) = 'fun_app$ak'(X2,'fun_app$j'(X3,X4)) )
& ( 'comp$n'(X0,X1) = 'comp$n'(X2,X3) ) ),
inference(true_and_false_elimination,[],[f632]) ).
tff(f632,axiom,
! [X0: 'C_option_c_fun$',X1: 'C_c_option_fun$',X2: 'C_option_c_fun$',X3: 'C_c_option_fun$'] :
( ( ( ! [X4: 'C$'] : ( 'fun_app$ak'(X0,'fun_app$j'(X1,X4)) = 'fun_app$ak'(X2,'fun_app$j'(X3,X4)) )
=> $false )
& ( 'comp$n'(X0,X1) = 'comp$n'(X2,X3) ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom630) ).
tff(f16239,plain,
spl249_1098,
inference(avatar_split_clause,[],[f3022,f16237]) ).
tff(f16237,plain,
( spl249_1098
<=> ! [X2: 'B$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$g'(X1,sK201(X0,X1,X2)) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$ac'('bind$c'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1098])]) ).
tff(f3022,plain,
! [X2: 'B$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$g'(X1,sK201(X0,X1,X2)) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$ac'('bind$c'(X0),X1) ) ),
inference(cnf_transformation,[],[f1792]) ).
tff(f1792,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'fun_app$ac'('bind$c'(X0),X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$g'('some$',X2) != 'fun_app$g'(X1,X3) )
| ( 'fun_app$g'('some$',X3) != X0 ) ) )
& ( ( ( 'fun_app$g'('some$',X2) = 'fun_app$g'(X1,sK201(X0,X1,X2)) )
& ( 'fun_app$g'('some$',sK201(X0,X1,X2)) = X0 ) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$ac'('bind$c'(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK201])],[f1790,f1791]) ).
tff(f1791,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$',X2: 'B$'] :
( ? [X4: 'B$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$g'(X1,X4) )
& ( 'fun_app$g'('some$',X4) = X0 ) )
=> ( ( 'fun_app$g'('some$',X2) = 'fun_app$g'(X1,sK201(X0,X1,X2)) )
& ( 'fun_app$g'('some$',sK201(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1790,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'fun_app$ac'('bind$c'(X0),X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$g'('some$',X2) != 'fun_app$g'(X1,X3) )
| ( 'fun_app$g'('some$',X3) != X0 ) ) )
& ( ? [X4: 'B$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$g'(X1,X4) )
& ( 'fun_app$g'('some$',X4) = X0 ) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$ac'('bind$c'(X0),X1) ) ) ),
inference(rectify,[],[f1789]) ).
tff(f1789,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'fun_app$ac'('bind$c'(X0),X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$g'('some$',X2) != 'fun_app$g'(X1,X3) )
| ( 'fun_app$g'('some$',X3) != X0 ) ) )
& ( ? [X3: 'B$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$g'(X1,X3) )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$ac'('bind$c'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f418]) ).
tff(f418,axiom,
! [X0: 'B_option$',X1: 'B_b_option_fun$',X2: 'B$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$ac'('bind$c'(X0),X1) )
<=> ? [X3: 'B$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$g'(X1,X3) )
& ( 'fun_app$g'('some$',X3) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom416) ).
tff(f16235,plain,
spl249_1097,
inference(avatar_split_clause,[],[f3013,f16233]) ).
tff(f16233,plain,
( spl249_1097
<=> ! [X2: 'C$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$j'(X1,sK198(X0,X1,X2)) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$ab'('bind$'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1097])]) ).
tff(f3013,plain,
! [X2: 'C$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$j'(X1,sK198(X0,X1,X2)) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$ab'('bind$'(X0),X1) ) ),
inference(cnf_transformation,[],[f1780]) ).
tff(f1780,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$ab'('bind$'(X0),X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$j'('some$a',X2) != 'fun_app$j'(X1,X3) )
| ( 'fun_app$j'('some$a',X3) != X0 ) ) )
& ( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$j'(X1,sK198(X0,X1,X2)) )
& ( 'fun_app$j'('some$a',sK198(X0,X1,X2)) = X0 ) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$ab'('bind$'(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK198])],[f1778,f1779]) ).
tff(f1779,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$',X2: 'C$'] :
( ? [X4: 'C$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$j'(X1,X4) )
& ( 'fun_app$j'('some$a',X4) = X0 ) )
=> ( ( 'fun_app$j'('some$a',X2) = 'fun_app$j'(X1,sK198(X0,X1,X2)) )
& ( 'fun_app$j'('some$a',sK198(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1778,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$ab'('bind$'(X0),X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$j'('some$a',X2) != 'fun_app$j'(X1,X3) )
| ( 'fun_app$j'('some$a',X3) != X0 ) ) )
& ( ? [X4: 'C$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$j'(X1,X4) )
& ( 'fun_app$j'('some$a',X4) = X0 ) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$ab'('bind$'(X0),X1) ) ) ),
inference(rectify,[],[f1777]) ).
tff(f1777,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$ab'('bind$'(X0),X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$j'('some$a',X2) != 'fun_app$j'(X1,X3) )
| ( 'fun_app$j'('some$a',X3) != X0 ) ) )
& ( ? [X3: 'C$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$j'(X1,X3) )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$ab'('bind$'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f415]) ).
tff(f415,axiom,
! [X0: 'C_option$',X1: 'C_c_option_fun$',X2: 'C$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$ab'('bind$'(X0),X1) )
<=> ? [X3: 'C$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$j'(X1,X3) )
& ( 'fun_app$j'('some$a',X3) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom413) ).
tff(f16231,plain,
spl249_1096,
inference(avatar_split_clause,[],[f2998,f16229]) ).
tff(f16229,plain,
( spl249_1096
<=> ! [X2: 'A$',X0: 'A_option$',X1: 'A_a_option_fun$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$q'(X1,sK193(X0,X1,X2)) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bp'('bind$h'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1096])]) ).
tff(f2998,plain,
! [X2: 'A$',X0: 'A_option$',X1: 'A_a_option_fun$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$q'(X1,sK193(X0,X1,X2)) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bp'('bind$h'(X0),X1) ) ),
inference(cnf_transformation,[],[f1760]) ).
tff(f1760,plain,
! [X0: 'A_option$',X1: 'A_a_option_fun$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$bp'('bind$h'(X0),X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$q'('some$b',X2) != 'fun_app$q'(X1,X3) )
| ( 'fun_app$q'('some$b',X3) != X0 ) ) )
& ( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$q'(X1,sK193(X0,X1,X2)) )
& ( 'fun_app$q'('some$b',sK193(X0,X1,X2)) = X0 ) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bp'('bind$h'(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK193])],[f1758,f1759]) ).
tff(f1759,plain,
! [X0: 'A_option$',X1: 'A_a_option_fun$',X2: 'A$'] :
( ? [X4: 'A$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$q'(X1,X4) )
& ( 'fun_app$q'('some$b',X4) = X0 ) )
=> ( ( 'fun_app$q'('some$b',X2) = 'fun_app$q'(X1,sK193(X0,X1,X2)) )
& ( 'fun_app$q'('some$b',sK193(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1758,plain,
! [X0: 'A_option$',X1: 'A_a_option_fun$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$bp'('bind$h'(X0),X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$q'('some$b',X2) != 'fun_app$q'(X1,X3) )
| ( 'fun_app$q'('some$b',X3) != X0 ) ) )
& ( ? [X4: 'A$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$q'(X1,X4) )
& ( 'fun_app$q'('some$b',X4) = X0 ) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bp'('bind$h'(X0),X1) ) ) ),
inference(rectify,[],[f1757]) ).
tff(f1757,plain,
! [X0: 'A_option$',X1: 'A_a_option_fun$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$bp'('bind$h'(X0),X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$q'('some$b',X2) != 'fun_app$q'(X1,X3) )
| ( 'fun_app$q'('some$b',X3) != X0 ) ) )
& ( ? [X3: 'A$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$q'(X1,X3) )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bp'('bind$h'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f414]) ).
tff(f414,axiom,
! [X0: 'A_option$',X1: 'A_a_option_fun$',X2: 'A$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bp'('bind$h'(X0),X1) )
<=> ? [X3: 'A$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$q'(X1,X3) )
& ( 'fun_app$q'('some$b',X3) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom412) ).
tff(f16225,plain,
spl249_1095,
inference(avatar_split_clause,[],[f2348,f16223]) ).
tff(f16223,plain,
( spl249_1095
<=> ! [X10: 'B$',X8: 'A$',X0: 'B_a_fun$',X9: 'A$',X1: 'A_b_b_fun_fun$'] :
( ( 'fun_app$h'('fun_app$i'(X1,X8),'fun_app$h'('fun_app$i'(X1,X9),X10)) = 'fun_app$h'('fun_app$i'(X1,X8),X10) )
| ~ 'valid_getter_setter$a'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1095])]) ).
tff(f2348,plain,
! [X10: 'B$',X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$',X8: 'A$',X9: 'A$'] :
( ( 'fun_app$h'('fun_app$i'(X1,X8),'fun_app$h'('fun_app$i'(X1,X9),X10)) = 'fun_app$h'('fun_app$i'(X1,X8),X10) )
| ~ 'valid_getter_setter$a'(X0,X1) ),
inference(cnf_transformation,[],[f1427]) ).
tff(f16221,plain,
spl249_1094,
inference(avatar_split_clause,[],[f2344,f16219]) ).
tff(f16219,plain,
( spl249_1094
<=> ! [X10: 'C$',X8: 'B$',X0: 'C_b_fun$',X9: 'B$',X1: 'B_c_c_fun_fun$'] :
( ( 'fun_app$k'('fun_app$y'(X1,X8),'fun_app$k'('fun_app$y'(X1,X9),X10)) = 'fun_app$k'('fun_app$y'(X1,X8),X10) )
| ~ 'valid_getter_setter$'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1094])]) ).
tff(f2344,plain,
! [X10: 'C$',X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$',X8: 'B$',X9: 'B$'] :
( ( 'fun_app$k'('fun_app$y'(X1,X8),'fun_app$k'('fun_app$y'(X1,X9),X10)) = 'fun_app$k'('fun_app$y'(X1,X8),X10) )
| ~ 'valid_getter_setter$'(X0,X1) ),
inference(cnf_transformation,[],[f1420]) ).
tff(f15109,plain,
spl249_1093,
inference(avatar_split_clause,[],[f3601,f15107]) ).
tff(f15107,plain,
( spl249_1093
<=> ! [X0: 'B_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X2,'bind$b'(X0,X1))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP39(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1093])]) ).
tff(f3601,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X2,'bind$b'(X0,X1))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP39(X0,X1,X2,X3) ),
inference(inner_rewriting,[],[f3300]) ).
tff(f3300,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X2,'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP39(X0,X1,X2,X3) ),
inference(definition_unfolding,[],[f3186,f2234]) ).
tff(f3186,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X2,'fun_app$n'(X1,'fun_app$al'('the$',X0)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP39(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1895]) ).
tff(f1895,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$',X2: 'C_option_bool_fun$',X3: 'C_option$'] :
( ( sP39(X0,X1,X2,X3)
| ( ~ 'fun_app$'(X2,'fun_app$n'(X1,'fun_app$al'('the$',X0)))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 ) )
| ( ~ 'fun_app$'(X2,X3)
& ( 'none$a' = X0 ) ) )
& ( ( ( 'fun_app$'(X2,'fun_app$n'(X1,'fun_app$al'('the$',X0)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 ) )
& ( 'fun_app$'(X2,X3)
| ( 'none$a' != X0 ) ) )
| ~ sP39(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1894]) ).
tff(f1894,plain,
! [X3: 'B_option$',X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( sP39(X3,X2,X0,X1)
| ( ~ 'fun_app$'(X0,'fun_app$n'(X2,'fun_app$al'('the$',X3)))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$'(X0,X1)
& ( 'none$a' = X3 ) ) )
& ( ( ( 'fun_app$'(X0,'fun_app$n'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$a' != X3 ) ) )
| ~ sP39(X3,X2,X0,X1) ) ),
inference(flattening,[],[f1893]) ).
tff(f1893,plain,
! [X3: 'B_option$',X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( sP39(X3,X2,X0,X1)
| ( ~ 'fun_app$'(X0,'fun_app$n'(X2,'fun_app$al'('the$',X3)))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$'(X0,X1)
& ( 'none$a' = X3 ) ) )
& ( ( ( 'fun_app$'(X0,'fun_app$n'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$a' != X3 ) ) )
| ~ sP39(X3,X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1177]) ).
tff(f1177,plain,
! [X3: 'B_option$',X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( sP39(X3,X2,X0,X1)
<=> ( ( 'fun_app$'(X0,'fun_app$n'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$a' != X3 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP39])]) ).
tff(f15105,plain,
spl249_1092,
inference(avatar_split_clause,[],[f3600,f15103]) ).
tff(f15103,plain,
( spl249_1092
<=> ! [X0: 'B_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X2,'bind$b'(X0,X1))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP38(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1092])]) ).
tff(f3600,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X2,'bind$b'(X0,X1))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP38(X0,X1,X2,X3) ),
inference(inner_rewriting,[],[f3297]) ).
tff(f3297,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X2,'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP38(X0,X1,X2,X3) ),
inference(definition_unfolding,[],[f3178,f2234]) ).
tff(f3178,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X2,'fun_app$n'(X1,'fun_app$al'('the$',X0)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP38(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1891]) ).
tff(f1891,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$',X2: 'C_option_bool_fun$',X3: 'C_option$'] :
( ( sP38(X0,X1,X2,X3)
| ( ~ 'fun_app$'(X2,'fun_app$n'(X1,'fun_app$al'('the$',X0)))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 ) )
| ( ~ 'fun_app$'(X2,X3)
& ( 'none$a' = X0 ) ) )
& ( ( ( 'fun_app$'(X2,'fun_app$n'(X1,'fun_app$al'('the$',X0)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 ) )
& ( 'fun_app$'(X2,X3)
| ( 'none$a' != X0 ) ) )
| ~ sP38(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1890]) ).
tff(f1890,plain,
! [X3: 'B_option$',X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( sP38(X3,X2,X0,X1)
| ( ~ 'fun_app$'(X0,'fun_app$n'(X2,'fun_app$al'('the$',X3)))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$'(X0,X1)
& ( 'none$a' = X3 ) ) )
& ( ( ( 'fun_app$'(X0,'fun_app$n'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$a' != X3 ) ) )
| ~ sP38(X3,X2,X0,X1) ) ),
inference(flattening,[],[f1889]) ).
tff(f1889,plain,
! [X3: 'B_option$',X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( sP38(X3,X2,X0,X1)
| ( ~ 'fun_app$'(X0,'fun_app$n'(X2,'fun_app$al'('the$',X3)))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$'(X0,X1)
& ( 'none$a' = X3 ) ) )
& ( ( ( 'fun_app$'(X0,'fun_app$n'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$a' != X3 ) ) )
| ~ sP38(X3,X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1175]) ).
tff(f1175,plain,
! [X3: 'B_option$',X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( sP38(X3,X2,X0,X1)
<=> ( ( 'fun_app$'(X0,'fun_app$n'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$a' != X3 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP38])]) ).
tff(f15101,plain,
spl249_1091,
inference(avatar_split_clause,[],[f3551,f15099]) ).
tff(f15099,plain,
( spl249_1091
<=> ! [X2: 'B_b_option_fun$',X1: 'B_option$',X3: 'B_b_option_fun$'] :
( ( 'fun_app$ac'('bind$c'(X1),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ( 'fun_app$g'('some$',sK222(X1,X2,X3)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1091])]) ).
tff(f3551,plain,
! [X2: 'B_b_option_fun$',X3: 'B_b_option_fun$',X1: 'B_option$'] :
( ( 'fun_app$ac'('bind$c'(X1),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ( 'fun_app$g'('some$',sK222(X1,X2,X3)) = X1 ) ),
inference(equality_resolution,[],[f3091]) ).
tff(f3091,plain,
! [X2: 'B_b_option_fun$',X3: 'B_b_option_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$ac'('bind$c'(X0),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| ( 'fun_app$g'('some$',sK222(X1,X2,X3)) = X1 )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1840]) ).
tff(f15097,plain,
spl249_1090,
inference(avatar_split_clause,[],[f3549,f15095]) ).
tff(f15095,plain,
( spl249_1090
<=> ! [X2: 'B_b_fun$',X1: 'B_option$',X3: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X3),X1) = 'fun_app$s'('map_option$b'(X2),X1) )
| ( 'fun_app$g'('some$',sK221(X1,X2,X3)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1090])]) ).
tff(f3549,plain,
! [X2: 'B_b_fun$',X3: 'B_b_fun$',X1: 'B_option$'] :
( ( 'fun_app$s'('map_option$b'(X3),X1) = 'fun_app$s'('map_option$b'(X2),X1) )
| ( 'fun_app$g'('some$',sK221(X1,X2,X3)) = X1 ) ),
inference(equality_resolution,[],[f3089]) ).
tff(f3089,plain,
! [X2: 'B_b_fun$',X3: 'B_b_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$s'('map_option$b'(X2),X0) = 'fun_app$s'('map_option$b'(X3),X1) )
| ( 'fun_app$g'('some$',sK221(X1,X2,X3)) = X1 )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1838]) ).
tff(f15093,plain,
spl249_1089,
inference(avatar_split_clause,[],[f3545,f15091]) ).
tff(f15091,plain,
( spl249_1089
<=> ! [X2: 'B_c_fun$',X1: 'B_option$',X3: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X3),X1) = 'fun_app$an'('map_option$d'(X2),X1) )
| ( 'fun_app$g'('some$',sK219(X1,X2,X3)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1089])]) ).
tff(f3545,plain,
! [X2: 'B_c_fun$',X3: 'B_c_fun$',X1: 'B_option$'] :
( ( 'fun_app$an'('map_option$d'(X3),X1) = 'fun_app$an'('map_option$d'(X2),X1) )
| ( 'fun_app$g'('some$',sK219(X1,X2,X3)) = X1 ) ),
inference(equality_resolution,[],[f3085]) ).
tff(f3085,plain,
! [X2: 'B_c_fun$',X3: 'B_c_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$an'('map_option$d'(X2),X0) = 'fun_app$an'('map_option$d'(X3),X1) )
| ( 'fun_app$g'('some$',sK219(X1,X2,X3)) = X1 )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1834]) ).
tff(f15089,plain,
spl249_1088,
inference(avatar_split_clause,[],[f3543,f15087]) ).
tff(f15087,plain,
( spl249_1088
<=> ! [X2: 'C_c_option_fun$',X1: 'C_option$',X3: 'C_c_option_fun$'] :
( ( 'fun_app$ab'('bind$'(X1),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ( 'fun_app$j'('some$a',sK218(X1,X2,X3)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1088])]) ).
tff(f3543,plain,
! [X2: 'C_c_option_fun$',X3: 'C_c_option_fun$',X1: 'C_option$'] :
( ( 'fun_app$ab'('bind$'(X1),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ( 'fun_app$j'('some$a',sK218(X1,X2,X3)) = X1 ) ),
inference(equality_resolution,[],[f3083]) ).
tff(f3083,plain,
! [X2: 'C_c_option_fun$',X3: 'C_c_option_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$ab'('bind$'(X0),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| ( 'fun_app$j'('some$a',sK218(X1,X2,X3)) = X1 )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1832]) ).
tff(f15085,plain,
spl249_1087,
inference(avatar_split_clause,[],[f3541,f15083]) ).
tff(f15083,plain,
( spl249_1087
<=> ! [X2: 'C_b_fun$',X1: 'C_option$',X3: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X3),X1) = 'fun_app$bg'('map_option$'(X2),X1) )
| ( 'fun_app$j'('some$a',sK217(X1,X2,X3)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1087])]) ).
tff(f3541,plain,
! [X2: 'C_b_fun$',X3: 'C_b_fun$',X1: 'C_option$'] :
( ( 'fun_app$bg'('map_option$'(X3),X1) = 'fun_app$bg'('map_option$'(X2),X1) )
| ( 'fun_app$j'('some$a',sK217(X1,X2,X3)) = X1 ) ),
inference(equality_resolution,[],[f3081]) ).
tff(f3081,plain,
! [X2: 'C_b_fun$',X3: 'C_b_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$bg'('map_option$'(X2),X0) = 'fun_app$bg'('map_option$'(X3),X1) )
| ( 'fun_app$j'('some$a',sK217(X1,X2,X3)) = X1 )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1830]) ).
tff(f15081,plain,
spl249_1086,
inference(avatar_split_clause,[],[f3537,f15079]) ).
tff(f15079,plain,
( spl249_1086
<=> ! [X2: 'A_a_fun$',X1: 'A_option$',X3: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X3),X1) = 'fun_app$be'('map_option$a'(X2),X1) )
| ( 'fun_app$q'('some$b',sK215(X1,X2,X3)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1086])]) ).
tff(f3537,plain,
! [X2: 'A_a_fun$',X3: 'A_a_fun$',X1: 'A_option$'] :
( ( 'fun_app$be'('map_option$a'(X3),X1) = 'fun_app$be'('map_option$a'(X2),X1) )
| ( 'fun_app$q'('some$b',sK215(X1,X2,X3)) = X1 ) ),
inference(equality_resolution,[],[f3077]) ).
tff(f3077,plain,
! [X2: 'A_a_fun$',X3: 'A_a_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$be'('map_option$a'(X2),X0) = 'fun_app$be'('map_option$a'(X3),X1) )
| ( 'fun_app$q'('some$b',sK215(X1,X2,X3)) = X1 )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1826]) ).
tff(f15077,plain,
spl249_1085,
inference(avatar_split_clause,[],[f3535,f15075]) ).
tff(f15075,plain,
( spl249_1085
<=> ! [X2: 'A_b_fun$',X1: 'A_option$',X3: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X3),X1) = 'fun_app$av'('map_option$e'(X2),X1) )
| ( 'fun_app$q'('some$b',sK214(X1,X2,X3)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1085])]) ).
tff(f3535,plain,
! [X2: 'A_b_fun$',X3: 'A_b_fun$',X1: 'A_option$'] :
( ( 'fun_app$av'('map_option$e'(X3),X1) = 'fun_app$av'('map_option$e'(X2),X1) )
| ( 'fun_app$q'('some$b',sK214(X1,X2,X3)) = X1 ) ),
inference(equality_resolution,[],[f3075]) ).
tff(f3075,plain,
! [X2: 'A_b_fun$',X3: 'A_b_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$av'('map_option$e'(X2),X0) = 'fun_app$av'('map_option$e'(X3),X1) )
| ( 'fun_app$q'('some$b',sK214(X1,X2,X3)) = X1 )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1824]) ).
tff(f15072,plain,
spl249_1084,
inference(avatar_split_clause,[],[f3505,f15070]) ).
tff(f15070,plain,
( spl249_1084
<=> ! [X2: 'B$',X1: 'B_b_option_fun$',X3: 'B$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$ac'('bind$c'('fun_app$g'('some$',X3)),X1) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$g'(X1,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1084])]) ).
tff(f3505,plain,
! [X2: 'B$',X3: 'B$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$ac'('bind$c'('fun_app$g'('some$',X3)),X1) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$g'(X1,X3) ) ),
inference(equality_resolution,[],[f3023]) ).
tff(f3023,plain,
! [X2: 'B$',X3: 'B$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$ac'('bind$c'(X0),X1) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$g'(X1,X3) )
| ( 'fun_app$g'('some$',X3) != X0 ) ),
inference(cnf_transformation,[],[f1792]) ).
tff(f15068,plain,
spl249_1083,
inference(avatar_split_clause,[],[f3500,f15066]) ).
tff(f15066,plain,
( spl249_1083
<=> ! [X2: 'C$',X1: 'C_c_option_fun$',X3: 'C$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$ab'('bind$'('fun_app$j'('some$a',X3)),X1) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$j'(X1,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1083])]) ).
tff(f3500,plain,
! [X2: 'C$',X3: 'C$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$ab'('bind$'('fun_app$j'('some$a',X3)),X1) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$j'(X1,X3) ) ),
inference(equality_resolution,[],[f3014]) ).
tff(f3014,plain,
! [X2: 'C$',X3: 'C$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$ab'('bind$'(X0),X1) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$j'(X1,X3) )
| ( 'fun_app$j'('some$a',X3) != X0 ) ),
inference(cnf_transformation,[],[f1780]) ).
tff(f15064,plain,
spl249_1082,
inference(avatar_split_clause,[],[f3491,f15062]) ).
tff(f15062,plain,
( spl249_1082
<=> ! [X2: 'A$',X1: 'A_a_option_fun$',X3: 'A$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bp'('bind$h'('fun_app$q'('some$b',X3)),X1) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$q'(X1,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1082])]) ).
tff(f3491,plain,
! [X2: 'A$',X3: 'A$',X1: 'A_a_option_fun$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bp'('bind$h'('fun_app$q'('some$b',X3)),X1) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$q'(X1,X3) ) ),
inference(equality_resolution,[],[f2999]) ).
tff(f2999,plain,
! [X2: 'A$',X3: 'A$',X0: 'A_option$',X1: 'A_a_option_fun$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bp'('bind$h'(X0),X1) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$q'(X1,X3) )
| ( 'fun_app$q'('some$b',X3) != X0 ) ),
inference(cnf_transformation,[],[f1760]) ).
tff(f15060,plain,
spl249_1081,
inference(avatar_split_clause,[],[f3299,f15058]) ).
tff(f15058,plain,
( spl249_1081
<=> ! [X0: 'B_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( sP39(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1))
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1081])]) ).
tff(f3299,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( sP39(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1))
| ( 'none$a' = X0 ) ),
inference(definition_unfolding,[],[f3189,f2234]) ).
tff(f3189,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( sP39(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'fun_app$n'(X1,'fun_app$al'('the$',X0)))
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f1895]) ).
tff(f15056,plain,
spl249_1080,
inference(avatar_split_clause,[],[f3298,f15054]) ).
tff(f15054,plain,
( spl249_1080
<=> ! [X0: 'B_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( sP39(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1))
| ~ 'fun_app$'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1080])]) ).
tff(f3298,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( sP39(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1))
| ~ 'fun_app$'(X2,X3) ),
inference(definition_unfolding,[],[f3190,f2234]) ).
tff(f3190,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( sP39(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'fun_app$n'(X1,'fun_app$al'('the$',X0)))
| ~ 'fun_app$'(X2,X3) ),
inference(cnf_transformation,[],[f1895]) ).
tff(f15052,plain,
spl249_1079,
inference(avatar_split_clause,[],[f3296,f15050]) ).
tff(f15050,plain,
( spl249_1079
<=> ! [X0: 'B_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( sP38(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1))
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1079])]) ).
tff(f3296,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( sP38(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1))
| ( 'none$a' = X0 ) ),
inference(definition_unfolding,[],[f3181,f2234]) ).
tff(f3181,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( sP38(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'fun_app$n'(X1,'fun_app$al'('the$',X0)))
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f1891]) ).
tff(f15048,plain,
spl249_1078,
inference(avatar_split_clause,[],[f3295,f15046]) ).
tff(f15046,plain,
( spl249_1078
<=> ! [X0: 'B_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( sP38(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1))
| ~ 'fun_app$'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1078])]) ).
tff(f3295,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( sP38(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1))
| ~ 'fun_app$'(X2,X3) ),
inference(definition_unfolding,[],[f3182,f2234]) ).
tff(f3182,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( sP38(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'fun_app$n'(X1,'fun_app$al'('the$',X0)))
| ~ 'fun_app$'(X2,X3) ),
inference(cnf_transformation,[],[f1891]) ).
tff(f15044,plain,
spl249_1077,
inference(avatar_split_clause,[],[f3281,f15042]) ).
tff(f15042,plain,
( spl249_1077
<=> ! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP24(X0,X1,X2)
| ~ 'fun_app$a'(X1,'bind$a'('fun_app$j'('some$a',sK180(X0,X1,X2)),X0))
| ( 'none$' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1077])]) ).
tff(f3281,plain,
! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP24(X0,X1,X2)
| ~ 'fun_app$a'(X1,'bind$a'('fun_app$j'('some$a',sK180(X0,X1,X2)),X0))
| ( 'none$' = X2 ) ),
inference(definition_unfolding,[],[f2897,f2233]) ).
tff(f2897,plain,
! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP24(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$l'(X0,sK180(X0,X1,X2)))
| ( 'none$' = X2 ) ),
inference(cnf_transformation,[],[f1680]) ).
tff(f1680,plain,
! [X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'C_option$'] :
( ( sP24(X0,X1,X2)
| ( ~ 'fun_app$a'(X1,'fun_app$l'(X0,sK180(X0,X1,X2)))
& ( 'fun_app$j'('some$a',sK180(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$a'(X1,'none$a')
& ( 'none$' = X2 ) ) )
& ( ( ! [X4: 'C$'] :
( 'fun_app$a'(X1,'fun_app$l'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 ) )
& ( 'fun_app$a'(X1,'none$a')
| ( 'none$' != X2 ) ) )
| ~ sP24(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK180])],[f1678,f1679]) ).
tff(f1679,plain,
! [X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'C_option$'] :
( ? [X3: 'C$'] :
( ~ 'fun_app$a'(X1,'fun_app$l'(X0,X3))
& ( 'fun_app$j'('some$a',X3) = X2 ) )
=> ( ~ 'fun_app$a'(X1,'fun_app$l'(X0,sK180(X0,X1,X2)))
& ( 'fun_app$j'('some$a',sK180(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1678,plain,
! [X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'C_option$'] :
( ( sP24(X0,X1,X2)
| ? [X3: 'C$'] :
( ~ 'fun_app$a'(X1,'fun_app$l'(X0,X3))
& ( 'fun_app$j'('some$a',X3) = X2 ) )
| ( ~ 'fun_app$a'(X1,'none$a')
& ( 'none$' = X2 ) ) )
& ( ( ! [X4: 'C$'] :
( 'fun_app$a'(X1,'fun_app$l'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 ) )
& ( 'fun_app$a'(X1,'none$a')
| ( 'none$' != X2 ) ) )
| ~ sP24(X0,X1,X2) ) ),
inference(rectify,[],[f1677]) ).
tff(f1677,plain,
! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( ( sP24(X2,X0,X1)
| ? [X3: 'C$'] :
( ~ 'fun_app$a'(X0,'fun_app$l'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$' = X1 ) ) )
& ( ( ! [X3: 'C$'] :
( 'fun_app$a'(X0,'fun_app$l'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$' != X1 ) ) )
| ~ sP24(X2,X0,X1) ) ),
inference(flattening,[],[f1676]) ).
tff(f1676,plain,
! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( ( sP24(X2,X0,X1)
| ? [X3: 'C$'] :
( ~ 'fun_app$a'(X0,'fun_app$l'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$' = X1 ) ) )
& ( ( ! [X3: 'C$'] :
( 'fun_app$a'(X0,'fun_app$l'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$' != X1 ) ) )
| ~ sP24(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1147]) ).
tff(f1147,plain,
! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( sP24(X2,X0,X1)
<=> ( ! [X3: 'C$'] :
( 'fun_app$a'(X0,'fun_app$l'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).
tff(f15040,plain,
spl249_1076,
inference(avatar_split_clause,[],[f3280,f15038]) ).
tff(f15038,plain,
( spl249_1076
<=> ! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP24(X0,X1,X2)
| ~ 'fun_app$a'(X1,'bind$a'('fun_app$j'('some$a',sK180(X0,X1,X2)),X0))
| ~ 'fun_app$a'(X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1076])]) ).
tff(f3280,plain,
! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP24(X0,X1,X2)
| ~ 'fun_app$a'(X1,'bind$a'('fun_app$j'('some$a',sK180(X0,X1,X2)),X0))
| ~ 'fun_app$a'(X1,'none$a') ),
inference(definition_unfolding,[],[f2898,f2233]) ).
tff(f2898,plain,
! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP24(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$l'(X0,sK180(X0,X1,X2)))
| ~ 'fun_app$a'(X1,'none$a') ),
inference(cnf_transformation,[],[f1680]) ).
tff(f15036,plain,
spl249_1075,
inference(avatar_split_clause,[],[f3278,f15034]) ).
tff(f15034,plain,
( spl249_1075
<=> ! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP23(X0,X1,X2)
| ~ 'fun_app$a'(X1,'bind$a'('fun_app$j'('some$a',sK179(X0,X1,X2)),X0))
| ( 'none$' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1075])]) ).
tff(f3278,plain,
! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP23(X0,X1,X2)
| ~ 'fun_app$a'(X1,'bind$a'('fun_app$j'('some$a',sK179(X0,X1,X2)),X0))
| ( 'none$' = X2 ) ),
inference(definition_unfolding,[],[f2889,f2233]) ).
tff(f2889,plain,
! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP23(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$l'(X0,sK179(X0,X1,X2)))
| ( 'none$' = X2 ) ),
inference(cnf_transformation,[],[f1674]) ).
tff(f1674,plain,
! [X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'C_option$'] :
( ( sP23(X0,X1,X2)
| ( ~ 'fun_app$a'(X1,'fun_app$l'(X0,sK179(X0,X1,X2)))
& ( 'fun_app$j'('some$a',sK179(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$a'(X1,'none$a')
& ( 'none$' = X2 ) ) )
& ( ( ! [X4: 'C$'] :
( 'fun_app$a'(X1,'fun_app$l'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 ) )
& ( 'fun_app$a'(X1,'none$a')
| ( 'none$' != X2 ) ) )
| ~ sP23(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK179])],[f1672,f1673]) ).
tff(f1673,plain,
! [X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'C_option$'] :
( ? [X3: 'C$'] :
( ~ 'fun_app$a'(X1,'fun_app$l'(X0,X3))
& ( 'fun_app$j'('some$a',X3) = X2 ) )
=> ( ~ 'fun_app$a'(X1,'fun_app$l'(X0,sK179(X0,X1,X2)))
& ( 'fun_app$j'('some$a',sK179(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1672,plain,
! [X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'C_option$'] :
( ( sP23(X0,X1,X2)
| ? [X3: 'C$'] :
( ~ 'fun_app$a'(X1,'fun_app$l'(X0,X3))
& ( 'fun_app$j'('some$a',X3) = X2 ) )
| ( ~ 'fun_app$a'(X1,'none$a')
& ( 'none$' = X2 ) ) )
& ( ( ! [X4: 'C$'] :
( 'fun_app$a'(X1,'fun_app$l'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 ) )
& ( 'fun_app$a'(X1,'none$a')
| ( 'none$' != X2 ) ) )
| ~ sP23(X0,X1,X2) ) ),
inference(rectify,[],[f1671]) ).
tff(f1671,plain,
! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( ( sP23(X2,X0,X1)
| ? [X3: 'C$'] :
( ~ 'fun_app$a'(X0,'fun_app$l'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$' = X1 ) ) )
& ( ( ! [X3: 'C$'] :
( 'fun_app$a'(X0,'fun_app$l'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$' != X1 ) ) )
| ~ sP23(X2,X0,X1) ) ),
inference(flattening,[],[f1670]) ).
tff(f1670,plain,
! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( ( sP23(X2,X0,X1)
| ? [X3: 'C$'] :
( ~ 'fun_app$a'(X0,'fun_app$l'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$' = X1 ) ) )
& ( ( ! [X3: 'C$'] :
( 'fun_app$a'(X0,'fun_app$l'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$' != X1 ) ) )
| ~ sP23(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1145]) ).
tff(f1145,plain,
! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( sP23(X2,X0,X1)
<=> ( ! [X3: 'C$'] :
( 'fun_app$a'(X0,'fun_app$l'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).
tff(f15031,plain,
spl249_1074,
inference(avatar_split_clause,[],[f3277,f15029]) ).
tff(f15029,plain,
( spl249_1074
<=> ! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP23(X0,X1,X2)
| ~ 'fun_app$a'(X1,'bind$a'('fun_app$j'('some$a',sK179(X0,X1,X2)),X0))
| ~ 'fun_app$a'(X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1074])]) ).
tff(f3277,plain,
! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP23(X0,X1,X2)
| ~ 'fun_app$a'(X1,'bind$a'('fun_app$j'('some$a',sK179(X0,X1,X2)),X0))
| ~ 'fun_app$a'(X1,'none$a') ),
inference(definition_unfolding,[],[f2890,f2233]) ).
tff(f2890,plain,
! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP23(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$l'(X0,sK179(X0,X1,X2)))
| ~ 'fun_app$a'(X1,'none$a') ),
inference(cnf_transformation,[],[f1674]) ).
tff(f15027,plain,
spl249_1073,
inference(avatar_split_clause,[],[f3275,f15025]) ).
tff(f15025,plain,
( spl249_1073
<=> ! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP19(X0,X1,X2)
| ~ 'fun_app$'(X1,'bind$b'('fun_app$g'('some$',sK176(X0,X1,X2)),X0))
| ( 'none$a' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1073])]) ).
tff(f3275,plain,
! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP19(X0,X1,X2)
| ~ 'fun_app$'(X1,'bind$b'('fun_app$g'('some$',sK176(X0,X1,X2)),X0))
| ( 'none$a' = X2 ) ),
inference(definition_unfolding,[],[f2857,f2234]) ).
tff(f2857,plain,
! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP19(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$n'(X0,sK176(X0,X1,X2)))
| ( 'none$a' = X2 ) ),
inference(cnf_transformation,[],[f1652]) ).
tff(f1652,plain,
! [X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'B_option$'] :
( ( sP19(X0,X1,X2)
| ( ~ 'fun_app$'(X1,'fun_app$n'(X0,sK176(X0,X1,X2)))
& ( 'fun_app$g'('some$',sK176(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$'(X1,'none$')
& ( 'none$a' = X2 ) ) )
& ( ( ! [X4: 'B$'] :
( 'fun_app$'(X1,'fun_app$n'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 ) )
& ( 'fun_app$'(X1,'none$')
| ( 'none$a' != X2 ) ) )
| ~ sP19(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK176])],[f1650,f1651]) ).
tff(f1651,plain,
! [X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'B_option$'] :
( ? [X3: 'B$'] :
( ~ 'fun_app$'(X1,'fun_app$n'(X0,X3))
& ( 'fun_app$g'('some$',X3) = X2 ) )
=> ( ~ 'fun_app$'(X1,'fun_app$n'(X0,sK176(X0,X1,X2)))
& ( 'fun_app$g'('some$',sK176(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1650,plain,
! [X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'B_option$'] :
( ( sP19(X0,X1,X2)
| ? [X3: 'B$'] :
( ~ 'fun_app$'(X1,'fun_app$n'(X0,X3))
& ( 'fun_app$g'('some$',X3) = X2 ) )
| ( ~ 'fun_app$'(X1,'none$')
& ( 'none$a' = X2 ) ) )
& ( ( ! [X4: 'B$'] :
( 'fun_app$'(X1,'fun_app$n'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 ) )
& ( 'fun_app$'(X1,'none$')
| ( 'none$a' != X2 ) ) )
| ~ sP19(X0,X1,X2) ) ),
inference(rectify,[],[f1649]) ).
tff(f1649,plain,
! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( ( sP19(X2,X0,X1)
| ? [X3: 'B$'] :
( ~ 'fun_app$'(X0,'fun_app$n'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$a' = X1 ) ) )
& ( ( ! [X3: 'B$'] :
( 'fun_app$'(X0,'fun_app$n'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$a' != X1 ) ) )
| ~ sP19(X2,X0,X1) ) ),
inference(flattening,[],[f1648]) ).
tff(f1648,plain,
! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( ( sP19(X2,X0,X1)
| ? [X3: 'B$'] :
( ~ 'fun_app$'(X0,'fun_app$n'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$a' = X1 ) ) )
& ( ( ! [X3: 'B$'] :
( 'fun_app$'(X0,'fun_app$n'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$a' != X1 ) ) )
| ~ sP19(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1137]) ).
tff(f1137,plain,
! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( sP19(X2,X0,X1)
<=> ( ! [X3: 'B$'] :
( 'fun_app$'(X0,'fun_app$n'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$a' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
tff(f15023,plain,
spl249_1072,
inference(avatar_split_clause,[],[f3274,f15021]) ).
tff(f15021,plain,
( spl249_1072
<=> ! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP19(X0,X1,X2)
| ~ 'fun_app$'(X1,'bind$b'('fun_app$g'('some$',sK176(X0,X1,X2)),X0))
| ~ 'fun_app$'(X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1072])]) ).
tff(f3274,plain,
! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP19(X0,X1,X2)
| ~ 'fun_app$'(X1,'bind$b'('fun_app$g'('some$',sK176(X0,X1,X2)),X0))
| ~ 'fun_app$'(X1,'none$') ),
inference(definition_unfolding,[],[f2858,f2234]) ).
tff(f2858,plain,
! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP19(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$n'(X0,sK176(X0,X1,X2)))
| ~ 'fun_app$'(X1,'none$') ),
inference(cnf_transformation,[],[f1652]) ).
tff(f15019,plain,
spl249_1071,
inference(avatar_split_clause,[],[f3272,f15017]) ).
tff(f15017,plain,
( spl249_1071
<=> ! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP18(X0,X1,X2)
| ~ 'fun_app$'(X1,'bind$b'('fun_app$g'('some$',sK175(X0,X1,X2)),X0))
| ( 'none$a' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1071])]) ).
tff(f3272,plain,
! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP18(X0,X1,X2)
| ~ 'fun_app$'(X1,'bind$b'('fun_app$g'('some$',sK175(X0,X1,X2)),X0))
| ( 'none$a' = X2 ) ),
inference(definition_unfolding,[],[f2849,f2234]) ).
tff(f2849,plain,
! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP18(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$n'(X0,sK175(X0,X1,X2)))
| ( 'none$a' = X2 ) ),
inference(cnf_transformation,[],[f1646]) ).
tff(f1646,plain,
! [X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'B_option$'] :
( ( sP18(X0,X1,X2)
| ( ~ 'fun_app$'(X1,'fun_app$n'(X0,sK175(X0,X1,X2)))
& ( 'fun_app$g'('some$',sK175(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$'(X1,'none$')
& ( 'none$a' = X2 ) ) )
& ( ( ! [X4: 'B$'] :
( 'fun_app$'(X1,'fun_app$n'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 ) )
& ( 'fun_app$'(X1,'none$')
| ( 'none$a' != X2 ) ) )
| ~ sP18(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK175])],[f1644,f1645]) ).
tff(f1645,plain,
! [X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'B_option$'] :
( ? [X3: 'B$'] :
( ~ 'fun_app$'(X1,'fun_app$n'(X0,X3))
& ( 'fun_app$g'('some$',X3) = X2 ) )
=> ( ~ 'fun_app$'(X1,'fun_app$n'(X0,sK175(X0,X1,X2)))
& ( 'fun_app$g'('some$',sK175(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1644,plain,
! [X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'B_option$'] :
( ( sP18(X0,X1,X2)
| ? [X3: 'B$'] :
( ~ 'fun_app$'(X1,'fun_app$n'(X0,X3))
& ( 'fun_app$g'('some$',X3) = X2 ) )
| ( ~ 'fun_app$'(X1,'none$')
& ( 'none$a' = X2 ) ) )
& ( ( ! [X4: 'B$'] :
( 'fun_app$'(X1,'fun_app$n'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 ) )
& ( 'fun_app$'(X1,'none$')
| ( 'none$a' != X2 ) ) )
| ~ sP18(X0,X1,X2) ) ),
inference(rectify,[],[f1643]) ).
tff(f1643,plain,
! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( ( sP18(X2,X0,X1)
| ? [X3: 'B$'] :
( ~ 'fun_app$'(X0,'fun_app$n'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$a' = X1 ) ) )
& ( ( ! [X3: 'B$'] :
( 'fun_app$'(X0,'fun_app$n'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$a' != X1 ) ) )
| ~ sP18(X2,X0,X1) ) ),
inference(flattening,[],[f1642]) ).
tff(f1642,plain,
! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( ( sP18(X2,X0,X1)
| ? [X3: 'B$'] :
( ~ 'fun_app$'(X0,'fun_app$n'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$a' = X1 ) ) )
& ( ( ! [X3: 'B$'] :
( 'fun_app$'(X0,'fun_app$n'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$a' != X1 ) ) )
| ~ sP18(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1135]) ).
tff(f1135,plain,
! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( sP18(X2,X0,X1)
<=> ( ! [X3: 'B$'] :
( 'fun_app$'(X0,'fun_app$n'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$a' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
tff(f15015,plain,
spl249_1070,
inference(avatar_split_clause,[],[f3271,f15013]) ).
tff(f15013,plain,
( spl249_1070
<=> ! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP18(X0,X1,X2)
| ~ 'fun_app$'(X1,'bind$b'('fun_app$g'('some$',sK175(X0,X1,X2)),X0))
| ~ 'fun_app$'(X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1070])]) ).
tff(f3271,plain,
! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP18(X0,X1,X2)
| ~ 'fun_app$'(X1,'bind$b'('fun_app$g'('some$',sK175(X0,X1,X2)),X0))
| ~ 'fun_app$'(X1,'none$') ),
inference(definition_unfolding,[],[f2850,f2234]) ).
tff(f2850,plain,
! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP18(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$n'(X0,sK175(X0,X1,X2)))
| ~ 'fun_app$'(X1,'none$') ),
inference(cnf_transformation,[],[f1646]) ).
tff(f15011,plain,
spl249_1069,
inference(avatar_split_clause,[],[f3253,f15009]) ).
tff(f15009,plain,
( spl249_1069
<=> ! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$a'('fun_app$j'('some$a','fun_app$ak'('the$a',X0)),X1))
| 'fun_app$'('is_none$a',X0)
| ~ 'fun_app$a'('is_none$','bind$a'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1069])]) ).
tff(f3253,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$a'('fun_app$j'('some$a','fun_app$ak'('the$a',X0)),X1))
| 'fun_app$'('is_none$a',X0)
| ~ 'fun_app$a'('is_none$','bind$a'(X0,X1)) ),
inference(definition_unfolding,[],[f2449,f2233]) ).
tff(f2449,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( 'fun_app$a'('is_none$','fun_app$l'(X1,'fun_app$ak'('the$a',X0)))
| 'fun_app$'('is_none$a',X0)
| ~ 'fun_app$a'('is_none$','bind$a'(X0,X1)) ),
inference(cnf_transformation,[],[f1483]) ).
tff(f1483,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( 'fun_app$a'('is_none$','bind$a'(X0,X1))
| ( ~ 'fun_app$a'('is_none$','fun_app$l'(X1,'fun_app$ak'('the$a',X0)))
& ~ 'fun_app$'('is_none$a',X0) ) )
& ( 'fun_app$a'('is_none$','fun_app$l'(X1,'fun_app$ak'('the$a',X0)))
| 'fun_app$'('is_none$a',X0)
| ~ 'fun_app$a'('is_none$','bind$a'(X0,X1)) ) ),
inference(flattening,[],[f1482]) ).
tff(f1482,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( 'fun_app$a'('is_none$','bind$a'(X0,X1))
| ( ~ 'fun_app$a'('is_none$','fun_app$l'(X1,'fun_app$ak'('the$a',X0)))
& ~ 'fun_app$'('is_none$a',X0) ) )
& ( 'fun_app$a'('is_none$','fun_app$l'(X1,'fun_app$ak'('the$a',X0)))
| 'fun_app$'('is_none$a',X0)
| ~ 'fun_app$a'('is_none$','bind$a'(X0,X1)) ) ),
inference(nnf_transformation,[],[f399]) ).
tff(f399,axiom,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$a'(X0,X1))
<=> ( 'fun_app$a'('is_none$','fun_app$l'(X1,'fun_app$ak'('the$a',X0)))
| 'fun_app$'('is_none$a',X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom397) ).
tff(f15007,plain,
spl249_1068,
inference(avatar_split_clause,[],[f3251,f15005]) ).
tff(f15005,plain,
( spl249_1068
<=> ! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1))
| 'fun_app$a'('is_none$',X0)
| ~ 'fun_app$'('is_none$a','bind$b'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1068])]) ).
tff(f3251,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1))
| 'fun_app$a'('is_none$',X0)
| ~ 'fun_app$'('is_none$a','bind$b'(X0,X1)) ),
inference(definition_unfolding,[],[f2437,f2234]) ).
tff(f2437,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'('is_none$a','fun_app$n'(X1,'fun_app$al'('the$',X0)))
| 'fun_app$a'('is_none$',X0)
| ~ 'fun_app$'('is_none$a','bind$b'(X0,X1)) ),
inference(cnf_transformation,[],[f1476]) ).
tff(f1476,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( 'fun_app$'('is_none$a','bind$b'(X0,X1))
| ( ~ 'fun_app$'('is_none$a','fun_app$n'(X1,'fun_app$al'('the$',X0)))
& ~ 'fun_app$a'('is_none$',X0) ) )
& ( 'fun_app$'('is_none$a','fun_app$n'(X1,'fun_app$al'('the$',X0)))
| 'fun_app$a'('is_none$',X0)
| ~ 'fun_app$'('is_none$a','bind$b'(X0,X1)) ) ),
inference(flattening,[],[f1475]) ).
tff(f1475,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( 'fun_app$'('is_none$a','bind$b'(X0,X1))
| ( ~ 'fun_app$'('is_none$a','fun_app$n'(X1,'fun_app$al'('the$',X0)))
& ~ 'fun_app$a'('is_none$',X0) ) )
& ( 'fun_app$'('is_none$a','fun_app$n'(X1,'fun_app$al'('the$',X0)))
| 'fun_app$a'('is_none$',X0)
| ~ 'fun_app$'('is_none$a','bind$b'(X0,X1)) ) ),
inference(nnf_transformation,[],[f398]) ).
tff(f398,axiom,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$b'(X0,X1))
<=> ( 'fun_app$'('is_none$a','fun_app$n'(X1,'fun_app$al'('the$',X0)))
| 'fun_app$a'('is_none$',X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom396) ).
tff(f15003,plain,
spl249_1067,
inference(avatar_split_clause,[],[f3249,f15001]) ).
tff(f15001,plain,
( spl249_1067
<=> ! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( 'none$a' = 'bind$a'('fun_app$j'('some$a','fun_app$ak'('the$a',X0)),X1) )
| ( 'none$' = X0 )
| ( 'none$a' != 'bind$a'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1067])]) ).
tff(f3249,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( 'none$a' = 'bind$a'('fun_app$j'('some$a','fun_app$ak'('the$a',X0)),X1) )
| ( 'none$' = X0 )
| ( 'none$a' != 'bind$a'(X0,X1) ) ),
inference(definition_unfolding,[],[f2421,f2233]) ).
tff(f2421,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( 'none$a' = 'fun_app$l'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 )
| ( 'none$a' != 'bind$a'(X0,X1) ) ),
inference(cnf_transformation,[],[f1467]) ).
tff(f1467,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( ( 'none$a' = 'bind$a'(X0,X1) )
| ( ( 'none$a' != 'fun_app$l'(X1,'fun_app$ak'('the$a',X0)) )
& ( 'none$' != X0 ) ) )
& ( ( 'none$a' = 'fun_app$l'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 )
| ( 'none$a' != 'bind$a'(X0,X1) ) ) ),
inference(flattening,[],[f1466]) ).
tff(f1466,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( ( 'none$a' = 'bind$a'(X0,X1) )
| ( ( 'none$a' != 'fun_app$l'(X1,'fun_app$ak'('the$a',X0)) )
& ( 'none$' != X0 ) ) )
& ( ( 'none$a' = 'fun_app$l'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 )
| ( 'none$a' != 'bind$a'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f344]) ).
tff(f344,axiom,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( 'none$a' = 'bind$a'(X0,X1) )
<=> ( ( 'none$a' = 'fun_app$l'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom342) ).
tff(f14999,plain,
spl249_1066,
inference(avatar_split_clause,[],[f3247,f14997]) ).
tff(f14997,plain,
( spl249_1066
<=> ! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( 'none$' = 'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1) )
| ( 'none$a' = X0 )
| ( 'none$' != 'bind$b'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1066])]) ).
tff(f3247,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( 'none$' = 'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1) )
| ( 'none$a' = X0 )
| ( 'none$' != 'bind$b'(X0,X1) ) ),
inference(definition_unfolding,[],[f2415,f2234]) ).
tff(f2415,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( 'none$' = 'fun_app$n'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 )
| ( 'none$' != 'bind$b'(X0,X1) ) ),
inference(cnf_transformation,[],[f1463]) ).
tff(f1463,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( ( 'none$' = 'bind$b'(X0,X1) )
| ( ( 'none$' != 'fun_app$n'(X1,'fun_app$al'('the$',X0)) )
& ( 'none$a' != X0 ) ) )
& ( ( 'none$' = 'fun_app$n'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 )
| ( 'none$' != 'bind$b'(X0,X1) ) ) ),
inference(flattening,[],[f1462]) ).
tff(f1462,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( ( 'none$' = 'bind$b'(X0,X1) )
| ( ( 'none$' != 'fun_app$n'(X1,'fun_app$al'('the$',X0)) )
& ( 'none$a' != X0 ) ) )
& ( ( 'none$' = 'fun_app$n'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 )
| ( 'none$' != 'bind$b'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f343]) ).
tff(f343,axiom,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( 'none$' = 'bind$b'(X0,X1) )
<=> ( ( 'none$' = 'fun_app$n'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom341) ).
tff(f14995,plain,
spl249_1065,
inference(avatar_split_clause,[],[f3150,f14993]) ).
tff(f14993,plain,
( spl249_1065
<=> ! [X0: 'B_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'B_bool_fun$'] :
( 'fun_app$ag'(X2,def_17(X1,X0))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP35(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1065])]) ).
tff(f3150,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( 'fun_app$ag'(X2,def_17(X1,X0))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP35(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1877]) ).
tff(f1877,plain,
! [X0: 'B_option$',X1: 'B_bool_fun$',X2: 'Bool_bool_fun$',X3: tlbool] :
( ( sP35(X0,X1,X2,X3)
| ( ~ 'fun_app$ag'(X2,def_17(X1,X0))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 ) )
| ( ~ 'fun_app$ag'(X2,X3)
& ( 'none$a' = X0 ) ) )
& ( ( ( 'fun_app$ag'(X2,def_17(X1,X0))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 ) )
& ( 'fun_app$ag'(X2,X3)
| ( 'none$a' != X0 ) ) )
| ~ sP35(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1876]) ).
tff(f1876,plain,
! [X3: 'B_option$',X2: 'B_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
( ( sP35(X3,X2,X0,X1)
| ( ~ 'fun_app$ag'(X0,def_17(X2,X3))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$ag'(X0,X1)
& ( 'none$a' = X3 ) ) )
& ( ( ( 'fun_app$ag'(X0,def_17(X2,X3))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$a' != X3 ) ) )
| ~ sP35(X3,X2,X0,X1) ) ),
inference(flattening,[],[f1875]) ).
tff(f1875,plain,
! [X3: 'B_option$',X2: 'B_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
( ( sP35(X3,X2,X0,X1)
| ( ~ 'fun_app$ag'(X0,def_17(X2,X3))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$ag'(X0,X1)
& ( 'none$a' = X3 ) ) )
& ( ( ( 'fun_app$ag'(X0,def_17(X2,X3))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$a' != X3 ) ) )
| ~ sP35(X3,X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1169]) ).
tff(f1169,plain,
! [X3: 'B_option$',X2: 'B_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
( sP35(X3,X2,X0,X1)
<=> ( ( 'fun_app$ag'(X0,def_17(X2,X3))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$a' != X3 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP35])]) ).
tff(f14990,plain,
spl249_1064,
inference(avatar_split_clause,[],[f3142,f14988]) ).
tff(f14988,plain,
( spl249_1064
<=> ! [X0: 'C_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'C_bool_fun$'] :
( 'fun_app$ag'(X2,def_19(X1,X0))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) != X0 )
| ~ sP34(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1064])]) ).
tff(f3142,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( 'fun_app$ag'(X2,def_19(X1,X0))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) != X0 )
| ~ sP34(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1873]) ).
tff(f1873,plain,
! [X0: 'C_option$',X1: 'C_bool_fun$',X2: 'Bool_bool_fun$',X3: tlbool] :
( ( sP34(X0,X1,X2,X3)
| ( ~ 'fun_app$ag'(X2,def_19(X1,X0))
& ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 ) )
| ( ~ 'fun_app$ag'(X2,X3)
& ( 'none$' = X0 ) ) )
& ( ( ( 'fun_app$ag'(X2,def_19(X1,X0))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) != X0 ) )
& ( 'fun_app$ag'(X2,X3)
| ( 'none$' != X0 ) ) )
| ~ sP34(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1872]) ).
tff(f1872,plain,
! [X3: 'C_option$',X2: 'C_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
( ( sP34(X3,X2,X0,X1)
| ( ~ 'fun_app$ag'(X0,def_19(X2,X3))
& ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) = X3 ) )
| ( ~ 'fun_app$ag'(X0,X1)
& ( 'none$' = X3 ) ) )
& ( ( ( 'fun_app$ag'(X0,def_19(X2,X3))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$' != X3 ) ) )
| ~ sP34(X3,X2,X0,X1) ) ),
inference(flattening,[],[f1871]) ).
tff(f1871,plain,
! [X3: 'C_option$',X2: 'C_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
( ( sP34(X3,X2,X0,X1)
| ( ~ 'fun_app$ag'(X0,def_19(X2,X3))
& ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) = X3 ) )
| ( ~ 'fun_app$ag'(X0,X1)
& ( 'none$' = X3 ) ) )
& ( ( ( 'fun_app$ag'(X0,def_19(X2,X3))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$' != X3 ) ) )
| ~ sP34(X3,X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1167]) ).
tff(f1167,plain,
! [X3: 'C_option$',X2: 'C_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
( sP34(X3,X2,X0,X1)
<=> ( ( 'fun_app$ag'(X0,def_19(X2,X3))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$' != X3 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP34])]) ).
tff(f14986,plain,
spl249_1063,
inference(avatar_split_clause,[],[f3134,f14984]) ).
tff(f14984,plain,
( spl249_1063
<=> ! [X0: 'B_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'B_bool_fun$'] :
( 'fun_app$ag'(X2,def_21(X1,X0))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP33(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1063])]) ).
tff(f3134,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( 'fun_app$ag'(X2,def_21(X1,X0))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 )
| ~ sP33(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1869]) ).
tff(f1869,plain,
! [X0: 'B_option$',X1: 'B_bool_fun$',X2: 'Bool_bool_fun$',X3: tlbool] :
( ( sP33(X0,X1,X2,X3)
| ( ~ 'fun_app$ag'(X2,def_21(X1,X0))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 ) )
| ( ~ 'fun_app$ag'(X2,X3)
& ( 'none$a' = X0 ) ) )
& ( ( ( 'fun_app$ag'(X2,def_21(X1,X0))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) != X0 ) )
& ( 'fun_app$ag'(X2,X3)
| ( 'none$a' != X0 ) ) )
| ~ sP33(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1868]) ).
tff(f1868,plain,
! [X3: 'B_option$',X2: 'B_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
( ( sP33(X3,X2,X0,X1)
| ( ~ 'fun_app$ag'(X0,def_21(X2,X3))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$ag'(X0,X1)
& ( 'none$a' = X3 ) ) )
& ( ( ( 'fun_app$ag'(X0,def_21(X2,X3))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$a' != X3 ) ) )
| ~ sP33(X3,X2,X0,X1) ) ),
inference(flattening,[],[f1867]) ).
tff(f1867,plain,
! [X3: 'B_option$',X2: 'B_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
( ( sP33(X3,X2,X0,X1)
| ( ~ 'fun_app$ag'(X0,def_21(X2,X3))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$ag'(X0,X1)
& ( 'none$a' = X3 ) ) )
& ( ( ( 'fun_app$ag'(X0,def_21(X2,X3))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$a' != X3 ) ) )
| ~ sP33(X3,X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1165]) ).
tff(f1165,plain,
! [X3: 'B_option$',X2: 'B_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
( sP33(X3,X2,X0,X1)
<=> ( ( 'fun_app$ag'(X0,def_21(X2,X3))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$a' != X3 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP33])]) ).
tff(f14982,plain,
spl249_1062,
inference(avatar_split_clause,[],[f3126,f14980]) ).
tff(f14980,plain,
( spl249_1062
<=> ! [X0: 'C_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'C_bool_fun$'] :
( 'fun_app$ag'(X2,def_23(X1,X0))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) != X0 )
| ~ sP32(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1062])]) ).
tff(f3126,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( 'fun_app$ag'(X2,def_23(X1,X0))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) != X0 )
| ~ sP32(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1865]) ).
tff(f1865,plain,
! [X0: 'C_option$',X1: 'C_bool_fun$',X2: 'Bool_bool_fun$',X3: tlbool] :
( ( sP32(X0,X1,X2,X3)
| ( ~ 'fun_app$ag'(X2,def_23(X1,X0))
& ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 ) )
| ( ~ 'fun_app$ag'(X2,X3)
& ( 'none$' = X0 ) ) )
& ( ( ( 'fun_app$ag'(X2,def_23(X1,X0))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) != X0 ) )
& ( 'fun_app$ag'(X2,X3)
| ( 'none$' != X0 ) ) )
| ~ sP32(X0,X1,X2,X3) ) ),
inference(rectify,[],[f1864]) ).
tff(f1864,plain,
! [X3: 'C_option$',X2: 'C_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
( ( sP32(X3,X2,X0,X1)
| ( ~ 'fun_app$ag'(X0,def_23(X2,X3))
& ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) = X3 ) )
| ( ~ 'fun_app$ag'(X0,X1)
& ( 'none$' = X3 ) ) )
& ( ( ( 'fun_app$ag'(X0,def_23(X2,X3))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$' != X3 ) ) )
| ~ sP32(X3,X2,X0,X1) ) ),
inference(flattening,[],[f1863]) ).
tff(f1863,plain,
! [X3: 'C_option$',X2: 'C_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
( ( sP32(X3,X2,X0,X1)
| ( ~ 'fun_app$ag'(X0,def_23(X2,X3))
& ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) = X3 ) )
| ( ~ 'fun_app$ag'(X0,X1)
& ( 'none$' = X3 ) ) )
& ( ( ( 'fun_app$ag'(X0,def_23(X2,X3))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$' != X3 ) ) )
| ~ sP32(X3,X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1163]) ).
tff(f1163,plain,
! [X3: 'C_option$',X2: 'C_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
( sP32(X3,X2,X0,X1)
<=> ( ( 'fun_app$ag'(X0,def_23(X2,X3))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$' != X3 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP32])]) ).
tff(f14978,plain,
spl249_1061,
inference(avatar_split_clause,[],[f3046,f14976]) ).
tff(f14976,plain,
( spl249_1061
<=> ! [X0: 'B_option_b_option_fun$',X3: 'A_option$',X2: 'A_b_option_fun$',X1: 'B_option$'] : ( 'fun_app$s'(X0,'fun_app$av'('case_option$d'(X1,X2),X3)) = 'fun_app$av'('case_option$d'('fun_app$s'(X0,X1),'uui$'(X0,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1061])]) ).
tff(f3046,plain,
! [X2: 'A_b_option_fun$',X3: 'A_option$',X0: 'B_option_b_option_fun$',X1: 'B_option$'] : ( 'fun_app$s'(X0,'fun_app$av'('case_option$d'(X1,X2),X3)) = 'fun_app$av'('case_option$d'('fun_app$s'(X0,X1),'uui$'(X0,X2)),X3) ),
inference(cnf_transformation,[],[f144]) ).
tff(f144,axiom,
! [X0: 'B_option_b_option_fun$',X1: 'B_option$',X2: 'A_b_option_fun$',X3: 'A_option$'] : ( 'fun_app$s'(X0,'fun_app$av'('case_option$d'(X1,X2),X3)) = 'fun_app$av'('case_option$d'('fun_app$s'(X0,X1),'uui$'(X0,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom142) ).
tff(f14974,plain,
spl249_1060,
inference(avatar_split_clause,[],[f3045,f14972]) ).
tff(f14972,plain,
( spl249_1060
<=> ! [X0: 'C_option_c_option_fun$',X3: 'B_option$',X2: 'B_c_option_fun$',X1: 'C_option$'] : ( 'fun_app$u'(X0,'fun_app$an'('case_option$c'(X1,X2),X3)) = 'fun_app$an'('case_option$c'('fun_app$u'(X0,X1),'uuh$'(X0,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1060])]) ).
tff(f3045,plain,
! [X2: 'B_c_option_fun$',X3: 'B_option$',X0: 'C_option_c_option_fun$',X1: 'C_option$'] : ( 'fun_app$u'(X0,'fun_app$an'('case_option$c'(X1,X2),X3)) = 'fun_app$an'('case_option$c'('fun_app$u'(X0,X1),'uuh$'(X0,X2)),X3) ),
inference(cnf_transformation,[],[f143]) ).
tff(f143,axiom,
! [X0: 'C_option_c_option_fun$',X1: 'C_option$',X2: 'B_c_option_fun$',X3: 'B_option$'] : ( 'fun_app$u'(X0,'fun_app$an'('case_option$c'(X1,X2),X3)) = 'fun_app$an'('case_option$c'('fun_app$u'(X0,X1),'uuh$'(X0,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom141) ).
tff(f14970,plain,
spl249_1059,
inference(avatar_split_clause,[],[f2988,f14968]) ).
tff(f14968,plain,
( spl249_1059
<=> ! [X2: 'B$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$f'(X1,sK191(X0,X1,X2)) )
| ( 'fun_app$g'('some$',X2) != 'bind$e'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1059])]) ).
tff(f2988,plain,
! [X2: 'B$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$f'(X1,sK191(X0,X1,X2)) )
| ( 'fun_app$g'('some$',X2) != 'bind$e'(X0,X1) ) ),
inference(cnf_transformation,[],[f1750]) ).
tff(f1750,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'bind$e'(X0,X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$g'('some$',X2) != 'fun_app$f'(X1,X3) )
| ( 'fun_app$q'('some$b',X3) != X0 ) ) )
& ( ( ( 'fun_app$g'('some$',X2) = 'fun_app$f'(X1,sK191(X0,X1,X2)) )
& ( 'fun_app$q'('some$b',sK191(X0,X1,X2)) = X0 ) )
| ( 'fun_app$g'('some$',X2) != 'bind$e'(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK191])],[f1748,f1749]) ).
tff(f1749,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$',X2: 'B$'] :
( ? [X4: 'A$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$f'(X1,X4) )
& ( 'fun_app$q'('some$b',X4) = X0 ) )
=> ( ( 'fun_app$g'('some$',X2) = 'fun_app$f'(X1,sK191(X0,X1,X2)) )
& ( 'fun_app$q'('some$b',sK191(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1748,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'bind$e'(X0,X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$g'('some$',X2) != 'fun_app$f'(X1,X3) )
| ( 'fun_app$q'('some$b',X3) != X0 ) ) )
& ( ? [X4: 'A$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$f'(X1,X4) )
& ( 'fun_app$q'('some$b',X4) = X0 ) )
| ( 'fun_app$g'('some$',X2) != 'bind$e'(X0,X1) ) ) ),
inference(rectify,[],[f1747]) ).
tff(f1747,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'bind$e'(X0,X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$g'('some$',X2) != 'fun_app$f'(X1,X3) )
| ( 'fun_app$q'('some$b',X3) != X0 ) ) )
& ( ? [X3: 'A$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$f'(X1,X3) )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ( 'fun_app$g'('some$',X2) != 'bind$e'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f411]) ).
tff(f411,axiom,
! [X0: 'A_option$',X1: 'A_b_option_fun$',X2: 'B$'] :
( ( 'fun_app$g'('some$',X2) = 'bind$e'(X0,X1) )
<=> ? [X3: 'A$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$f'(X1,X3) )
& ( 'fun_app$q'('some$b',X3) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom409) ).
tff(f14966,plain,
spl249_1058,
inference(avatar_split_clause,[],[f2982,f14964]) ).
tff(f14964,plain,
( spl249_1058
<=> ! [X2: 'C$',X0: 'A_option$',X1: 'A_c_option_fun$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$bm'(X1,sK189(X0,X1,X2)) )
| ( 'fun_app$j'('some$a',X2) != 'bind$d'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1058])]) ).
tff(f2982,plain,
! [X2: 'C$',X0: 'A_option$',X1: 'A_c_option_fun$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$bm'(X1,sK189(X0,X1,X2)) )
| ( 'fun_app$j'('some$a',X2) != 'bind$d'(X0,X1) ) ),
inference(cnf_transformation,[],[f1742]) ).
tff(f1742,plain,
! [X0: 'A_option$',X1: 'A_c_option_fun$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'bind$d'(X0,X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$j'('some$a',X2) != 'fun_app$bm'(X1,X3) )
| ( 'fun_app$q'('some$b',X3) != X0 ) ) )
& ( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$bm'(X1,sK189(X0,X1,X2)) )
& ( 'fun_app$q'('some$b',sK189(X0,X1,X2)) = X0 ) )
| ( 'fun_app$j'('some$a',X2) != 'bind$d'(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK189])],[f1740,f1741]) ).
tff(f1741,plain,
! [X0: 'A_option$',X1: 'A_c_option_fun$',X2: 'C$'] :
( ? [X4: 'A$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$bm'(X1,X4) )
& ( 'fun_app$q'('some$b',X4) = X0 ) )
=> ( ( 'fun_app$j'('some$a',X2) = 'fun_app$bm'(X1,sK189(X0,X1,X2)) )
& ( 'fun_app$q'('some$b',sK189(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1740,plain,
! [X0: 'A_option$',X1: 'A_c_option_fun$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'bind$d'(X0,X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$j'('some$a',X2) != 'fun_app$bm'(X1,X3) )
| ( 'fun_app$q'('some$b',X3) != X0 ) ) )
& ( ? [X4: 'A$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$bm'(X1,X4) )
& ( 'fun_app$q'('some$b',X4) = X0 ) )
| ( 'fun_app$j'('some$a',X2) != 'bind$d'(X0,X1) ) ) ),
inference(rectify,[],[f1739]) ).
tff(f1739,plain,
! [X0: 'A_option$',X1: 'A_c_option_fun$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'bind$d'(X0,X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$j'('some$a',X2) != 'fun_app$bm'(X1,X3) )
| ( 'fun_app$q'('some$b',X3) != X0 ) ) )
& ( ? [X3: 'A$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$bm'(X1,X3) )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ( 'fun_app$j'('some$a',X2) != 'bind$d'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f410]) ).
tff(f410,axiom,
! [X0: 'A_option$',X1: 'A_c_option_fun$',X2: 'C$'] :
( ( 'fun_app$j'('some$a',X2) = 'bind$d'(X0,X1) )
<=> ? [X3: 'A$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$bm'(X1,X3) )
& ( 'fun_app$q'('some$b',X3) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom408) ).
tff(f14962,plain,
spl249_1057,
inference(avatar_split_clause,[],[f2979,f14960]) ).
tff(f14960,plain,
( spl249_1057
<=> ! [X2: 'A$',X0: 'B_option$',X1: 'B_a_option_fun$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bo'(X1,sK188(X0,X1,X2)) )
| ( 'fun_app$q'('some$b',X2) != 'bind$g'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1057])]) ).
tff(f2979,plain,
! [X2: 'A$',X0: 'B_option$',X1: 'B_a_option_fun$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bo'(X1,sK188(X0,X1,X2)) )
| ( 'fun_app$q'('some$b',X2) != 'bind$g'(X0,X1) ) ),
inference(cnf_transformation,[],[f1738]) ).
tff(f1738,plain,
! [X0: 'B_option$',X1: 'B_a_option_fun$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'bind$g'(X0,X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$q'('some$b',X2) != 'fun_app$bo'(X1,X3) )
| ( 'fun_app$g'('some$',X3) != X0 ) ) )
& ( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$bo'(X1,sK188(X0,X1,X2)) )
& ( 'fun_app$g'('some$',sK188(X0,X1,X2)) = X0 ) )
| ( 'fun_app$q'('some$b',X2) != 'bind$g'(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK188])],[f1736,f1737]) ).
tff(f1737,plain,
! [X0: 'B_option$',X1: 'B_a_option_fun$',X2: 'A$'] :
( ? [X4: 'B$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bo'(X1,X4) )
& ( 'fun_app$g'('some$',X4) = X0 ) )
=> ( ( 'fun_app$q'('some$b',X2) = 'fun_app$bo'(X1,sK188(X0,X1,X2)) )
& ( 'fun_app$g'('some$',sK188(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1736,plain,
! [X0: 'B_option$',X1: 'B_a_option_fun$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'bind$g'(X0,X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$q'('some$b',X2) != 'fun_app$bo'(X1,X3) )
| ( 'fun_app$g'('some$',X3) != X0 ) ) )
& ( ? [X4: 'B$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bo'(X1,X4) )
& ( 'fun_app$g'('some$',X4) = X0 ) )
| ( 'fun_app$q'('some$b',X2) != 'bind$g'(X0,X1) ) ) ),
inference(rectify,[],[f1735]) ).
tff(f1735,plain,
! [X0: 'B_option$',X1: 'B_a_option_fun$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'bind$g'(X0,X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$q'('some$b',X2) != 'fun_app$bo'(X1,X3) )
| ( 'fun_app$g'('some$',X3) != X0 ) ) )
& ( ? [X3: 'B$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bo'(X1,X3) )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ( 'fun_app$q'('some$b',X2) != 'bind$g'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f413]) ).
tff(f413,axiom,
! [X0: 'B_option$',X1: 'B_a_option_fun$',X2: 'A$'] :
( ( 'fun_app$q'('some$b',X2) = 'bind$g'(X0,X1) )
<=> ? [X3: 'B$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bo'(X1,X3) )
& ( 'fun_app$g'('some$',X3) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom411) ).
tff(f14958,plain,
spl249_1056,
inference(avatar_split_clause,[],[f2976,f14956]) ).
tff(f14956,plain,
( spl249_1056
<=> ! [X2: 'A$',X0: 'C_option$',X1: 'C_a_option_fun$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bn'(X1,sK187(X0,X1,X2)) )
| ( 'fun_app$q'('some$b',X2) != 'bind$f'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1056])]) ).
tff(f2976,plain,
! [X2: 'A$',X0: 'C_option$',X1: 'C_a_option_fun$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bn'(X1,sK187(X0,X1,X2)) )
| ( 'fun_app$q'('some$b',X2) != 'bind$f'(X0,X1) ) ),
inference(cnf_transformation,[],[f1734]) ).
tff(f1734,plain,
! [X0: 'C_option$',X1: 'C_a_option_fun$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'bind$f'(X0,X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$q'('some$b',X2) != 'fun_app$bn'(X1,X3) )
| ( 'fun_app$j'('some$a',X3) != X0 ) ) )
& ( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$bn'(X1,sK187(X0,X1,X2)) )
& ( 'fun_app$j'('some$a',sK187(X0,X1,X2)) = X0 ) )
| ( 'fun_app$q'('some$b',X2) != 'bind$f'(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK187])],[f1732,f1733]) ).
tff(f1733,plain,
! [X0: 'C_option$',X1: 'C_a_option_fun$',X2: 'A$'] :
( ? [X4: 'C$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bn'(X1,X4) )
& ( 'fun_app$j'('some$a',X4) = X0 ) )
=> ( ( 'fun_app$q'('some$b',X2) = 'fun_app$bn'(X1,sK187(X0,X1,X2)) )
& ( 'fun_app$j'('some$a',sK187(X0,X1,X2)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1732,plain,
! [X0: 'C_option$',X1: 'C_a_option_fun$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'bind$f'(X0,X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$q'('some$b',X2) != 'fun_app$bn'(X1,X3) )
| ( 'fun_app$j'('some$a',X3) != X0 ) ) )
& ( ? [X4: 'C$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bn'(X1,X4) )
& ( 'fun_app$j'('some$a',X4) = X0 ) )
| ( 'fun_app$q'('some$b',X2) != 'bind$f'(X0,X1) ) ) ),
inference(rectify,[],[f1731]) ).
tff(f1731,plain,
! [X0: 'C_option$',X1: 'C_a_option_fun$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'bind$f'(X0,X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$q'('some$b',X2) != 'fun_app$bn'(X1,X3) )
| ( 'fun_app$j'('some$a',X3) != X0 ) ) )
& ( ? [X3: 'C$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bn'(X1,X3) )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ( 'fun_app$q'('some$b',X2) != 'bind$f'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f412]) ).
tff(f412,axiom,
! [X0: 'C_option$',X1: 'C_a_option_fun$',X2: 'A$'] :
( ( 'fun_app$q'('some$b',X2) = 'bind$f'(X0,X1) )
<=> ? [X3: 'C$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bn'(X1,X3) )
& ( 'fun_app$j'('some$a',X3) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom410) ).
tff(f14954,plain,
spl249_1055,
inference(avatar_split_clause,[],[f1953,f14952]) ).
tff(f14952,plain,
( spl249_1055
<=> ! [X2: 'A_a_option_fun$',X3: 'B$'] : ( 'fun_app$g'('fun_app$au'('f$',X2),X3) = 'fun_app$av'('case_option$d'('none$a','uua$'(sK46,X3)),'fun_app$q'(X2,'fun_app$ao'(sK47,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1055])]) ).
tff(f1953,plain,
! [X2: 'A_a_option_fun$',X3: 'B$'] : ( 'fun_app$g'('fun_app$au'('f$',X2),X3) = 'fun_app$av'('case_option$d'('none$a','uua$'(sK46,X3)),'fun_app$q'(X2,'fun_app$ao'(sK47,X3))) ),
inference(cnf_transformation,[],[f1190]) ).
tff(f1190,plain,
( 'valid_getter_setter$a'(sK47,sK46)
& ! [X2: 'A_a_option_fun$',X3: 'B$'] : ( 'fun_app$g'('fun_app$au'('f$',X2),X3) = 'fun_app$av'('case_option$d'('none$a','uua$'(sK46,X3)),'fun_app$q'(X2,'fun_app$ao'(sK47,X3))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47])],[f863,f1189]) ).
tff(f1189,plain,
( ? [X0: 'A_b_b_fun_fun$',X1: 'B_a_fun$'] :
( 'valid_getter_setter$a'(X1,X0)
& ! [X2: 'A_a_option_fun$',X3: 'B$'] : ( 'fun_app$g'('fun_app$au'('f$',X2),X3) = 'fun_app$av'('case_option$d'('none$a','uua$'(X0,X3)),'fun_app$q'(X2,'fun_app$ao'(X1,X3))) ) )
=> ( 'valid_getter_setter$a'(sK47,sK46)
& ! [X3: 'B$',X2: 'A_a_option_fun$'] : ( 'fun_app$g'('fun_app$au'('f$',X2),X3) = 'fun_app$av'('case_option$d'('none$a','uua$'(sK46,X3)),'fun_app$q'(X2,'fun_app$ao'(sK47,X3))) ) ) ),
introduced(choice_axiom,[]) ).
tff(f863,plain,
? [X0: 'A_b_b_fun_fun$',X1: 'B_a_fun$'] :
( 'valid_getter_setter$a'(X1,X0)
& ! [X2: 'A_a_option_fun$',X3: 'B$'] : ( 'fun_app$g'('fun_app$au'('f$',X2),X3) = 'fun_app$av'('case_option$d'('none$a','uua$'(X0,X3)),'fun_app$q'(X2,'fun_app$ao'(X1,X3))) ) ),
inference(ennf_transformation,[],[f738]) ).
tff(f738,plain,
~ ! [X0: 'A_b_b_fun_fun$',X1: 'B_a_fun$'] :
~ ( 'valid_getter_setter$a'(X1,X0)
& ! [X2: 'A_a_option_fun$',X3: 'B$'] : ( 'fun_app$g'('fun_app$au'('f$',X2),X3) = 'fun_app$av'('case_option$d'('none$a','uua$'(X0,X3)),'fun_app$q'(X2,'fun_app$ao'(X1,X3))) ) ),
inference(true_and_false_elimination,[],[f125]) ).
tff(f125,axiom,
( ! [X0: 'A_b_b_fun_fun$',X1: 'B_a_fun$'] :
( ( 'valid_getter_setter$a'(X1,X0)
& ! [X2: 'A_a_option_fun$',X3: 'B$'] : ( 'fun_app$g'('fun_app$au'('f$',X2),X3) = 'fun_app$av'('case_option$d'('none$a','uua$'(X0,X3)),'fun_app$q'(X2,'fun_app$ao'(X1,X3))) ) )
=> $false )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom123) ).
tff(f14854,plain,
( spl249_1054
| ~ spl249_251
| ~ spl249_703 ),
inference(avatar_split_clause,[],[f9018,f8270,f4732,f14852]) ).
tff(f4732,plain,
( spl249_251
<=> ! [X0: 'C_option$'] : ~ 'fun_app$'('bot$h',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_251])]) ).
tff(f8270,plain,
( spl249_703
<=> ! [X2: 'B$',X0: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X0,'bind$b'('fun_app$g'('some$',X2),X1))
| ~ 'fun_app$c'('uul$'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_703])]) ).
tff(f9018,plain,
( ! [X0: 'B_c_option_fun$',X1: 'B$'] : ~ 'fun_app$c'('uul$'('bot$h',X0),X1)
| ~ spl249_251
| ~ spl249_703 ),
inference(resolution,[],[f8271,f4733]) ).
tff(f4733,plain,
( ! [X0: 'C_option$'] : ~ 'fun_app$'('bot$h',X0)
| ~ spl249_251 ),
inference(avatar_component_clause,[],[f4732]) ).
tff(f8271,plain,
( ! [X2: 'B$',X0: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X0,'bind$b'('fun_app$g'('some$',X2),X1))
| ~ 'fun_app$c'('uul$'(X0,X1),X2) )
| ~ spl249_703 ),
inference(avatar_component_clause,[],[f8270]) ).
tff(f14531,plain,
( spl249_1053
| ~ spl249_252
| ~ spl249_699 ),
inference(avatar_split_clause,[],[f8944,f8254,f4736,f14529]) ).
tff(f14529,plain,
( spl249_1053
<=> ! [X2: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ~ sP43(X0,X1,'bot$g',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1053])]) ).
tff(f4736,plain,
( spl249_252
<=> ! [X0: 'B_option$'] : ~ 'fun_app$a'('bot$g',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_252])]) ).
tff(f8254,plain,
( spl249_699
<=> ! [X0: 'B_option_bool_fun$',X3: 'B_option$',X2: 'B_b_option_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
| ~ sP43(X3,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_699])]) ).
tff(f8944,plain,
( ! [X2: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ~ sP43(X0,X1,'bot$g',X2)
| ~ spl249_252
| ~ spl249_699 ),
inference(resolution,[],[f8255,f4737]) ).
tff(f4737,plain,
( ! [X0: 'B_option$'] : ~ 'fun_app$a'('bot$g',X0)
| ~ spl249_252 ),
inference(avatar_component_clause,[],[f4736]) ).
tff(f8255,plain,
( ! [X2: 'B_b_option_fun$',X3: 'B_option$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
| ~ sP43(X3,X2,X0,X1) )
| ~ spl249_699 ),
inference(avatar_component_clause,[],[f8254]) ).
tff(f14413,plain,
( spl249_1052
| ~ spl249_252
| ~ spl249_697 ),
inference(avatar_split_clause,[],[f8910,f8246,f4736,f14411]) ).
tff(f14411,plain,
( spl249_1052
<=> ! [X2: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ~ sP42(X0,X1,'bot$g',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1052])]) ).
tff(f8246,plain,
( spl249_697
<=> ! [X0: 'B_option_bool_fun$',X3: 'B_option$',X2: 'B_b_option_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
| ~ sP42(X3,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_697])]) ).
tff(f8910,plain,
( ! [X2: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ~ sP42(X0,X1,'bot$g',X2)
| ~ spl249_252
| ~ spl249_697 ),
inference(resolution,[],[f8247,f4737]) ).
tff(f8247,plain,
( ! [X2: 'B_b_option_fun$',X3: 'B_option$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
| ~ sP42(X3,X2,X0,X1) )
| ~ spl249_697 ),
inference(avatar_component_clause,[],[f8246]) ).
tff(f14246,plain,
( spl249_1051
| ~ spl249_252
| ~ spl249_695 ),
inference(avatar_split_clause,[],[f8875,f8236,f4736,f14244]) ).
tff(f14244,plain,
( spl249_1051
<=> ! [X2: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] : ~ sP41(X0,X1,'bot$g',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1051])]) ).
tff(f8236,plain,
( spl249_695
<=> ! [X0: 'B_option_bool_fun$',X3: 'A_option$',X2: 'A_b_option_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3))
| ~ sP41(X3,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_695])]) ).
tff(f8875,plain,
( ! [X2: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] : ~ sP41(X0,X1,'bot$g',X2)
| ~ spl249_252
| ~ spl249_695 ),
inference(resolution,[],[f8237,f4737]) ).
tff(f8237,plain,
( ! [X2: 'A_b_option_fun$',X3: 'A_option$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3))
| ~ sP41(X3,X2,X0,X1) )
| ~ spl249_695 ),
inference(avatar_component_clause,[],[f8236]) ).
tff(f14131,plain,
( spl249_1050
| ~ spl249_252
| ~ spl249_693 ),
inference(avatar_split_clause,[],[f8843,f8228,f4736,f14129]) ).
tff(f14129,plain,
( spl249_1050
<=> ! [X2: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] : ~ sP40(X0,X1,'bot$g',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1050])]) ).
tff(f8228,plain,
( spl249_693
<=> ! [X0: 'B_option_bool_fun$',X3: 'A_option$',X2: 'A_b_option_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3))
| ~ sP40(X3,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_693])]) ).
tff(f8843,plain,
( ! [X2: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] : ~ sP40(X0,X1,'bot$g',X2)
| ~ spl249_252
| ~ spl249_693 ),
inference(resolution,[],[f8229,f4737]) ).
tff(f8229,plain,
( ! [X2: 'A_b_option_fun$',X3: 'A_option$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3))
| ~ sP40(X3,X2,X0,X1) )
| ~ spl249_693 ),
inference(avatar_component_clause,[],[f8228]) ).
tff(f13968,plain,
( spl249_1049
| ~ spl249_251
| ~ spl249_691 ),
inference(avatar_split_clause,[],[f8812,f8220,f4732,f13966]) ).
tff(f13966,plain,
( spl249_1049
<=> ! [X2: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] : ~ sP39(X0,X1,'bot$h',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1049])]) ).
tff(f8220,plain,
( spl249_691
<=> ! [X0: 'C_option_bool_fun$',X3: 'B_option$',X2: 'B_c_option_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
| ~ sP39(X3,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_691])]) ).
tff(f8812,plain,
( ! [X2: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] : ~ sP39(X0,X1,'bot$h',X2)
| ~ spl249_251
| ~ spl249_691 ),
inference(resolution,[],[f8221,f4733]) ).
tff(f8221,plain,
( ! [X2: 'B_c_option_fun$',X3: 'B_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
| ~ sP39(X3,X2,X0,X1) )
| ~ spl249_691 ),
inference(avatar_component_clause,[],[f8220]) ).
tff(f13832,plain,
spl249_1048,
inference(avatar_split_clause,[],[f3589,f13830]) ).
tff(f13830,plain,
( spl249_1048
<=> ! [X2: 'B$',X0: 'B_b_b_fun_fun$',X1: 'B$'] : ( 'fun_app$s'('combine_options$b'(X0,'fun_app$g'('some$',X1)),'fun_app$g'('some$',X2)) = 'fun_app$g'('uve$'('fun_app$ai'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1048])]) ).
tff(f3589,plain,
! [X2: 'B$',X0: 'B_b_b_fun_fun$',X1: 'B$'] : ( 'fun_app$s'('combine_options$b'(X0,'fun_app$g'('some$',X1)),'fun_app$g'('some$',X2)) = 'fun_app$g'('uve$'('fun_app$ai'(X0,X1)),X2) ),
inference(forward_demodulation,[],[f2665,f2245]) ).
tff(f2665,plain,
! [X2: 'B$',X0: 'B_b_b_fun_fun$',X1: 'B$'] : ( 'fun_app$g'('some$','fun_app$h'('fun_app$ai'(X0,X1),X2)) = 'fun_app$s'('combine_options$b'(X0,'fun_app$g'('some$',X1)),'fun_app$g'('some$',X2)) ),
inference(cnf_transformation,[],[f245]) ).
tff(f245,axiom,
! [X0: 'B_b_b_fun_fun$',X1: 'B$',X2: 'B$'] : ( 'fun_app$g'('some$','fun_app$h'('fun_app$ai'(X0,X1),X2)) = 'fun_app$s'('combine_options$b'(X0,'fun_app$g'('some$',X1)),'fun_app$g'('some$',X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom243) ).
tff(f13828,plain,
spl249_1047,
inference(avatar_split_clause,[],[f3588,f13826]) ).
tff(f13826,plain,
( spl249_1047
<=> ! [X2: 'C$',X0: 'C_c_c_fun_fun$',X1: 'C$'] : ( 'fun_app$u'('combine_options$a'(X0,'fun_app$j'('some$a',X1)),'fun_app$j'('some$a',X2)) = 'fun_app$j'('uvf$'('fun_app$ah'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1047])]) ).
tff(f3588,plain,
! [X2: 'C$',X0: 'C_c_c_fun_fun$',X1: 'C$'] : ( 'fun_app$u'('combine_options$a'(X0,'fun_app$j'('some$a',X1)),'fun_app$j'('some$a',X2)) = 'fun_app$j'('uvf$'('fun_app$ah'(X0,X1)),X2) ),
inference(forward_demodulation,[],[f2664,f2244]) ).
tff(f2244,plain,
! [X0: 'C_c_fun$',X1: 'C$'] : ( 'fun_app$j'('uvf$'(X0),X1) = 'fun_app$j'('some$a','fun_app$k'(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
tff(f14,axiom,
! [X0: 'C_c_fun$',X1: 'C$'] : ( 'fun_app$j'('uvf$'(X0),X1) = 'fun_app$j'('some$a','fun_app$k'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom13) ).
tff(f2664,plain,
! [X2: 'C$',X0: 'C_c_c_fun_fun$',X1: 'C$'] : ( 'fun_app$j'('some$a','fun_app$k'('fun_app$ah'(X0,X1),X2)) = 'fun_app$u'('combine_options$a'(X0,'fun_app$j'('some$a',X1)),'fun_app$j'('some$a',X2)) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,axiom,
! [X0: 'C_c_c_fun_fun$',X1: 'C$',X2: 'C$'] : ( 'fun_app$j'('some$a','fun_app$k'('fun_app$ah'(X0,X1),X2)) = 'fun_app$u'('combine_options$a'(X0,'fun_app$j'('some$a',X1)),'fun_app$j'('some$a',X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom242) ).
tff(f13812,plain,
( spl249_1046
| ~ spl249_251
| ~ spl249_689 ),
inference(avatar_split_clause,[],[f8782,f8212,f4732,f13810]) ).
tff(f13810,plain,
( spl249_1046
<=> ! [X2: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] : ~ sP38(X0,X1,'bot$h',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1046])]) ).
tff(f8212,plain,
( spl249_689
<=> ! [X0: 'C_option_bool_fun$',X3: 'B_option$',X2: 'B_c_option_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
| ~ sP38(X3,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_689])]) ).
tff(f8782,plain,
( ! [X2: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] : ~ sP38(X0,X1,'bot$h',X2)
| ~ spl249_251
| ~ spl249_689 ),
inference(resolution,[],[f8213,f4733]) ).
tff(f8213,plain,
( ! [X2: 'B_c_option_fun$',X3: 'B_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
| ~ sP38(X3,X2,X0,X1) )
| ~ spl249_689 ),
inference(avatar_component_clause,[],[f8212]) ).
tff(f13808,plain,
( spl249_1045
| ~ spl249_460
| ~ spl249_725
| ~ spl249_1044 ),
inference(avatar_split_clause,[],[f13804,f13801,f9104,f6385,f13806]) ).
tff(f13806,plain,
( spl249_1045
<=> ! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A$'] : ( 'fun_app$q'('uuw$'(X0,X1),X2) = 'fun_app$be'('combine_options$'(X0,'fun_app$q'('some$b',X1)),'fun_app$q'('some$b',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1045])]) ).
tff(f13801,plain,
( spl249_1044
<=> ! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A$'] : ( 'fun_app$be'('combine_options$'(X0,'fun_app$q'('some$b',X1)),'fun_app$q'('some$b',X2)) = 'fun_app$q'('uvd$'('fun_app$aj'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1044])]) ).
tff(f13804,plain,
( ! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A$'] : ( 'fun_app$q'('uuw$'(X0,X1),X2) = 'fun_app$be'('combine_options$'(X0,'fun_app$q'('some$b',X1)),'fun_app$q'('some$b',X2)) )
| ~ spl249_460
| ~ spl249_725
| ~ spl249_1044 ),
inference(forward_demodulation,[],[f13802,f9422]) ).
tff(f9422,plain,
( ! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A$'] : ( 'fun_app$q'('uuw$'(X0,X1),X2) = 'fun_app$q'('uvd$'('fun_app$aj'(X0,X1)),X2) )
| ~ spl249_460
| ~ spl249_725 ),
inference(superposition,[],[f9105,f6386]) ).
tff(f13802,plain,
( ! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A$'] : ( 'fun_app$be'('combine_options$'(X0,'fun_app$q'('some$b',X1)),'fun_app$q'('some$b',X2)) = 'fun_app$q'('uvd$'('fun_app$aj'(X0,X1)),X2) )
| ~ spl249_1044 ),
inference(avatar_component_clause,[],[f13801]) ).
tff(f13803,plain,
spl249_1044,
inference(avatar_split_clause,[],[f3587,f13801]) ).
tff(f3587,plain,
! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A$'] : ( 'fun_app$be'('combine_options$'(X0,'fun_app$q'('some$b',X1)),'fun_app$q'('some$b',X2)) = 'fun_app$q'('uvd$'('fun_app$aj'(X0,X1)),X2) ),
inference(forward_demodulation,[],[f2663,f2243]) ).
tff(f2243,plain,
! [X0: 'A_a_fun$',X1: 'A$'] : ( 'fun_app$q'('uvd$'(X0),X1) = 'fun_app$q'('some$b','fun_app$r'(X0,X1)) ),
inference(cnf_transformation,[],[f19]) ).
tff(f19,axiom,
! [X0: 'A_a_fun$',X1: 'A$'] : ( 'fun_app$q'('uvd$'(X0),X1) = 'fun_app$q'('some$b','fun_app$r'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom18) ).
tff(f2663,plain,
! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A$'] : ( 'fun_app$q'('some$b','fun_app$r'('fun_app$aj'(X0,X1),X2)) = 'fun_app$be'('combine_options$'(X0,'fun_app$q'('some$b',X1)),'fun_app$q'('some$b',X2)) ),
inference(cnf_transformation,[],[f243]) ).
tff(f243,axiom,
! [X0: 'A_a_a_fun_fun$',X1: 'A$',X2: 'A$'] : ( 'fun_app$q'('some$b','fun_app$r'('fun_app$aj'(X0,X1),X2)) = 'fun_app$be'('combine_options$'(X0,'fun_app$q'('some$b',X1)),'fun_app$q'('some$b',X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom241) ).
tff(f13799,plain,
spl249_1043,
inference(avatar_split_clause,[],[f3533,f13797]) ).
tff(f13797,plain,
( spl249_1043
<=> ! [X2: 'B_b_option_fun$',X1: 'B_option$',X3: 'B_b_option_fun$'] :
( ( 'fun_app$ac'('bind$c'(X1),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| 'member$c'(sK213(X1,X2,X3),'set_option$d'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1043])]) ).
tff(f3533,plain,
! [X2: 'B_b_option_fun$',X3: 'B_b_option_fun$',X1: 'B_option$'] :
( ( 'fun_app$ac'('bind$c'(X1),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| 'member$c'(sK213(X1,X2,X3),'set_option$d'(X1)) ),
inference(equality_resolution,[],[f3073]) ).
tff(f3073,plain,
! [X2: 'B_b_option_fun$',X3: 'B_b_option_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$ac'('bind$c'(X0),X2) = 'fun_app$ac'('bind$c'(X1),X3) )
| 'member$c'(sK213(X1,X2,X3),'set_option$d'(X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1822]) ).
tff(f13795,plain,
spl249_1042,
inference(avatar_split_clause,[],[f3531,f13793]) ).
tff(f13793,plain,
( spl249_1042
<=> ! [X2: 'B_b_fun$',X1: 'B_option$',X3: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X3),X1) = 'fun_app$s'('map_option$b'(X2),X1) )
| 'member$c'(sK212(X1,X2,X3),'set_option$d'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1042])]) ).
tff(f3531,plain,
! [X2: 'B_b_fun$',X3: 'B_b_fun$',X1: 'B_option$'] :
( ( 'fun_app$s'('map_option$b'(X3),X1) = 'fun_app$s'('map_option$b'(X2),X1) )
| 'member$c'(sK212(X1,X2,X3),'set_option$d'(X1)) ),
inference(equality_resolution,[],[f3071]) ).
tff(f3071,plain,
! [X2: 'B_b_fun$',X3: 'B_b_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$s'('map_option$b'(X2),X0) = 'fun_app$s'('map_option$b'(X3),X1) )
| 'member$c'(sK212(X1,X2,X3),'set_option$d'(X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1820]) ).
tff(f13791,plain,
spl249_1041,
inference(avatar_split_clause,[],[f3527,f13789]) ).
tff(f13789,plain,
( spl249_1041
<=> ! [X2: 'B_c_fun$',X1: 'B_option$',X3: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X3),X1) = 'fun_app$an'('map_option$d'(X2),X1) )
| 'member$c'(sK210(X1,X2,X3),'set_option$d'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1041])]) ).
tff(f3527,plain,
! [X2: 'B_c_fun$',X3: 'B_c_fun$',X1: 'B_option$'] :
( ( 'fun_app$an'('map_option$d'(X3),X1) = 'fun_app$an'('map_option$d'(X2),X1) )
| 'member$c'(sK210(X1,X2,X3),'set_option$d'(X1)) ),
inference(equality_resolution,[],[f3067]) ).
tff(f3067,plain,
! [X2: 'B_c_fun$',X3: 'B_c_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$an'('map_option$d'(X2),X0) = 'fun_app$an'('map_option$d'(X3),X1) )
| 'member$c'(sK210(X1,X2,X3),'set_option$d'(X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1816]) ).
tff(f13787,plain,
spl249_1040,
inference(avatar_split_clause,[],[f3525,f13785]) ).
tff(f13785,plain,
( spl249_1040
<=> ! [X2: 'C_c_option_fun$',X1: 'C_option$',X3: 'C_c_option_fun$'] :
( ( 'fun_app$ab'('bind$'(X1),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| 'member$b'(sK209(X1,X2,X3),'set_option$c'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1040])]) ).
tff(f3525,plain,
! [X2: 'C_c_option_fun$',X3: 'C_c_option_fun$',X1: 'C_option$'] :
( ( 'fun_app$ab'('bind$'(X1),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| 'member$b'(sK209(X1,X2,X3),'set_option$c'(X1)) ),
inference(equality_resolution,[],[f3065]) ).
tff(f3065,plain,
! [X2: 'C_c_option_fun$',X3: 'C_c_option_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$ab'('bind$'(X0),X2) = 'fun_app$ab'('bind$'(X1),X3) )
| 'member$b'(sK209(X1,X2,X3),'set_option$c'(X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1814]) ).
tff(f13783,plain,
spl249_1039,
inference(avatar_split_clause,[],[f3523,f13781]) ).
tff(f13781,plain,
( spl249_1039
<=> ! [X2: 'C_b_fun$',X1: 'C_option$',X3: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X3),X1) = 'fun_app$bg'('map_option$'(X2),X1) )
| 'member$b'(sK208(X1,X2,X3),'set_option$c'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1039])]) ).
tff(f3523,plain,
! [X2: 'C_b_fun$',X3: 'C_b_fun$',X1: 'C_option$'] :
( ( 'fun_app$bg'('map_option$'(X3),X1) = 'fun_app$bg'('map_option$'(X2),X1) )
| 'member$b'(sK208(X1,X2,X3),'set_option$c'(X1)) ),
inference(equality_resolution,[],[f3063]) ).
tff(f3063,plain,
! [X2: 'C_b_fun$',X3: 'C_b_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$bg'('map_option$'(X2),X0) = 'fun_app$bg'('map_option$'(X3),X1) )
| 'member$b'(sK208(X1,X2,X3),'set_option$c'(X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1812]) ).
tff(f13779,plain,
spl249_1038,
inference(avatar_split_clause,[],[f3519,f13777]) ).
tff(f13777,plain,
( spl249_1038
<=> ! [X2: 'A_a_fun$',X1: 'A_option$',X3: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X3),X1) = 'fun_app$be'('map_option$a'(X2),X1) )
| 'member$d'(sK206(X1,X2,X3),'set_option$b'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1038])]) ).
tff(f3519,plain,
! [X2: 'A_a_fun$',X3: 'A_a_fun$',X1: 'A_option$'] :
( ( 'fun_app$be'('map_option$a'(X3),X1) = 'fun_app$be'('map_option$a'(X2),X1) )
| 'member$d'(sK206(X1,X2,X3),'set_option$b'(X1)) ),
inference(equality_resolution,[],[f3059]) ).
tff(f3059,plain,
! [X2: 'A_a_fun$',X3: 'A_a_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$be'('map_option$a'(X2),X0) = 'fun_app$be'('map_option$a'(X3),X1) )
| 'member$d'(sK206(X1,X2,X3),'set_option$b'(X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1808]) ).
tff(f13775,plain,
spl249_1037,
inference(avatar_split_clause,[],[f3517,f13773]) ).
tff(f13773,plain,
( spl249_1037
<=> ! [X2: 'A_b_fun$',X1: 'A_option$',X3: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X3),X1) = 'fun_app$av'('map_option$e'(X2),X1) )
| 'member$d'(sK205(X1,X2,X3),'set_option$b'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1037])]) ).
tff(f3517,plain,
! [X2: 'A_b_fun$',X3: 'A_b_fun$',X1: 'A_option$'] :
( ( 'fun_app$av'('map_option$e'(X3),X1) = 'fun_app$av'('map_option$e'(X2),X1) )
| 'member$d'(sK205(X1,X2,X3),'set_option$b'(X1)) ),
inference(equality_resolution,[],[f3057]) ).
tff(f3057,plain,
! [X2: 'A_b_fun$',X3: 'A_b_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$av'('map_option$e'(X2),X0) = 'fun_app$av'('map_option$e'(X3),X1) )
| 'member$d'(sK205(X1,X2,X3),'set_option$b'(X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1806]) ).
tff(f13771,plain,
spl249_1036,
inference(avatar_split_clause,[],[f3489,f13769]) ).
tff(f13769,plain,
( spl249_1036
<=> ! [X2: 'B$',X1: 'A_b_option_fun$',X3: 'A$'] :
( ( 'fun_app$g'('some$',X2) = 'bind$e'('fun_app$q'('some$b',X3),X1) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$f'(X1,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1036])]) ).
tff(f3489,plain,
! [X2: 'B$',X3: 'A$',X1: 'A_b_option_fun$'] :
( ( 'fun_app$g'('some$',X2) = 'bind$e'('fun_app$q'('some$b',X3),X1) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$f'(X1,X3) ) ),
inference(equality_resolution,[],[f2989]) ).
tff(f2989,plain,
! [X2: 'B$',X3: 'A$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( ( 'fun_app$g'('some$',X2) = 'bind$e'(X0,X1) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$f'(X1,X3) )
| ( 'fun_app$q'('some$b',X3) != X0 ) ),
inference(cnf_transformation,[],[f1750]) ).
tff(f13767,plain,
( spl249_1035
| ~ spl249_251
| ~ spl249_687 ),
inference(avatar_split_clause,[],[f8753,f8204,f4732,f13765]) ).
tff(f13765,plain,
( spl249_1035
<=> ! [X2: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ~ sP37(X0,X1,'bot$h',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1035])]) ).
tff(f8204,plain,
( spl249_687
<=> ! [X0: 'C_option_bool_fun$',X3: 'C_option$',X2: 'C_c_option_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
| ~ sP37(X3,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_687])]) ).
tff(f8753,plain,
( ! [X2: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ~ sP37(X0,X1,'bot$h',X2)
| ~ spl249_251
| ~ spl249_687 ),
inference(resolution,[],[f8205,f4733]) ).
tff(f8205,plain,
( ! [X2: 'C_c_option_fun$',X3: 'C_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
| ~ sP37(X3,X2,X0,X1) )
| ~ spl249_687 ),
inference(avatar_component_clause,[],[f8204]) ).
tff(f13763,plain,
spl249_1034,
inference(avatar_split_clause,[],[f3487,f13761]) ).
tff(f13761,plain,
( spl249_1034
<=> ! [X2: 'C$',X1: 'A_c_option_fun$',X3: 'A$'] :
( ( 'fun_app$j'('some$a',X2) = 'bind$d'('fun_app$q'('some$b',X3),X1) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$bm'(X1,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1034])]) ).
tff(f3487,plain,
! [X2: 'C$',X3: 'A$',X1: 'A_c_option_fun$'] :
( ( 'fun_app$j'('some$a',X2) = 'bind$d'('fun_app$q'('some$b',X3),X1) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$bm'(X1,X3) ) ),
inference(equality_resolution,[],[f2983]) ).
tff(f2983,plain,
! [X2: 'C$',X3: 'A$',X0: 'A_option$',X1: 'A_c_option_fun$'] :
( ( 'fun_app$j'('some$a',X2) = 'bind$d'(X0,X1) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$bm'(X1,X3) )
| ( 'fun_app$q'('some$b',X3) != X0 ) ),
inference(cnf_transformation,[],[f1742]) ).
tff(f13759,plain,
spl249_1033,
inference(avatar_split_clause,[],[f3486,f13757]) ).
tff(f13757,plain,
( spl249_1033
<=> ! [X2: 'A$',X1: 'B_a_option_fun$',X3: 'B$'] :
( ( 'fun_app$q'('some$b',X2) = 'bind$g'('fun_app$g'('some$',X3),X1) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bo'(X1,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1033])]) ).
tff(f3486,plain,
! [X2: 'A$',X3: 'B$',X1: 'B_a_option_fun$'] :
( ( 'fun_app$q'('some$b',X2) = 'bind$g'('fun_app$g'('some$',X3),X1) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bo'(X1,X3) ) ),
inference(equality_resolution,[],[f2980]) ).
tff(f2980,plain,
! [X2: 'A$',X3: 'B$',X0: 'B_option$',X1: 'B_a_option_fun$'] :
( ( 'fun_app$q'('some$b',X2) = 'bind$g'(X0,X1) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bo'(X1,X3) )
| ( 'fun_app$g'('some$',X3) != X0 ) ),
inference(cnf_transformation,[],[f1738]) ).
tff(f13755,plain,
spl249_1032,
inference(avatar_split_clause,[],[f3485,f13753]) ).
tff(f13753,plain,
( spl249_1032
<=> ! [X2: 'A$',X1: 'C_a_option_fun$',X3: 'C$'] :
( ( 'fun_app$q'('some$b',X2) = 'bind$f'('fun_app$j'('some$a',X3),X1) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bn'(X1,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1032])]) ).
tff(f3485,plain,
! [X2: 'A$',X3: 'C$',X1: 'C_a_option_fun$'] :
( ( 'fun_app$q'('some$b',X2) = 'bind$f'('fun_app$j'('some$a',X3),X1) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bn'(X1,X3) ) ),
inference(equality_resolution,[],[f2977]) ).
tff(f2977,plain,
! [X2: 'A$',X3: 'C$',X0: 'C_option$',X1: 'C_a_option_fun$'] :
( ( 'fun_app$q'('some$b',X2) = 'bind$f'(X0,X1) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bn'(X1,X3) )
| ( 'fun_app$j'('some$a',X3) != X0 ) ),
inference(cnf_transformation,[],[f1734]) ).
tff(f13751,plain,
spl249_1031,
inference(avatar_split_clause,[],[f3268,f13749]) ).
tff(f13749,plain,
( spl249_1031
<=> ! [X2: 'B_option$',X0: 'C_option$',X1: 'B_c_option_fun$'] :
( ( 'fun_app$an'('case_option$c'(X0,X1),X2) = 'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X2)),X1) )
| ( 'none$a' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1031])]) ).
tff(f3268,plain,
! [X2: 'B_option$',X0: 'C_option$',X1: 'B_c_option_fun$'] :
( ( 'fun_app$an'('case_option$c'(X0,X1),X2) = 'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X2)),X1) )
| ( 'none$a' = X2 ) ),
inference(definition_unfolding,[],[f2677,f2234]) ).
tff(f2677,plain,
! [X2: 'B_option$',X0: 'C_option$',X1: 'B_c_option_fun$'] :
( ( 'fun_app$an'('case_option$c'(X0,X1),X2) = 'fun_app$n'(X1,'fun_app$al'('the$',X2)) )
| ( 'none$a' = X2 ) ),
inference(cnf_transformation,[],[f953]) ).
tff(f953,plain,
! [X0: 'C_option$',X1: 'B_c_option_fun$',X2: 'B_option$'] :
( ( ( 'fun_app$an'('case_option$c'(X0,X1),X2) = 'fun_app$n'(X1,'fun_app$al'('the$',X2)) )
| ( 'none$a' = X2 ) )
& ( ( 'fun_app$an'('case_option$c'(X0,X1),X2) = X0 )
| ( 'none$a' != X2 ) ) ),
inference(ennf_transformation,[],[f309]) ).
tff(f309,axiom,
! [X0: 'C_option$',X1: 'B_c_option_fun$',X2: 'B_option$'] :
( ( ( 'none$a' != X2 )
=> ( 'fun_app$an'('case_option$c'(X0,X1),X2) = 'fun_app$n'(X1,'fun_app$al'('the$',X2)) ) )
& ( ( 'none$a' = X2 )
=> ( 'fun_app$an'('case_option$c'(X0,X1),X2) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom307) ).
tff(f13747,plain,
spl249_1030,
inference(avatar_split_clause,[],[f3210,f13745]) ).
tff(f13745,plain,
( spl249_1030
<=> ! [X0: 'B_option_bool_fun$',X3: 'B_option$',X2: 'B_b_option_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
| ~ 'fun_app$a'('case_option$e'(def_14(X0,X1),'uup$'(X0,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1030])]) ).
tff(f3210,plain,
! [X2: 'B_b_option_fun$',X3: 'B_option$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
| ~ 'fun_app$a'('case_option$e'(def_14(X0,X1),'uup$'(X0,X2)),X3) ),
inference(cnf_transformation,[],[f1905]) ).
tff(f1905,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_option$'] :
( ( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
| ~ 'fun_app$a'('case_option$e'(def_14(X0,X1),'uup$'(X0,X2)),X3) )
& ( 'fun_app$a'('case_option$e'(def_14(X0,X1),'uup$'(X0,X2)),X3)
| ~ 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3)) ) ),
inference(nnf_transformation,[],[f151]) ).
tff(f151,axiom,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
<=> 'fun_app$a'('case_option$e'(def_14(X0,X1),'uup$'(X0,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom149) ).
tff(f13743,plain,
spl249_1029,
inference(avatar_split_clause,[],[f3209,f13741]) ).
tff(f13741,plain,
( spl249_1029
<=> ! [X0: 'B_option_bool_fun$',X3: 'B_option$',X2: 'B_b_option_fun$',X1: 'B_option$'] :
( 'fun_app$a'('case_option$e'(def_14(X0,X1),'uup$'(X0,X2)),X3)
| ~ 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1029])]) ).
tff(f3209,plain,
! [X2: 'B_b_option_fun$',X3: 'B_option$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'('case_option$e'(def_14(X0,X1),'uup$'(X0,X2)),X3)
| ~ 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3)) ),
inference(cnf_transformation,[],[f1905]) ).
tff(f13739,plain,
spl249_1028,
inference(avatar_split_clause,[],[f3176,f13737]) ).
tff(f13737,plain,
( spl249_1028
<=> ! [X0: 'C_option_bool_fun$',X3: 'B_option$',X2: 'B_c_option_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
| ~ 'fun_app$a'('case_option$e'(def_10(X0,X1),'uul$'(X0,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1028])]) ).
tff(f3176,plain,
! [X2: 'B_c_option_fun$',X3: 'B_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
| ~ 'fun_app$a'('case_option$e'(def_10(X0,X1),'uul$'(X0,X2)),X3) ),
inference(cnf_transformation,[],[f1888]) ).
tff(f1888,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'B_c_option_fun$',X3: 'B_option$'] :
( ( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
| ~ 'fun_app$a'('case_option$e'(def_10(X0,X1),'uul$'(X0,X2)),X3) )
& ( 'fun_app$a'('case_option$e'(def_10(X0,X1),'uul$'(X0,X2)),X3)
| ~ 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3)) ) ),
inference(nnf_transformation,[],[f147]) ).
tff(f147,axiom,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'B_c_option_fun$',X3: 'B_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
<=> 'fun_app$a'('case_option$e'(def_10(X0,X1),'uul$'(X0,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom145) ).
tff(f13735,plain,
spl249_1027,
inference(avatar_split_clause,[],[f3175,f13733]) ).
tff(f13733,plain,
( spl249_1027
<=> ! [X0: 'C_option_bool_fun$',X3: 'B_option$',X2: 'B_c_option_fun$',X1: 'C_option$'] :
( 'fun_app$a'('case_option$e'(def_10(X0,X1),'uul$'(X0,X2)),X3)
| ~ 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1027])]) ).
tff(f3175,plain,
! [X2: 'B_c_option_fun$',X3: 'B_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$a'('case_option$e'(def_10(X0,X1),'uul$'(X0,X2)),X3)
| ~ 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3)) ),
inference(cnf_transformation,[],[f1888]) ).
tff(f13731,plain,
spl249_1026,
inference(avatar_split_clause,[],[f3158,f13729]) ).
tff(f13729,plain,
( spl249_1026
<=> ! [X0: 'C_option_bool_fun$',X3: 'C_option$',X2: 'C_c_option_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
| ~ 'fun_app$'('case_option$f'(def_15(X0,X1),'uuq$'(X0,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1026])]) ).
tff(f3158,plain,
! [X2: 'C_c_option_fun$',X3: 'C_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
| ~ 'fun_app$'('case_option$f'(def_15(X0,X1),'uuq$'(X0,X2)),X3) ),
inference(cnf_transformation,[],[f1879]) ).
tff(f1879,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_option$'] :
( ( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
| ~ 'fun_app$'('case_option$f'(def_15(X0,X1),'uuq$'(X0,X2)),X3) )
& ( 'fun_app$'('case_option$f'(def_15(X0,X1),'uuq$'(X0,X2)),X3)
| ~ 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3)) ) ),
inference(nnf_transformation,[],[f152]) ).
tff(f152,axiom,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
<=> 'fun_app$'('case_option$f'(def_15(X0,X1),'uuq$'(X0,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom150) ).
tff(f13727,plain,
spl249_1025,
inference(avatar_split_clause,[],[f3157,f13725]) ).
tff(f13725,plain,
( spl249_1025
<=> ! [X0: 'C_option_bool_fun$',X3: 'C_option$',X2: 'C_c_option_fun$',X1: 'C_option$'] :
( 'fun_app$'('case_option$f'(def_15(X0,X1),'uuq$'(X0,X2)),X3)
| ~ 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1025])]) ).
tff(f3157,plain,
! [X2: 'C_c_option_fun$',X3: 'C_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'('case_option$f'(def_15(X0,X1),'uuq$'(X0,X2)),X3)
| ~ 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3)) ),
inference(cnf_transformation,[],[f1879]) ).
tff(f13723,plain,
( spl249_1024
| ~ spl249_251
| ~ spl249_685 ),
inference(avatar_split_clause,[],[f8717,f8194,f4732,f13721]) ).
tff(f13721,plain,
( spl249_1024
<=> ! [X2: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ~ sP36(X0,X1,'bot$h',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1024])]) ).
tff(f8194,plain,
( spl249_685
<=> ! [X0: 'C_option_bool_fun$',X3: 'C_option$',X2: 'C_c_option_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
| ~ sP36(X3,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_685])]) ).
tff(f8717,plain,
( ! [X2: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ~ sP36(X0,X1,'bot$h',X2)
| ~ spl249_251
| ~ spl249_685 ),
inference(resolution,[],[f8195,f4733]) ).
tff(f8195,plain,
( ! [X2: 'C_c_option_fun$',X3: 'C_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
| ~ sP36(X3,X2,X0,X1) )
| ~ spl249_685 ),
inference(avatar_component_clause,[],[f8194]) ).
tff(f13719,plain,
spl249_1023,
inference(avatar_split_clause,[],[f3056,f13717]) ).
tff(f13717,plain,
( spl249_1023
<=> ! [X0: 'B_option_b_fun$',X3: 'B$',X2: 'B_b_fun$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$h'(X2,X3) = 'fun_app$al'(X0,'fun_app$g'(X1,X3)) )
| ( 'comp$m'(X0,X1) != 'comp$ai'('id$b',X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1023])]) ).
tff(f3056,plain,
! [X2: 'B_b_fun$',X3: 'B$',X0: 'B_option_b_fun$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$h'(X2,X3) = 'fun_app$al'(X0,'fun_app$g'(X1,X3)) )
| ( 'comp$m'(X0,X1) != 'comp$ai'('id$b',X2) ) ),
inference(cnf_transformation,[],[f1026]) ).
tff(f1026,plain,
! [X0: 'B_option_b_fun$',X1: 'B_b_option_fun$',X2: 'B_b_fun$',X3: 'B$'] :
( ( 'fun_app$h'(X2,X3) = 'fun_app$al'(X0,'fun_app$g'(X1,X3)) )
| ( 'comp$m'(X0,X1) != 'comp$ai'('id$b',X2) ) ),
inference(ennf_transformation,[],[f659]) ).
tff(f659,axiom,
! [X0: 'B_option_b_fun$',X1: 'B_b_option_fun$',X2: 'B_b_fun$',X3: 'B$'] :
( ( 'comp$m'(X0,X1) = 'comp$ai'('id$b',X2) )
=> ( 'fun_app$h'(X2,X3) = 'fun_app$al'(X0,'fun_app$g'(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom657) ).
tff(f13715,plain,
spl249_1022,
inference(avatar_split_clause,[],[f3054,f13713]) ).
tff(f13713,plain,
( spl249_1022
<=> ! [X0: 'A_b_option_fun$',X3: 'A$',X2: 'A_b_option_fun$',X1: 'A_a_fun$'] :
( ( 'fun_app$f'(X2,X3) = 'fun_app$f'(X0,'fun_app$r'(X1,X3)) )
| ( 'comp$g'(X0,X1) != 'comp$bf'('id$d',X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1022])]) ).
tff(f3054,plain,
! [X2: 'A_b_option_fun$',X3: 'A$',X0: 'A_b_option_fun$',X1: 'A_a_fun$'] :
( ( 'fun_app$f'(X2,X3) = 'fun_app$f'(X0,'fun_app$r'(X1,X3)) )
| ( 'comp$g'(X0,X1) != 'comp$bf'('id$d',X2) ) ),
inference(cnf_transformation,[],[f1024]) ).
tff(f1024,plain,
! [X0: 'A_b_option_fun$',X1: 'A_a_fun$',X2: 'A_b_option_fun$',X3: 'A$'] :
( ( 'fun_app$f'(X2,X3) = 'fun_app$f'(X0,'fun_app$r'(X1,X3)) )
| ( 'comp$g'(X0,X1) != 'comp$bf'('id$d',X2) ) ),
inference(ennf_transformation,[],[f657]) ).
tff(f657,axiom,
! [X0: 'A_b_option_fun$',X1: 'A_a_fun$',X2: 'A_b_option_fun$',X3: 'A$'] :
( ( 'comp$g'(X0,X1) = 'comp$bf'('id$d',X2) )
=> ( 'fun_app$f'(X2,X3) = 'fun_app$f'(X0,'fun_app$r'(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom655) ).
tff(f13711,plain,
spl249_1021,
inference(avatar_split_clause,[],[f3053,f13709]) ).
tff(f13709,plain,
( spl249_1021
<=> ! [X0: 'C_option_c_fun$',X3: 'C$',X2: 'C_c_fun$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$ak'(X0,'fun_app$j'(X1,X3)) = 'fun_app$k'(X2,X3) )
| ( 'comp$n'(X0,X1) != 'comp$bc'('id$a',X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1021])]) ).
tff(f3053,plain,
! [X2: 'C_c_fun$',X3: 'C$',X0: 'C_option_c_fun$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$ak'(X0,'fun_app$j'(X1,X3)) = 'fun_app$k'(X2,X3) )
| ( 'comp$n'(X0,X1) != 'comp$bc'('id$a',X2) ) ),
inference(cnf_transformation,[],[f1023]) ).
tff(f1023,plain,
! [X0: 'C_option_c_fun$',X1: 'C_c_option_fun$',X2: 'C_c_fun$',X3: 'C$'] :
( ( 'fun_app$ak'(X0,'fun_app$j'(X1,X3)) = 'fun_app$k'(X2,X3) )
| ( 'comp$n'(X0,X1) != 'comp$bc'('id$a',X2) ) ),
inference(ennf_transformation,[],[f660]) ).
tff(f660,axiom,
! [X0: 'C_option_c_fun$',X1: 'C_c_option_fun$',X2: 'C_c_fun$',X3: 'C$'] :
( ( 'comp$n'(X0,X1) = 'comp$bc'('id$a',X2) )
=> ( 'fun_app$ak'(X0,'fun_app$j'(X1,X3)) = 'fun_app$k'(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom658) ).
tff(f13707,plain,
spl249_1020,
inference(avatar_split_clause,[],[f3044,f13705]) ).
tff(f13705,plain,
( spl249_1020
<=> ! [X0: 'C_option$',X3: 'B_option$',X2: 'B_b_fun$',X1: 'B_c_option_fun$'] : ( 'fun_app$an'('case_option$c'(X0,X1),'fun_app$s'('map_option$b'(X2),X3)) = 'fun_app$an'('case_option$c'(X0,'comp$f'(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1020])]) ).
tff(f3044,plain,
! [X2: 'B_b_fun$',X3: 'B_option$',X0: 'C_option$',X1: 'B_c_option_fun$'] : ( 'fun_app$an'('case_option$c'(X0,X1),'fun_app$s'('map_option$b'(X2),X3)) = 'fun_app$an'('case_option$c'(X0,'comp$f'(X1,X2)),X3) ),
inference(cnf_transformation,[],[f491]) ).
tff(f491,axiom,
! [X0: 'C_option$',X1: 'B_c_option_fun$',X2: 'B_b_fun$',X3: 'B_option$'] : ( 'fun_app$an'('case_option$c'(X0,X1),'fun_app$s'('map_option$b'(X2),X3)) = 'fun_app$an'('case_option$c'(X0,'comp$f'(X1,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom489) ).
tff(f13703,plain,
spl249_1019,
inference(avatar_split_clause,[],[f3043,f13701]) ).
tff(f13701,plain,
( spl249_1019
<=> ! [X0: 'B_option$',X3: 'A_option$',X2: 'A_a_fun$',X1: 'A_b_option_fun$'] : ( 'fun_app$av'('case_option$d'(X0,X1),'fun_app$be'('map_option$a'(X2),X3)) = 'fun_app$av'('case_option$d'(X0,'comp$g'(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1019])]) ).
tff(f3043,plain,
! [X2: 'A_a_fun$',X3: 'A_option$',X0: 'B_option$',X1: 'A_b_option_fun$'] : ( 'fun_app$av'('case_option$d'(X0,X1),'fun_app$be'('map_option$a'(X2),X3)) = 'fun_app$av'('case_option$d'(X0,'comp$g'(X1,X2)),X3) ),
inference(cnf_transformation,[],[f492]) ).
tff(f492,axiom,
! [X0: 'B_option$',X1: 'A_b_option_fun$',X2: 'A_a_fun$',X3: 'A_option$'] : ( 'fun_app$av'('case_option$d'(X0,X1),'fun_app$be'('map_option$a'(X2),X3)) = 'fun_app$av'('case_option$d'(X0,'comp$g'(X1,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom490) ).
tff(f13699,plain,
spl249_1018,
inference(avatar_split_clause,[],[f3041,f13697]) ).
tff(f13697,plain,
( spl249_1018
<=> ! [X0: 'A_b_option_fun$',X3: 'A$',X2: 'A$',X1: 'A_a_fun$'] : ( 'comp$g'(X0,'fun_app$aj'('fun_upd$'(X1,X2),X3)) = 'fun_upd$a'('comp$g'(X0,X1),X2,'fun_app$f'(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1018])]) ).
tff(f3041,plain,
! [X2: 'A$',X3: 'A$',X0: 'A_b_option_fun$',X1: 'A_a_fun$'] : ( 'comp$g'(X0,'fun_app$aj'('fun_upd$'(X1,X2),X3)) = 'fun_upd$a'('comp$g'(X0,X1),X2,'fun_app$f'(X0,X3)) ),
inference(cnf_transformation,[],[f666]) ).
tff(f666,axiom,
! [X0: 'A_b_option_fun$',X1: 'A_a_fun$',X2: 'A$',X3: 'A$'] : ( 'comp$g'(X0,'fun_app$aj'('fun_upd$'(X1,X2),X3)) = 'fun_upd$a'('comp$g'(X0,X1),X2,'fun_app$f'(X0,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom664) ).
tff(f13695,plain,
spl249_1017,
inference(avatar_split_clause,[],[f3040,f13693]) ).
tff(f13693,plain,
( spl249_1017
<=> ! [X0: 'B_option_b_fun$',X3: 'B_option$',X2: 'B$',X1: 'B_b_option_fun$'] : ( 'comp$m'(X0,'fun_upd$d'(X1,X2,X3)) = 'fun_app$ai'('fun_upd$b'('comp$m'(X0,X1),X2),'fun_app$al'(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1017])]) ).
tff(f3040,plain,
! [X2: 'B$',X3: 'B_option$',X0: 'B_option_b_fun$',X1: 'B_b_option_fun$'] : ( 'comp$m'(X0,'fun_upd$d'(X1,X2,X3)) = 'fun_app$ai'('fun_upd$b'('comp$m'(X0,X1),X2),'fun_app$al'(X0,X3)) ),
inference(cnf_transformation,[],[f668]) ).
tff(f668,axiom,
! [X0: 'B_option_b_fun$',X1: 'B_b_option_fun$',X2: 'B$',X3: 'B_option$'] : ( 'comp$m'(X0,'fun_upd$d'(X1,X2,X3)) = 'fun_app$ai'('fun_upd$b'('comp$m'(X0,X1),X2),'fun_app$al'(X0,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom666) ).
tff(f13691,plain,
spl249_1016,
inference(avatar_split_clause,[],[f3039,f13689]) ).
tff(f13689,plain,
( spl249_1016
<=> ! [X0: 'C_option_c_fun$',X3: 'C_option$',X2: 'C$',X1: 'C_c_option_fun$'] : ( 'comp$n'(X0,'fun_upd$e'(X1,X2,X3)) = 'fun_app$ah'('fun_upd$f'('comp$n'(X0,X1),X2),'fun_app$ak'(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1016])]) ).
tff(f3039,plain,
! [X2: 'C$',X3: 'C_option$',X0: 'C_option_c_fun$',X1: 'C_c_option_fun$'] : ( 'comp$n'(X0,'fun_upd$e'(X1,X2,X3)) = 'fun_app$ah'('fun_upd$f'('comp$n'(X0,X1),X2),'fun_app$ak'(X0,X3)) ),
inference(cnf_transformation,[],[f669]) ).
tff(f669,axiom,
! [X0: 'C_option_c_fun$',X1: 'C_c_option_fun$',X2: 'C$',X3: 'C_option$'] : ( 'comp$n'(X0,'fun_upd$e'(X1,X2,X3)) = 'fun_app$ah'('fun_upd$f'('comp$n'(X0,X1),X2),'fun_app$ak'(X0,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom667) ).
tff(f13687,plain,
spl249_1015,
inference(avatar_split_clause,[],[f3038,f13685]) ).
tff(f13685,plain,
( spl249_1015
<=> ! [X0: 'Bool_c_option_fun$',X3: 'B_option$',X2: 'B_bool_fun$',X1: tlbool] : ( 'fun_app$ae'(X0,def_11(X1,X2,X3)) = 'fun_app$an'('case_option$c'('fun_app$ae'(X0,X1),'uum$'(X0,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1015])]) ).
tff(f3038,plain,
! [X2: 'B_bool_fun$',X3: 'B_option$',X0: 'Bool_c_option_fun$',X1: tlbool] : ( 'fun_app$ae'(X0,def_11(X1,X2,X3)) = 'fun_app$an'('case_option$c'('fun_app$ae'(X0,X1),'uum$'(X0,X2)),X3) ),
inference(cnf_transformation,[],[f148]) ).
tff(f148,axiom,
! [X0: 'Bool_c_option_fun$',X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] : ( 'fun_app$ae'(X0,def_11(X1,X2,X3)) = 'fun_app$an'('case_option$c'('fun_app$ae'(X0,X1),'uum$'(X0,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom146) ).
tff(f13683,plain,
spl249_1014,
inference(avatar_split_clause,[],[f3037,f13681]) ).
tff(f13681,plain,
( spl249_1014
<=> ! [X0: 'Bool_c_option_fun$',X3: 'C_option$',X2: 'C_bool_fun$',X1: tlbool] : ( 'fun_app$ae'(X0,def_13(X1,X2,X3)) = 'fun_app$u'('case_option$a'('fun_app$ae'(X0,X1),'uuo$'(X0,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1014])]) ).
tff(f3037,plain,
! [X2: 'C_bool_fun$',X3: 'C_option$',X0: 'Bool_c_option_fun$',X1: tlbool] : ( 'fun_app$ae'(X0,def_13(X1,X2,X3)) = 'fun_app$u'('case_option$a'('fun_app$ae'(X0,X1),'uuo$'(X0,X2)),X3) ),
inference(cnf_transformation,[],[f150]) ).
tff(f150,axiom,
! [X0: 'Bool_c_option_fun$',X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] : ( 'fun_app$ae'(X0,def_13(X1,X2,X3)) = 'fun_app$u'('case_option$a'('fun_app$ae'(X0,X1),'uuo$'(X0,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom148) ).
tff(f13679,plain,
spl249_1013,
inference(avatar_split_clause,[],[f3036,f13677]) ).
tff(f13677,plain,
( spl249_1013
<=> ! [X0: 'Bool_b_option_fun$',X3: 'B_option$',X2: 'B_bool_fun$',X1: tlbool] : ( 'fun_app$af'(X0,def_12(X1,X2,X3)) = 'fun_app$s'('case_option$'('fun_app$af'(X0,X1),'uun$'(X0,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1013])]) ).
tff(f3036,plain,
! [X2: 'B_bool_fun$',X3: 'B_option$',X0: 'Bool_b_option_fun$',X1: tlbool] : ( 'fun_app$af'(X0,def_12(X1,X2,X3)) = 'fun_app$s'('case_option$'('fun_app$af'(X0,X1),'uun$'(X0,X2)),X3) ),
inference(cnf_transformation,[],[f149]) ).
tff(f149,axiom,
! [X0: 'Bool_b_option_fun$',X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] : ( 'fun_app$af'(X0,def_12(X1,X2,X3)) = 'fun_app$s'('case_option$'('fun_app$af'(X0,X1),'uun$'(X0,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom147) ).
tff(f13675,plain,
spl249_1012,
inference(avatar_split_clause,[],[f3031,f13673]) ).
tff(f13673,plain,
( spl249_1012
<=> ! [X2: 'B$',X0: 'B_b_fun$',X1: 'B_option$'] :
( ( 'fun_app$h'(X0,sK204(X0,X1,X2)) = X2 )
| ( 'fun_app$g'('some$',X2) != 'fun_app$s'('map_option$b'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1012])]) ).
tff(f3031,plain,
! [X2: 'B$',X0: 'B_b_fun$',X1: 'B_option$'] :
( ( 'fun_app$h'(X0,sK204(X0,X1,X2)) = X2 )
| ( 'fun_app$g'('some$',X2) != 'fun_app$s'('map_option$b'(X0),X1) ) ),
inference(cnf_transformation,[],[f1804]) ).
tff(f1804,plain,
! [X0: 'B_b_fun$',X1: 'B_option$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'fun_app$s'('map_option$b'(X0),X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$h'(X0,X3) != X2 )
| ( 'fun_app$g'('some$',X3) != X1 ) ) )
& ( ( ( 'fun_app$h'(X0,sK204(X0,X1,X2)) = X2 )
& ( 'fun_app$g'('some$',sK204(X0,X1,X2)) = X1 ) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$s'('map_option$b'(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK204])],[f1802,f1803]) ).
tff(f1803,plain,
! [X0: 'B_b_fun$',X1: 'B_option$',X2: 'B$'] :
( ? [X4: 'B$'] :
( ( 'fun_app$h'(X0,X4) = X2 )
& ( 'fun_app$g'('some$',X4) = X1 ) )
=> ( ( 'fun_app$h'(X0,sK204(X0,X1,X2)) = X2 )
& ( 'fun_app$g'('some$',sK204(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1802,plain,
! [X0: 'B_b_fun$',X1: 'B_option$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'fun_app$s'('map_option$b'(X0),X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$h'(X0,X3) != X2 )
| ( 'fun_app$g'('some$',X3) != X1 ) ) )
& ( ? [X4: 'B$'] :
( ( 'fun_app$h'(X0,X4) = X2 )
& ( 'fun_app$g'('some$',X4) = X1 ) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$s'('map_option$b'(X0),X1) ) ) ),
inference(rectify,[],[f1801]) ).
tff(f1801,plain,
! [X0: 'B_b_fun$',X1: 'B_option$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'fun_app$s'('map_option$b'(X0),X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$h'(X0,X3) != X2 )
| ( 'fun_app$g'('some$',X3) != X1 ) ) )
& ( ? [X3: 'B$'] :
( ( 'fun_app$h'(X0,X3) = X2 )
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$s'('map_option$b'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f236]) ).
tff(f236,axiom,
! [X0: 'B_b_fun$',X1: 'B_option$',X2: 'B$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$s'('map_option$b'(X0),X1) )
<=> ? [X3: 'B$'] :
( ( 'fun_app$h'(X0,X3) = X2 )
& ( 'fun_app$g'('some$',X3) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom234) ).
tff(f13671,plain,
spl249_1011,
inference(avatar_split_clause,[],[f3030,f13669]) ).
tff(f13669,plain,
( spl249_1011
<=> ! [X2: 'B$',X0: 'B_b_fun$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',sK204(X0,X1,X2)) = X1 )
| ( 'fun_app$g'('some$',X2) != 'fun_app$s'('map_option$b'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1011])]) ).
tff(f3030,plain,
! [X2: 'B$',X0: 'B_b_fun$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',sK204(X0,X1,X2)) = X1 )
| ( 'fun_app$g'('some$',X2) != 'fun_app$s'('map_option$b'(X0),X1) ) ),
inference(cnf_transformation,[],[f1804]) ).
tff(f13667,plain,
spl249_1010,
inference(avatar_split_clause,[],[f3028,f13665]) ).
tff(f13665,plain,
( spl249_1010
<=> ! [X2: 'B$',X0: 'A_b_fun$',X1: 'A_option$'] :
( ( 'fun_app$p'(X0,sK203(X0,X1,X2)) = X2 )
| ( 'fun_app$g'('some$',X2) != 'fun_app$av'('map_option$e'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1010])]) ).
tff(f3028,plain,
! [X2: 'B$',X0: 'A_b_fun$',X1: 'A_option$'] :
( ( 'fun_app$p'(X0,sK203(X0,X1,X2)) = X2 )
| ( 'fun_app$g'('some$',X2) != 'fun_app$av'('map_option$e'(X0),X1) ) ),
inference(cnf_transformation,[],[f1800]) ).
tff(f1800,plain,
! [X0: 'A_b_fun$',X1: 'A_option$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'fun_app$av'('map_option$e'(X0),X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$p'(X0,X3) != X2 )
| ( 'fun_app$q'('some$b',X3) != X1 ) ) )
& ( ( ( 'fun_app$p'(X0,sK203(X0,X1,X2)) = X2 )
& ( 'fun_app$q'('some$b',sK203(X0,X1,X2)) = X1 ) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$av'('map_option$e'(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK203])],[f1798,f1799]) ).
tff(f1799,plain,
! [X0: 'A_b_fun$',X1: 'A_option$',X2: 'B$'] :
( ? [X4: 'A$'] :
( ( 'fun_app$p'(X0,X4) = X2 )
& ( 'fun_app$q'('some$b',X4) = X1 ) )
=> ( ( 'fun_app$p'(X0,sK203(X0,X1,X2)) = X2 )
& ( 'fun_app$q'('some$b',sK203(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1798,plain,
! [X0: 'A_b_fun$',X1: 'A_option$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'fun_app$av'('map_option$e'(X0),X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$p'(X0,X3) != X2 )
| ( 'fun_app$q'('some$b',X3) != X1 ) ) )
& ( ? [X4: 'A$'] :
( ( 'fun_app$p'(X0,X4) = X2 )
& ( 'fun_app$q'('some$b',X4) = X1 ) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$av'('map_option$e'(X0),X1) ) ) ),
inference(rectify,[],[f1797]) ).
tff(f1797,plain,
! [X0: 'A_b_fun$',X1: 'A_option$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'fun_app$av'('map_option$e'(X0),X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$p'(X0,X3) != X2 )
| ( 'fun_app$q'('some$b',X3) != X1 ) ) )
& ( ? [X3: 'A$'] :
( ( 'fun_app$p'(X0,X3) = X2 )
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$av'('map_option$e'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f231]) ).
tff(f231,axiom,
! [X0: 'A_b_fun$',X1: 'A_option$',X2: 'B$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$av'('map_option$e'(X0),X1) )
<=> ? [X3: 'A$'] :
( ( 'fun_app$p'(X0,X3) = X2 )
& ( 'fun_app$q'('some$b',X3) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom229) ).
tff(f13663,plain,
spl249_1009,
inference(avatar_split_clause,[],[f3027,f13661]) ).
tff(f13661,plain,
( spl249_1009
<=> ! [X2: 'B$',X0: 'A_b_fun$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK203(X0,X1,X2)) = X1 )
| ( 'fun_app$g'('some$',X2) != 'fun_app$av'('map_option$e'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1009])]) ).
tff(f3027,plain,
! [X2: 'B$',X0: 'A_b_fun$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK203(X0,X1,X2)) = X1 )
| ( 'fun_app$g'('some$',X2) != 'fun_app$av'('map_option$e'(X0),X1) ) ),
inference(cnf_transformation,[],[f1800]) ).
tff(f13659,plain,
spl249_1008,
inference(avatar_split_clause,[],[f3025,f13657]) ).
tff(f13657,plain,
( spl249_1008
<=> ! [X2: 'B$',X0: 'C_b_fun$',X1: 'C_option$'] :
( ( 'fun_app$m'(X0,sK202(X0,X1,X2)) = X2 )
| ( 'fun_app$g'('some$',X2) != 'fun_app$bg'('map_option$'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1008])]) ).
tff(f3025,plain,
! [X2: 'B$',X0: 'C_b_fun$',X1: 'C_option$'] :
( ( 'fun_app$m'(X0,sK202(X0,X1,X2)) = X2 )
| ( 'fun_app$g'('some$',X2) != 'fun_app$bg'('map_option$'(X0),X1) ) ),
inference(cnf_transformation,[],[f1796]) ).
tff(f1796,plain,
! [X0: 'C_b_fun$',X1: 'C_option$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'fun_app$bg'('map_option$'(X0),X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$m'(X0,X3) != X2 )
| ( 'fun_app$j'('some$a',X3) != X1 ) ) )
& ( ( ( 'fun_app$m'(X0,sK202(X0,X1,X2)) = X2 )
& ( 'fun_app$j'('some$a',sK202(X0,X1,X2)) = X1 ) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$bg'('map_option$'(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK202])],[f1794,f1795]) ).
tff(f1795,plain,
! [X0: 'C_b_fun$',X1: 'C_option$',X2: 'B$'] :
( ? [X4: 'C$'] :
( ( 'fun_app$m'(X0,X4) = X2 )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
=> ( ( 'fun_app$m'(X0,sK202(X0,X1,X2)) = X2 )
& ( 'fun_app$j'('some$a',sK202(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1794,plain,
! [X0: 'C_b_fun$',X1: 'C_option$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'fun_app$bg'('map_option$'(X0),X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$m'(X0,X3) != X2 )
| ( 'fun_app$j'('some$a',X3) != X1 ) ) )
& ( ? [X4: 'C$'] :
( ( 'fun_app$m'(X0,X4) = X2 )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$bg'('map_option$'(X0),X1) ) ) ),
inference(rectify,[],[f1793]) ).
tff(f1793,plain,
! [X0: 'C_b_fun$',X1: 'C_option$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = 'fun_app$bg'('map_option$'(X0),X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$m'(X0,X3) != X2 )
| ( 'fun_app$j'('some$a',X3) != X1 ) ) )
& ( ? [X3: 'C$'] :
( ( 'fun_app$m'(X0,X3) = X2 )
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( 'fun_app$g'('some$',X2) != 'fun_app$bg'('map_option$'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f235]) ).
tff(f235,axiom,
! [X0: 'C_b_fun$',X1: 'C_option$',X2: 'B$'] :
( ( 'fun_app$g'('some$',X2) = 'fun_app$bg'('map_option$'(X0),X1) )
<=> ? [X3: 'C$'] :
( ( 'fun_app$m'(X0,X3) = X2 )
& ( 'fun_app$j'('some$a',X3) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom233) ).
tff(f13655,plain,
spl249_1007,
inference(avatar_split_clause,[],[f3024,f13653]) ).
tff(f13653,plain,
( spl249_1007
<=> ! [X2: 'B$',X0: 'C_b_fun$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK202(X0,X1,X2)) = X1 )
| ( 'fun_app$g'('some$',X2) != 'fun_app$bg'('map_option$'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1007])]) ).
tff(f3024,plain,
! [X2: 'B$',X0: 'C_b_fun$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK202(X0,X1,X2)) = X1 )
| ( 'fun_app$g'('some$',X2) != 'fun_app$bg'('map_option$'(X0),X1) ) ),
inference(cnf_transformation,[],[f1796]) ).
tff(f13651,plain,
spl249_1006,
inference(avatar_split_clause,[],[f3021,f13649]) ).
tff(f13649,plain,
( spl249_1006
<=> ! [X2: 'B$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$g'('some$',sK201(X0,X1,X2)) = X0 )
| ( 'fun_app$g'('some$',X2) != 'fun_app$ac'('bind$c'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1006])]) ).
tff(f3021,plain,
! [X2: 'B$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$g'('some$',sK201(X0,X1,X2)) = X0 )
| ( 'fun_app$g'('some$',X2) != 'fun_app$ac'('bind$c'(X0),X1) ) ),
inference(cnf_transformation,[],[f1792]) ).
tff(f13647,plain,
spl249_1005,
inference(avatar_split_clause,[],[f3019,f13645]) ).
tff(f13645,plain,
( spl249_1005
<=> ! [X2: 'C$',X0: 'B_c_fun$',X1: 'B_option$'] :
( ( 'fun_app$o'(X0,sK200(X0,X1,X2)) = X2 )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$an'('map_option$d'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1005])]) ).
tff(f3019,plain,
! [X2: 'C$',X0: 'B_c_fun$',X1: 'B_option$'] :
( ( 'fun_app$o'(X0,sK200(X0,X1,X2)) = X2 )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$an'('map_option$d'(X0),X1) ) ),
inference(cnf_transformation,[],[f1788]) ).
tff(f1788,plain,
! [X0: 'B_c_fun$',X1: 'B_option$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$an'('map_option$d'(X0),X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$o'(X0,X3) != X2 )
| ( 'fun_app$g'('some$',X3) != X1 ) ) )
& ( ( ( 'fun_app$o'(X0,sK200(X0,X1,X2)) = X2 )
& ( 'fun_app$g'('some$',sK200(X0,X1,X2)) = X1 ) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$an'('map_option$d'(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK200])],[f1786,f1787]) ).
tff(f1787,plain,
! [X0: 'B_c_fun$',X1: 'B_option$',X2: 'C$'] :
( ? [X4: 'B$'] :
( ( 'fun_app$o'(X0,X4) = X2 )
& ( 'fun_app$g'('some$',X4) = X1 ) )
=> ( ( 'fun_app$o'(X0,sK200(X0,X1,X2)) = X2 )
& ( 'fun_app$g'('some$',sK200(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1786,plain,
! [X0: 'B_c_fun$',X1: 'B_option$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$an'('map_option$d'(X0),X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$o'(X0,X3) != X2 )
| ( 'fun_app$g'('some$',X3) != X1 ) ) )
& ( ? [X4: 'B$'] :
( ( 'fun_app$o'(X0,X4) = X2 )
& ( 'fun_app$g'('some$',X4) = X1 ) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$an'('map_option$d'(X0),X1) ) ) ),
inference(rectify,[],[f1785]) ).
tff(f1785,plain,
! [X0: 'B_c_fun$',X1: 'B_option$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$an'('map_option$d'(X0),X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$o'(X0,X3) != X2 )
| ( 'fun_app$g'('some$',X3) != X1 ) ) )
& ( ? [X3: 'B$'] :
( ( 'fun_app$o'(X0,X3) = X2 )
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$an'('map_option$d'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f234]) ).
tff(f234,axiom,
! [X0: 'B_c_fun$',X1: 'B_option$',X2: 'C$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$an'('map_option$d'(X0),X1) )
<=> ? [X3: 'B$'] :
( ( 'fun_app$o'(X0,X3) = X2 )
& ( 'fun_app$g'('some$',X3) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom232) ).
tff(f13643,plain,
spl249_1004,
inference(avatar_split_clause,[],[f3018,f13641]) ).
tff(f13641,plain,
( spl249_1004
<=> ! [X2: 'C$',X0: 'B_c_fun$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',sK200(X0,X1,X2)) = X1 )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$an'('map_option$d'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1004])]) ).
tff(f3018,plain,
! [X2: 'C$',X0: 'B_c_fun$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',sK200(X0,X1,X2)) = X1 )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$an'('map_option$d'(X0),X1) ) ),
inference(cnf_transformation,[],[f1788]) ).
tff(f13639,plain,
spl249_1003,
inference(avatar_split_clause,[],[f3016,f13637]) ).
tff(f13637,plain,
( spl249_1003
<=> ! [X2: 'C$',X0: 'C_c_fun$',X1: 'C_option$'] :
( ( 'fun_app$k'(X0,sK199(X0,X1,X2)) = X2 )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$u'('map_option$c'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1003])]) ).
tff(f3016,plain,
! [X2: 'C$',X0: 'C_c_fun$',X1: 'C_option$'] :
( ( 'fun_app$k'(X0,sK199(X0,X1,X2)) = X2 )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$u'('map_option$c'(X0),X1) ) ),
inference(cnf_transformation,[],[f1784]) ).
tff(f1784,plain,
! [X0: 'C_c_fun$',X1: 'C_option$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$u'('map_option$c'(X0),X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$k'(X0,X3) != X2 )
| ( 'fun_app$j'('some$a',X3) != X1 ) ) )
& ( ( ( 'fun_app$k'(X0,sK199(X0,X1,X2)) = X2 )
& ( 'fun_app$j'('some$a',sK199(X0,X1,X2)) = X1 ) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$u'('map_option$c'(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK199])],[f1782,f1783]) ).
tff(f1783,plain,
! [X0: 'C_c_fun$',X1: 'C_option$',X2: 'C$'] :
( ? [X4: 'C$'] :
( ( 'fun_app$k'(X0,X4) = X2 )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
=> ( ( 'fun_app$k'(X0,sK199(X0,X1,X2)) = X2 )
& ( 'fun_app$j'('some$a',sK199(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1782,plain,
! [X0: 'C_c_fun$',X1: 'C_option$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$u'('map_option$c'(X0),X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$k'(X0,X3) != X2 )
| ( 'fun_app$j'('some$a',X3) != X1 ) ) )
& ( ? [X4: 'C$'] :
( ( 'fun_app$k'(X0,X4) = X2 )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$u'('map_option$c'(X0),X1) ) ) ),
inference(rectify,[],[f1781]) ).
tff(f1781,plain,
! [X0: 'C_c_fun$',X1: 'C_option$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$u'('map_option$c'(X0),X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$k'(X0,X3) != X2 )
| ( 'fun_app$j'('some$a',X3) != X1 ) ) )
& ( ? [X3: 'C$'] :
( ( 'fun_app$k'(X0,X3) = X2 )
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$u'('map_option$c'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f233]) ).
tff(f233,axiom,
! [X0: 'C_c_fun$',X1: 'C_option$',X2: 'C$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$u'('map_option$c'(X0),X1) )
<=> ? [X3: 'C$'] :
( ( 'fun_app$k'(X0,X3) = X2 )
& ( 'fun_app$j'('some$a',X3) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom231) ).
tff(f13635,plain,
spl249_1002,
inference(avatar_split_clause,[],[f3015,f13633]) ).
tff(f13633,plain,
( spl249_1002
<=> ! [X2: 'C$',X0: 'C_c_fun$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK199(X0,X1,X2)) = X1 )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$u'('map_option$c'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1002])]) ).
tff(f3015,plain,
! [X2: 'C$',X0: 'C_c_fun$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK199(X0,X1,X2)) = X1 )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$u'('map_option$c'(X0),X1) ) ),
inference(cnf_transformation,[],[f1784]) ).
tff(f13631,plain,
spl249_1001,
inference(avatar_split_clause,[],[f3012,f13629]) ).
tff(f13629,plain,
( spl249_1001
<=> ! [X2: 'C$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$j'('some$a',sK198(X0,X1,X2)) = X0 )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$ab'('bind$'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1001])]) ).
tff(f3012,plain,
! [X2: 'C$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$j'('some$a',sK198(X0,X1,X2)) = X0 )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$ab'('bind$'(X0),X1) ) ),
inference(cnf_transformation,[],[f1780]) ).
tff(f13627,plain,
spl249_1000,
inference(avatar_split_clause,[],[f3010,f13625]) ).
tff(f13625,plain,
( spl249_1000
<=> ! [X2: 'C$',X0: 'A_c_fun$',X1: 'A_option$'] :
( ( 'fun_app$bk'(X0,sK197(X0,X1,X2)) = X2 )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$bh'('map_option$f'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_1000])]) ).
tff(f3010,plain,
! [X2: 'C$',X0: 'A_c_fun$',X1: 'A_option$'] :
( ( 'fun_app$bk'(X0,sK197(X0,X1,X2)) = X2 )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$bh'('map_option$f'(X0),X1) ) ),
inference(cnf_transformation,[],[f1776]) ).
tff(f1776,plain,
! [X0: 'A_c_fun$',X1: 'A_option$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$bh'('map_option$f'(X0),X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$bk'(X0,X3) != X2 )
| ( 'fun_app$q'('some$b',X3) != X1 ) ) )
& ( ( ( 'fun_app$bk'(X0,sK197(X0,X1,X2)) = X2 )
& ( 'fun_app$q'('some$b',sK197(X0,X1,X2)) = X1 ) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$bh'('map_option$f'(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK197])],[f1774,f1775]) ).
tff(f1775,plain,
! [X0: 'A_c_fun$',X1: 'A_option$',X2: 'C$'] :
( ? [X4: 'A$'] :
( ( 'fun_app$bk'(X0,X4) = X2 )
& ( 'fun_app$q'('some$b',X4) = X1 ) )
=> ( ( 'fun_app$bk'(X0,sK197(X0,X1,X2)) = X2 )
& ( 'fun_app$q'('some$b',sK197(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1774,plain,
! [X0: 'A_c_fun$',X1: 'A_option$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$bh'('map_option$f'(X0),X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$bk'(X0,X3) != X2 )
| ( 'fun_app$q'('some$b',X3) != X1 ) ) )
& ( ? [X4: 'A$'] :
( ( 'fun_app$bk'(X0,X4) = X2 )
& ( 'fun_app$q'('some$b',X4) = X1 ) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$bh'('map_option$f'(X0),X1) ) ) ),
inference(rectify,[],[f1773]) ).
tff(f1773,plain,
! [X0: 'A_c_fun$',X1: 'A_option$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = 'fun_app$bh'('map_option$f'(X0),X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$bk'(X0,X3) != X2 )
| ( 'fun_app$q'('some$b',X3) != X1 ) ) )
& ( ? [X3: 'A$'] :
( ( 'fun_app$bk'(X0,X3) = X2 )
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$bh'('map_option$f'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f228]) ).
tff(f228,axiom,
! [X0: 'A_c_fun$',X1: 'A_option$',X2: 'C$'] :
( ( 'fun_app$j'('some$a',X2) = 'fun_app$bh'('map_option$f'(X0),X1) )
<=> ? [X3: 'A$'] :
( ( 'fun_app$bk'(X0,X3) = X2 )
& ( 'fun_app$q'('some$b',X3) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom226) ).
tff(f13623,plain,
spl249_999,
inference(avatar_split_clause,[],[f3009,f13621]) ).
tff(f13621,plain,
( spl249_999
<=> ! [X2: 'C$',X0: 'A_c_fun$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK197(X0,X1,X2)) = X1 )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$bh'('map_option$f'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_999])]) ).
tff(f3009,plain,
! [X2: 'C$',X0: 'A_c_fun$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK197(X0,X1,X2)) = X1 )
| ( 'fun_app$j'('some$a',X2) != 'fun_app$bh'('map_option$f'(X0),X1) ) ),
inference(cnf_transformation,[],[f1776]) ).
tff(f13619,plain,
spl249_998,
inference(avatar_split_clause,[],[f3007,f13617]) ).
tff(f13617,plain,
( spl249_998
<=> ! [X2: 'A$',X0: 'A_a_fun$',X1: 'A_option$'] :
( ( 'fun_app$r'(X0,sK196(X0,X1,X2)) = X2 )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$be'('map_option$a'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_998])]) ).
tff(f3007,plain,
! [X2: 'A$',X0: 'A_a_fun$',X1: 'A_option$'] :
( ( 'fun_app$r'(X0,sK196(X0,X1,X2)) = X2 )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$be'('map_option$a'(X0),X1) ) ),
inference(cnf_transformation,[],[f1772]) ).
tff(f1772,plain,
! [X0: 'A_a_fun$',X1: 'A_option$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$be'('map_option$a'(X0),X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$r'(X0,X3) != X2 )
| ( 'fun_app$q'('some$b',X3) != X1 ) ) )
& ( ( ( 'fun_app$r'(X0,sK196(X0,X1,X2)) = X2 )
& ( 'fun_app$q'('some$b',sK196(X0,X1,X2)) = X1 ) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$be'('map_option$a'(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK196])],[f1770,f1771]) ).
tff(f1771,plain,
! [X0: 'A_a_fun$',X1: 'A_option$',X2: 'A$'] :
( ? [X4: 'A$'] :
( ( 'fun_app$r'(X0,X4) = X2 )
& ( 'fun_app$q'('some$b',X4) = X1 ) )
=> ( ( 'fun_app$r'(X0,sK196(X0,X1,X2)) = X2 )
& ( 'fun_app$q'('some$b',sK196(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1770,plain,
! [X0: 'A_a_fun$',X1: 'A_option$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$be'('map_option$a'(X0),X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$r'(X0,X3) != X2 )
| ( 'fun_app$q'('some$b',X3) != X1 ) ) )
& ( ? [X4: 'A$'] :
( ( 'fun_app$r'(X0,X4) = X2 )
& ( 'fun_app$q'('some$b',X4) = X1 ) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$be'('map_option$a'(X0),X1) ) ) ),
inference(rectify,[],[f1769]) ).
tff(f1769,plain,
! [X0: 'A_a_fun$',X1: 'A_option$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$be'('map_option$a'(X0),X1) )
| ! [X3: 'A$'] :
( ( 'fun_app$r'(X0,X3) != X2 )
| ( 'fun_app$q'('some$b',X3) != X1 ) ) )
& ( ? [X3: 'A$'] :
( ( 'fun_app$r'(X0,X3) = X2 )
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$be'('map_option$a'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f232]) ).
tff(f232,axiom,
! [X0: 'A_a_fun$',X1: 'A_option$',X2: 'A$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$be'('map_option$a'(X0),X1) )
<=> ? [X3: 'A$'] :
( ( 'fun_app$r'(X0,X3) = X2 )
& ( 'fun_app$q'('some$b',X3) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom230) ).
tff(f13615,plain,
spl249_997,
inference(avatar_split_clause,[],[f3006,f13613]) ).
tff(f13613,plain,
( spl249_997
<=> ! [X2: 'A$',X0: 'A_a_fun$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK196(X0,X1,X2)) = X1 )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$be'('map_option$a'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_997])]) ).
tff(f3006,plain,
! [X2: 'A$',X0: 'A_a_fun$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK196(X0,X1,X2)) = X1 )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$be'('map_option$a'(X0),X1) ) ),
inference(cnf_transformation,[],[f1772]) ).
tff(f13611,plain,
spl249_996,
inference(avatar_split_clause,[],[f3004,f13609]) ).
tff(f13609,plain,
( spl249_996
<=> ! [X2: 'A$',X0: 'B_a_fun$',X1: 'B_option$'] :
( ( 'fun_app$ao'(X0,sK195(X0,X1,X2)) = X2 )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bj'('map_option$h'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_996])]) ).
tff(f3004,plain,
! [X2: 'A$',X0: 'B_a_fun$',X1: 'B_option$'] :
( ( 'fun_app$ao'(X0,sK195(X0,X1,X2)) = X2 )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bj'('map_option$h'(X0),X1) ) ),
inference(cnf_transformation,[],[f1768]) ).
tff(f1768,plain,
! [X0: 'B_a_fun$',X1: 'B_option$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$bj'('map_option$h'(X0),X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$ao'(X0,X3) != X2 )
| ( 'fun_app$g'('some$',X3) != X1 ) ) )
& ( ( ( 'fun_app$ao'(X0,sK195(X0,X1,X2)) = X2 )
& ( 'fun_app$g'('some$',sK195(X0,X1,X2)) = X1 ) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bj'('map_option$h'(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK195])],[f1766,f1767]) ).
tff(f1767,plain,
! [X0: 'B_a_fun$',X1: 'B_option$',X2: 'A$'] :
( ? [X4: 'B$'] :
( ( 'fun_app$ao'(X0,X4) = X2 )
& ( 'fun_app$g'('some$',X4) = X1 ) )
=> ( ( 'fun_app$ao'(X0,sK195(X0,X1,X2)) = X2 )
& ( 'fun_app$g'('some$',sK195(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1766,plain,
! [X0: 'B_a_fun$',X1: 'B_option$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$bj'('map_option$h'(X0),X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$ao'(X0,X3) != X2 )
| ( 'fun_app$g'('some$',X3) != X1 ) ) )
& ( ? [X4: 'B$'] :
( ( 'fun_app$ao'(X0,X4) = X2 )
& ( 'fun_app$g'('some$',X4) = X1 ) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bj'('map_option$h'(X0),X1) ) ) ),
inference(rectify,[],[f1765]) ).
tff(f1765,plain,
! [X0: 'B_a_fun$',X1: 'B_option$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$bj'('map_option$h'(X0),X1) )
| ! [X3: 'B$'] :
( ( 'fun_app$ao'(X0,X3) != X2 )
| ( 'fun_app$g'('some$',X3) != X1 ) ) )
& ( ? [X3: 'B$'] :
( ( 'fun_app$ao'(X0,X3) = X2 )
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bj'('map_option$h'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f230]) ).
tff(f230,axiom,
! [X0: 'B_a_fun$',X1: 'B_option$',X2: 'A$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bj'('map_option$h'(X0),X1) )
<=> ? [X3: 'B$'] :
( ( 'fun_app$ao'(X0,X3) = X2 )
& ( 'fun_app$g'('some$',X3) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom228) ).
tff(f13607,plain,
spl249_995,
inference(avatar_split_clause,[],[f3003,f13605]) ).
tff(f13605,plain,
( spl249_995
<=> ! [X2: 'A$',X0: 'B_a_fun$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',sK195(X0,X1,X2)) = X1 )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bj'('map_option$h'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_995])]) ).
tff(f3003,plain,
! [X2: 'A$',X0: 'B_a_fun$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',sK195(X0,X1,X2)) = X1 )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bj'('map_option$h'(X0),X1) ) ),
inference(cnf_transformation,[],[f1768]) ).
tff(f13603,plain,
spl249_994,
inference(avatar_split_clause,[],[f3001,f13601]) ).
tff(f13601,plain,
( spl249_994
<=> ! [X2: 'A$',X0: 'C_a_fun$',X1: 'C_option$'] :
( ( 'fun_app$bl'(X0,sK194(X0,X1,X2)) = X2 )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bi'('map_option$g'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_994])]) ).
tff(f3001,plain,
! [X2: 'A$',X0: 'C_a_fun$',X1: 'C_option$'] :
( ( 'fun_app$bl'(X0,sK194(X0,X1,X2)) = X2 )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bi'('map_option$g'(X0),X1) ) ),
inference(cnf_transformation,[],[f1764]) ).
tff(f1764,plain,
! [X0: 'C_a_fun$',X1: 'C_option$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$bi'('map_option$g'(X0),X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$bl'(X0,X3) != X2 )
| ( 'fun_app$j'('some$a',X3) != X1 ) ) )
& ( ( ( 'fun_app$bl'(X0,sK194(X0,X1,X2)) = X2 )
& ( 'fun_app$j'('some$a',sK194(X0,X1,X2)) = X1 ) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bi'('map_option$g'(X0),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK194])],[f1762,f1763]) ).
tff(f1763,plain,
! [X0: 'C_a_fun$',X1: 'C_option$',X2: 'A$'] :
( ? [X4: 'C$'] :
( ( 'fun_app$bl'(X0,X4) = X2 )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
=> ( ( 'fun_app$bl'(X0,sK194(X0,X1,X2)) = X2 )
& ( 'fun_app$j'('some$a',sK194(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1762,plain,
! [X0: 'C_a_fun$',X1: 'C_option$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$bi'('map_option$g'(X0),X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$bl'(X0,X3) != X2 )
| ( 'fun_app$j'('some$a',X3) != X1 ) ) )
& ( ? [X4: 'C$'] :
( ( 'fun_app$bl'(X0,X4) = X2 )
& ( 'fun_app$j'('some$a',X4) = X1 ) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bi'('map_option$g'(X0),X1) ) ) ),
inference(rectify,[],[f1761]) ).
tff(f1761,plain,
! [X0: 'C_a_fun$',X1: 'C_option$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = 'fun_app$bi'('map_option$g'(X0),X1) )
| ! [X3: 'C$'] :
( ( 'fun_app$bl'(X0,X3) != X2 )
| ( 'fun_app$j'('some$a',X3) != X1 ) ) )
& ( ? [X3: 'C$'] :
( ( 'fun_app$bl'(X0,X3) = X2 )
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bi'('map_option$g'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f229]) ).
tff(f229,axiom,
! [X0: 'C_a_fun$',X1: 'C_option$',X2: 'A$'] :
( ( 'fun_app$q'('some$b',X2) = 'fun_app$bi'('map_option$g'(X0),X1) )
<=> ? [X3: 'C$'] :
( ( 'fun_app$bl'(X0,X3) = X2 )
& ( 'fun_app$j'('some$a',X3) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom227) ).
tff(f13597,plain,
spl249_993,
inference(avatar_split_clause,[],[f3000,f13595]) ).
tff(f13595,plain,
( spl249_993
<=> ! [X2: 'A$',X0: 'C_a_fun$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK194(X0,X1,X2)) = X1 )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bi'('map_option$g'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_993])]) ).
tff(f3000,plain,
! [X2: 'A$',X0: 'C_a_fun$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK194(X0,X1,X2)) = X1 )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bi'('map_option$g'(X0),X1) ) ),
inference(cnf_transformation,[],[f1764]) ).
tff(f13593,plain,
spl249_992,
inference(avatar_split_clause,[],[f2997,f13591]) ).
tff(f13591,plain,
( spl249_992
<=> ! [X2: 'A$',X0: 'A_option$',X1: 'A_a_option_fun$'] :
( ( 'fun_app$q'('some$b',sK193(X0,X1,X2)) = X0 )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bp'('bind$h'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_992])]) ).
tff(f2997,plain,
! [X2: 'A$',X0: 'A_option$',X1: 'A_a_option_fun$'] :
( ( 'fun_app$q'('some$b',sK193(X0,X1,X2)) = X0 )
| ( 'fun_app$q'('some$b',X2) != 'fun_app$bp'('bind$h'(X0),X1) ) ),
inference(cnf_transformation,[],[f1760]) ).
tff(f13589,plain,
spl249_991,
inference(avatar_split_clause,[],[f2779,f13587]) ).
tff(f13587,plain,
( spl249_991
<=> ! [X2: 'B_b_fun$',X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X1),X0) = 'fun_app$s'('map_option$b'(X2),X0) )
| 'member$c'(sK164(X0,X1,X2),'set_option$d'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_991])]) ).
tff(f2779,plain,
! [X2: 'B_b_fun$',X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X1),X0) = 'fun_app$s'('map_option$b'(X2),X0) )
| 'member$c'(sK164(X0,X1,X2),'set_option$d'(X0)) ),
inference(cnf_transformation,[],[f1594]) ).
tff(f13585,plain,
spl249_990,
inference(avatar_split_clause,[],[f2777,f13583]) ).
tff(f13583,plain,
( spl249_990
<=> ! [X2: 'B_c_fun$',X0: 'B_option$',X1: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X1),X0) = 'fun_app$an'('map_option$d'(X2),X0) )
| 'member$c'(sK163(X0,X1,X2),'set_option$d'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_990])]) ).
tff(f2777,plain,
! [X2: 'B_c_fun$',X0: 'B_option$',X1: 'B_c_fun$'] :
( ( 'fun_app$an'('map_option$d'(X1),X0) = 'fun_app$an'('map_option$d'(X2),X0) )
| 'member$c'(sK163(X0,X1,X2),'set_option$d'(X0)) ),
inference(cnf_transformation,[],[f1592]) ).
tff(f13581,plain,
spl249_989,
inference(avatar_split_clause,[],[f2775,f13579]) ).
tff(f13579,plain,
( spl249_989
<=> ! [X2: 'C_b_fun$',X0: 'C_option$',X1: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X1),X0) = 'fun_app$bg'('map_option$'(X2),X0) )
| 'member$b'(sK162(X0,X1,X2),'set_option$c'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_989])]) ).
tff(f2775,plain,
! [X2: 'C_b_fun$',X0: 'C_option$',X1: 'C_b_fun$'] :
( ( 'fun_app$bg'('map_option$'(X1),X0) = 'fun_app$bg'('map_option$'(X2),X0) )
| 'member$b'(sK162(X0,X1,X2),'set_option$c'(X0)) ),
inference(cnf_transformation,[],[f1590]) ).
tff(f13577,plain,
spl249_988,
inference(avatar_split_clause,[],[f2773,f13575]) ).
tff(f13575,plain,
( spl249_988
<=> ! [X2: 'A_a_fun$',X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X1),X0) = 'fun_app$be'('map_option$a'(X2),X0) )
| 'member$d'(sK161(X0,X1,X2),'set_option$b'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_988])]) ).
tff(f2773,plain,
! [X2: 'A_a_fun$',X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X1),X0) = 'fun_app$be'('map_option$a'(X2),X0) )
| 'member$d'(sK161(X0,X1,X2),'set_option$b'(X0)) ),
inference(cnf_transformation,[],[f1588]) ).
tff(f13573,plain,
spl249_987,
inference(avatar_split_clause,[],[f2771,f13571]) ).
tff(f13571,plain,
( spl249_987
<=> ! [X2: 'A_b_fun$',X0: 'A_option$',X1: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X1),X0) = 'fun_app$av'('map_option$e'(X2),X0) )
| 'member$d'(sK160(X0,X1,X2),'set_option$b'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_987])]) ).
tff(f2771,plain,
! [X2: 'A_b_fun$',X0: 'A_option$',X1: 'A_b_fun$'] :
( ( 'fun_app$av'('map_option$e'(X1),X0) = 'fun_app$av'('map_option$e'(X2),X0) )
| 'member$d'(sK160(X0,X1,X2),'set_option$b'(X0)) ),
inference(cnf_transformation,[],[f1586]) ).
tff(f13569,plain,
spl249_986,
inference(avatar_split_clause,[],[f2662,f13567]) ).
tff(f13567,plain,
( spl249_986
<=> ! [X2: 'B_b_option_fun$',X0: 'B_b_fun$',X1: 'B_option$'] : ( 'fun_app$s'('map_option$b'(X0),'fun_app$ac'('bind$c'(X1),X2)) = 'fun_app$ac'('bind$c'(X1),'fun_app$ad'('comp$ax'('map_option$b'(X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_986])]) ).
tff(f2662,plain,
! [X2: 'B_b_option_fun$',X0: 'B_b_fun$',X1: 'B_option$'] : ( 'fun_app$s'('map_option$b'(X0),'fun_app$ac'('bind$c'(X1),X2)) = 'fun_app$ac'('bind$c'(X1),'fun_app$ad'('comp$ax'('map_option$b'(X0)),X2)) ),
inference(cnf_transformation,[],[f552]) ).
tff(f552,axiom,
! [X0: 'B_b_fun$',X1: 'B_option$',X2: 'B_b_option_fun$'] : ( 'fun_app$s'('map_option$b'(X0),'fun_app$ac'('bind$c'(X1),X2)) = 'fun_app$ac'('bind$c'(X1),'fun_app$ad'('comp$ax'('map_option$b'(X0)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom550) ).
tff(f13565,plain,
spl249_985,
inference(avatar_split_clause,[],[f2661,f13563]) ).
tff(f13563,plain,
( spl249_985
<=> ! [X2: 'C_c_option_fun$',X0: 'C_c_fun$',X1: 'C_option$'] : ( 'fun_app$u'('map_option$c'(X0),'fun_app$ab'('bind$'(X1),X2)) = 'fun_app$ab'('bind$'(X1),'fun_app$aa'('comp$as'('map_option$c'(X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_985])]) ).
tff(f2661,plain,
! [X2: 'C_c_option_fun$',X0: 'C_c_fun$',X1: 'C_option$'] : ( 'fun_app$u'('map_option$c'(X0),'fun_app$ab'('bind$'(X1),X2)) = 'fun_app$ab'('bind$'(X1),'fun_app$aa'('comp$as'('map_option$c'(X0)),X2)) ),
inference(cnf_transformation,[],[f547]) ).
tff(f547,axiom,
! [X0: 'C_c_fun$',X1: 'C_option$',X2: 'C_c_option_fun$'] : ( 'fun_app$u'('map_option$c'(X0),'fun_app$ab'('bind$'(X1),X2)) = 'fun_app$ab'('bind$'(X1),'fun_app$aa'('comp$as'('map_option$c'(X0)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom545) ).
tff(f13561,plain,
spl249_984,
inference(avatar_split_clause,[],[f2660,f13559]) ).
tff(f13559,plain,
( spl249_984
<=> ! [X2: 'B$',X0: 'B_b_b_fun_fun$',X1: 'B_option$'] : ( 'fun_app$g'('uvb$'(X0,X1),X2) = 'fun_app$s'('case_option$'('fun_app$g'('some$',X2),'fun_app$t'('uva$'(X0),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_984])]) ).
tff(f2660,plain,
! [X2: 'B$',X0: 'B_b_b_fun_fun$',X1: 'B_option$'] : ( 'fun_app$g'('uvb$'(X0,X1),X2) = 'fun_app$s'('case_option$'('fun_app$g'('some$',X2),'fun_app$t'('uva$'(X0),X2)),X1) ),
inference(cnf_transformation,[],[f20]) ).
tff(f20,axiom,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$',X2: 'B$'] : ( 'fun_app$g'('uvb$'(X0,X1),X2) = 'fun_app$s'('case_option$'('fun_app$g'('some$',X2),'fun_app$t'('uva$'(X0),X2)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom19) ).
tff(f13556,plain,
spl249_983,
inference(avatar_split_clause,[],[f2659,f13554]) ).
tff(f13554,plain,
( spl249_983
<=> ! [X2: 'C$',X0: 'C_c_c_fun_fun$',X1: 'C_option$'] : ( 'fun_app$j'('uuz$'(X0,X1),X2) = 'fun_app$u'('case_option$a'('fun_app$j'('some$a',X2),'fun_app$v'('uuy$'(X0),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_983])]) ).
tff(f2659,plain,
! [X2: 'C$',X0: 'C_c_c_fun_fun$',X1: 'C_option$'] : ( 'fun_app$j'('uuz$'(X0,X1),X2) = 'fun_app$u'('case_option$a'('fun_app$j'('some$a',X2),'fun_app$v'('uuy$'(X0),X2)),X1) ),
inference(cnf_transformation,[],[f21]) ).
tff(f21,axiom,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$',X2: 'C$'] : ( 'fun_app$j'('uuz$'(X0,X1),X2) = 'fun_app$u'('case_option$a'('fun_app$j'('some$a',X2),'fun_app$v'('uuy$'(X0),X2)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom20) ).
tff(f13552,plain,
spl249_982,
inference(avatar_split_clause,[],[f2530,f13550]) ).
tff(f13550,plain,
( spl249_982
<=> ! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'('is_none$','fun_app$g'(X1,'fun_app$al'('the$',X0)))
| 'fun_app$a'('is_none$',X0)
| ~ 'fun_app$a'('is_none$','fun_app$ac'('bind$c'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_982])]) ).
tff(f2530,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'('is_none$','fun_app$g'(X1,'fun_app$al'('the$',X0)))
| 'fun_app$a'('is_none$',X0)
| ~ 'fun_app$a'('is_none$','fun_app$ac'('bind$c'(X0),X1)) ),
inference(cnf_transformation,[],[f1526]) ).
tff(f1526,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$a'('is_none$','fun_app$ac'('bind$c'(X0),X1))
| ( ~ 'fun_app$a'('is_none$','fun_app$g'(X1,'fun_app$al'('the$',X0)))
& ~ 'fun_app$a'('is_none$',X0) ) )
& ( 'fun_app$a'('is_none$','fun_app$g'(X1,'fun_app$al'('the$',X0)))
| 'fun_app$a'('is_none$',X0)
| ~ 'fun_app$a'('is_none$','fun_app$ac'('bind$c'(X0),X1)) ) ),
inference(flattening,[],[f1525]) ).
tff(f1525,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$a'('is_none$','fun_app$ac'('bind$c'(X0),X1))
| ( ~ 'fun_app$a'('is_none$','fun_app$g'(X1,'fun_app$al'('the$',X0)))
& ~ 'fun_app$a'('is_none$',X0) ) )
& ( 'fun_app$a'('is_none$','fun_app$g'(X1,'fun_app$al'('the$',X0)))
| 'fun_app$a'('is_none$',X0)
| ~ 'fun_app$a'('is_none$','fun_app$ac'('bind$c'(X0),X1)) ) ),
inference(nnf_transformation,[],[f397]) ).
tff(f397,axiom,
! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'('is_none$','fun_app$ac'('bind$c'(X0),X1))
<=> ( 'fun_app$a'('is_none$','fun_app$g'(X1,'fun_app$al'('the$',X0)))
| 'fun_app$a'('is_none$',X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom395) ).
tff(f13548,plain,
spl249_981,
inference(avatar_split_clause,[],[f2523,f13546]) ).
tff(f13546,plain,
( spl249_981
<=> ! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( 'fun_app$'('is_none$a','fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| 'fun_app$'('is_none$a',X0)
| ~ 'fun_app$'('is_none$a','fun_app$ab'('bind$'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_981])]) ).
tff(f2523,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( 'fun_app$'('is_none$a','fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| 'fun_app$'('is_none$a',X0)
| ~ 'fun_app$'('is_none$a','fun_app$ab'('bind$'(X0),X1)) ),
inference(cnf_transformation,[],[f1522]) ).
tff(f1522,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$'('is_none$a','fun_app$ab'('bind$'(X0),X1))
| ( ~ 'fun_app$'('is_none$a','fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
& ~ 'fun_app$'('is_none$a',X0) ) )
& ( 'fun_app$'('is_none$a','fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| 'fun_app$'('is_none$a',X0)
| ~ 'fun_app$'('is_none$a','fun_app$ab'('bind$'(X0),X1)) ) ),
inference(flattening,[],[f1521]) ).
tff(f1521,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$'('is_none$a','fun_app$ab'('bind$'(X0),X1))
| ( ~ 'fun_app$'('is_none$a','fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
& ~ 'fun_app$'('is_none$a',X0) ) )
& ( 'fun_app$'('is_none$a','fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| 'fun_app$'('is_none$a',X0)
| ~ 'fun_app$'('is_none$a','fun_app$ab'('bind$'(X0),X1)) ) ),
inference(nnf_transformation,[],[f400]) ).
tff(f400,axiom,
! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( 'fun_app$'('is_none$a','fun_app$ab'('bind$'(X0),X1))
<=> ( 'fun_app$'('is_none$a','fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| 'fun_app$'('is_none$a',X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom398) ).
tff(f13544,plain,
spl249_980,
inference(avatar_split_clause,[],[f2500,f13542]) ).
tff(f13542,plain,
( spl249_980
<=> ! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( 'none$a' = 'fun_app$g'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 )
| ( 'none$a' != 'fun_app$ac'('bind$c'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_980])]) ).
tff(f2500,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( 'none$a' = 'fun_app$g'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 )
| ( 'none$a' != 'fun_app$ac'('bind$c'(X0),X1) ) ),
inference(cnf_transformation,[],[f1510]) ).
tff(f1510,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( ( 'none$a' = 'fun_app$ac'('bind$c'(X0),X1) )
| ( ( 'none$a' != 'fun_app$g'(X1,'fun_app$al'('the$',X0)) )
& ( 'none$a' != X0 ) ) )
& ( ( 'none$a' = 'fun_app$g'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 )
| ( 'none$a' != 'fun_app$ac'('bind$c'(X0),X1) ) ) ),
inference(flattening,[],[f1509]) ).
tff(f1509,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( ( 'none$a' = 'fun_app$ac'('bind$c'(X0),X1) )
| ( ( 'none$a' != 'fun_app$g'(X1,'fun_app$al'('the$',X0)) )
& ( 'none$a' != X0 ) ) )
& ( ( 'none$a' = 'fun_app$g'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 )
| ( 'none$a' != 'fun_app$ac'('bind$c'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f345]) ).
tff(f345,axiom,
! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( 'none$a' = 'fun_app$ac'('bind$c'(X0),X1) )
<=> ( ( 'none$a' = 'fun_app$g'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom343) ).
tff(f13540,plain,
spl249_979,
inference(avatar_split_clause,[],[f2485,f13538]) ).
tff(f13538,plain,
( spl249_979
<=> ! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( 'none$' = 'fun_app$j'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 )
| ( 'none$' != 'fun_app$ab'('bind$'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_979])]) ).
tff(f2485,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( 'none$' = 'fun_app$j'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 )
| ( 'none$' != 'fun_app$ab'('bind$'(X0),X1) ) ),
inference(cnf_transformation,[],[f1502]) ).
tff(f1502,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( ( 'none$' = 'fun_app$ab'('bind$'(X0),X1) )
| ( ( 'none$' != 'fun_app$j'(X1,'fun_app$ak'('the$a',X0)) )
& ( 'none$' != X0 ) ) )
& ( ( 'none$' = 'fun_app$j'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 )
| ( 'none$' != 'fun_app$ab'('bind$'(X0),X1) ) ) ),
inference(flattening,[],[f1501]) ).
tff(f1501,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( ( 'none$' = 'fun_app$ab'('bind$'(X0),X1) )
| ( ( 'none$' != 'fun_app$j'(X1,'fun_app$ak'('the$a',X0)) )
& ( 'none$' != X0 ) ) )
& ( ( 'none$' = 'fun_app$j'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 )
| ( 'none$' != 'fun_app$ab'('bind$'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f342]) ).
tff(f342,axiom,
! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( 'none$' = 'fun_app$ab'('bind$'(X0),X1) )
<=> ( ( 'none$' = 'fun_app$j'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom340) ).
tff(f13536,plain,
spl249_978,
inference(avatar_split_clause,[],[f2458,f13534]) ).
tff(f13534,plain,
( spl249_978
<=> ! [X0: 'A_option$',X1: 'A_a_option_fun$'] :
( ( 'none$b' = 'fun_app$q'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 )
| ( 'none$b' != 'fun_app$bp'('bind$h'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_978])]) ).
tff(f2458,plain,
! [X0: 'A_option$',X1: 'A_a_option_fun$'] :
( ( 'none$b' = 'fun_app$q'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 )
| ( 'none$b' != 'fun_app$bp'('bind$h'(X0),X1) ) ),
inference(cnf_transformation,[],[f1488]) ).
tff(f1488,plain,
! [X0: 'A_option$',X1: 'A_a_option_fun$'] :
( ( ( 'none$b' = 'fun_app$bp'('bind$h'(X0),X1) )
| ( ( 'none$b' != 'fun_app$q'(X1,'fun_app$bf'('the$b',X0)) )
& ( 'none$b' != X0 ) ) )
& ( ( 'none$b' = 'fun_app$q'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 )
| ( 'none$b' != 'fun_app$bp'('bind$h'(X0),X1) ) ) ),
inference(flattening,[],[f1487]) ).
tff(f1487,plain,
! [X0: 'A_option$',X1: 'A_a_option_fun$'] :
( ( ( 'none$b' = 'fun_app$bp'('bind$h'(X0),X1) )
| ( ( 'none$b' != 'fun_app$q'(X1,'fun_app$bf'('the$b',X0)) )
& ( 'none$b' != X0 ) ) )
& ( ( 'none$b' = 'fun_app$q'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 )
| ( 'none$b' != 'fun_app$bp'('bind$h'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f341]) ).
tff(f341,axiom,
! [X0: 'A_option$',X1: 'A_a_option_fun$'] :
( ( 'none$b' = 'fun_app$bp'('bind$h'(X0),X1) )
<=> ( ( 'none$b' = 'fun_app$q'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom339) ).
tff(f13532,plain,
spl249_977,
inference(avatar_split_clause,[],[f2277,f13530]) ).
tff(f13530,plain,
( spl249_977
<=> ! [X0: 'A_a_option_fun$',X1: 'B$'] : ( 'fun_app$g'('fun_app$au'('f$',X0),X1) = 'fun_app$av'('case_option$d'('none$a','uur$'(X1)),'fun_app$q'(X0,'fun_app$ao'('gF$',X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_977])]) ).
tff(f2277,plain,
! [X0: 'A_a_option_fun$',X1: 'B$'] : ( 'fun_app$g'('fun_app$au'('f$',X0),X1) = 'fun_app$av'('case_option$d'('none$a','uur$'(X1)),'fun_app$q'(X0,'fun_app$ao'('gF$',X1))) ),
inference(cnf_transformation,[],[f167]) ).
tff(f167,axiom,
! [X0: 'A_a_option_fun$',X1: 'B$'] : ( 'fun_app$g'('fun_app$au'('f$',X0),X1) = 'fun_app$av'('case_option$d'('none$a','uur$'(X1)),'fun_app$q'(X0,'fun_app$ao'('gF$',X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom165) ).
tff(f11876,plain,
( spl249_976
| ~ spl249_110
| ~ spl249_770 ),
inference(avatar_split_clause,[],[f10022,f9876,f4087,f11874]) ).
tff(f11874,plain,
( spl249_976
<=> ! [X0: 'B_option_option$'] : ( 'map_option$i'('id$d',X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_976])]) ).
tff(f4087,plain,
( spl249_110
<=> ! [X0: 'B_option$'] : ( 'fun_app$s'('id$d',X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_110])]) ).
tff(f10022,plain,
( ! [X0: 'B_option_option$'] : ( 'map_option$i'('id$d',X0) = X0 )
| ~ spl249_110
| ~ spl249_770 ),
inference(trivial_inequality_removal,[],[f10017]) ).
tff(f10017,plain,
( ! [X0: 'B_option_option$'] :
( ( sK118(X0,'id$d') != sK118(X0,'id$d') )
| ( 'map_option$i'('id$d',X0) = X0 ) )
| ~ spl249_110
| ~ spl249_770 ),
inference(superposition,[],[f9877,f4088]) ).
tff(f4088,plain,
( ! [X0: 'B_option$'] : ( 'fun_app$s'('id$d',X0) = X0 )
| ~ spl249_110 ),
inference(avatar_component_clause,[],[f4087]) ).
tff(f11660,plain,
( spl249_975
| ~ spl249_109
| ~ spl249_769 ),
inference(avatar_split_clause,[],[f10016,f9872,f4083,f11658]) ).
tff(f11658,plain,
( spl249_975
<=> ! [X0: 'C_option_option$'] : ( 'map_option$j'('id$c',X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_975])]) ).
tff(f4083,plain,
( spl249_109
<=> ! [X0: 'C_option$'] : ( 'fun_app$u'('id$c',X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_109])]) ).
tff(f10016,plain,
( ! [X0: 'C_option_option$'] : ( 'map_option$j'('id$c',X0) = X0 )
| ~ spl249_109
| ~ spl249_769 ),
inference(trivial_inequality_removal,[],[f10011]) ).
tff(f10011,plain,
( ! [X0: 'C_option_option$'] :
( ( sK117(X0,'id$c') != sK117(X0,'id$c') )
| ( 'map_option$j'('id$c',X0) = X0 ) )
| ~ spl249_109
| ~ spl249_769 ),
inference(superposition,[],[f9873,f4084]) ).
tff(f4084,plain,
( ! [X0: 'C_option$'] : ( 'fun_app$u'('id$c',X0) = X0 )
| ~ spl249_109 ),
inference(avatar_component_clause,[],[f4083]) ).
tff(f11425,plain,
( spl249_974
| ~ spl249_22
| ~ spl249_703 ),
inference(avatar_split_clause,[],[f9009,f8270,f3700,f11423]) ).
tff(f3700,plain,
( spl249_22
<=> ! [X0: 'C_option$'] : ~ 'fun_app$'('uwg$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_22])]) ).
tff(f9009,plain,
( ! [X0: 'B_c_option_fun$',X1: 'B$'] : ~ 'fun_app$c'('uul$'('uwg$',X0),X1)
| ~ spl249_22
| ~ spl249_703 ),
inference(resolution,[],[f8271,f3701]) ).
tff(f3701,plain,
( ! [X0: 'C_option$'] : ~ 'fun_app$'('uwg$',X0)
| ~ spl249_22 ),
inference(avatar_component_clause,[],[f3700]) ).
tff(f11364,plain,
spl249_973,
inference(avatar_split_clause,[],[f3547,f11362]) ).
tff(f11362,plain,
( spl249_973
<=> ! [X2: 'B_c_option_fun$',X1: 'B_option$',X3: 'B_c_option_fun$'] :
( ( 'bind$b'(X1,X2) = 'bind$b'(X1,X3) )
| ( 'fun_app$g'('some$',sK220(X1,X2,X3)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_973])]) ).
tff(f3547,plain,
! [X2: 'B_c_option_fun$',X3: 'B_c_option_fun$',X1: 'B_option$'] :
( ( 'bind$b'(X1,X2) = 'bind$b'(X1,X3) )
| ( 'fun_app$g'('some$',sK220(X1,X2,X3)) = X1 ) ),
inference(equality_resolution,[],[f3087]) ).
tff(f3087,plain,
! [X2: 'B_c_option_fun$',X3: 'B_c_option_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'bind$b'(X0,X2) = 'bind$b'(X1,X3) )
| ( 'fun_app$g'('some$',sK220(X1,X2,X3)) = X1 )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1836]) ).
tff(f11360,plain,
spl249_972,
inference(avatar_split_clause,[],[f3539,f11358]) ).
tff(f11358,plain,
( spl249_972
<=> ! [X2: 'C_b_option_fun$',X1: 'C_option$',X3: 'C_b_option_fun$'] :
( ( 'bind$a'(X1,X2) = 'bind$a'(X1,X3) )
| ( 'fun_app$j'('some$a',sK216(X1,X2,X3)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_972])]) ).
tff(f3539,plain,
! [X2: 'C_b_option_fun$',X3: 'C_b_option_fun$',X1: 'C_option$'] :
( ( 'bind$a'(X1,X2) = 'bind$a'(X1,X3) )
| ( 'fun_app$j'('some$a',sK216(X1,X2,X3)) = X1 ) ),
inference(equality_resolution,[],[f3079]) ).
tff(f3079,plain,
! [X2: 'C_b_option_fun$',X3: 'C_b_option_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'bind$a'(X0,X2) = 'bind$a'(X1,X3) )
| ( 'fun_app$j'('some$a',sK216(X1,X2,X3)) = X1 )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1828]) ).
tff(f11356,plain,
spl249_971,
inference(avatar_split_clause,[],[f3259,f11354]) ).
tff(f11354,plain,
( spl249_971
<=> ! [X2: 'B$',X0: 'C_option_c_option_fun$',X1: 'B_c_option_fun$'] : ( 'bind$b'('fun_app$g'('some$',X2),'uuh$'(X0,X1)) = 'fun_app$u'(X0,'bind$b'('fun_app$g'('some$',X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_971])]) ).
tff(f3259,plain,
! [X2: 'B$',X0: 'C_option_c_option_fun$',X1: 'B_c_option_fun$'] : ( 'bind$b'('fun_app$g'('some$',X2),'uuh$'(X0,X1)) = 'fun_app$u'(X0,'bind$b'('fun_app$g'('some$',X2),X1)) ),
inference(definition_unfolding,[],[f2580,f2234,f2234]) ).
tff(f2580,plain,
! [X2: 'B$',X0: 'C_option_c_option_fun$',X1: 'B_c_option_fun$'] : ( 'fun_app$n'('uuh$'(X0,X1),X2) = 'fun_app$u'(X0,'fun_app$n'(X1,X2)) ),
inference(cnf_transformation,[],[f37]) ).
tff(f37,axiom,
! [X0: 'C_option_c_option_fun$',X1: 'B_c_option_fun$',X2: 'B$'] : ( 'fun_app$n'('uuh$'(X0,X1),X2) = 'fun_app$u'(X0,'fun_app$n'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom36) ).
tff(f11352,plain,
spl249_970,
inference(avatar_split_clause,[],[f3236,f11350]) ).
tff(f11350,plain,
( spl249_970
<=> ! [X0: tlbool,X3: 'B_option$',X2: 'B_b_fun$',X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$s'('map_option$b'(X2),X3))
| ~ 'fun_app$a'('case_option$e'(X0,'comp$i'(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_970])]) ).
tff(f3236,plain,
! [X2: 'B_b_fun$',X3: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$s'('map_option$b'(X2),X3))
| ~ 'fun_app$a'('case_option$e'(X0,'comp$i'(X1,X2)),X3) ),
inference(cnf_transformation,[],[f1918]) ).
tff(f1918,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_b_fun$',X3: 'B_option$'] :
( ( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$s'('map_option$b'(X2),X3))
| ~ 'fun_app$a'('case_option$e'(X0,'comp$i'(X1,X2)),X3) )
& ( 'fun_app$a'('case_option$e'(X0,'comp$i'(X1,X2)),X3)
| ~ 'fun_app$a'('case_option$e'(X0,X1),'fun_app$s'('map_option$b'(X2),X3)) ) ),
inference(nnf_transformation,[],[f494]) ).
tff(f494,axiom,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_b_fun$',X3: 'B_option$'] :
( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$s'('map_option$b'(X2),X3))
<=> 'fun_app$a'('case_option$e'(X0,'comp$i'(X1,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom492) ).
tff(f11348,plain,
spl249_969,
inference(avatar_split_clause,[],[f3235,f11346]) ).
tff(f11346,plain,
( spl249_969
<=> ! [X0: tlbool,X3: 'B_option$',X2: 'B_b_fun$',X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,'comp$i'(X1,X2)),X3)
| ~ 'fun_app$a'('case_option$e'(X0,X1),'fun_app$s'('map_option$b'(X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_969])]) ).
tff(f3235,plain,
! [X2: 'B_b_fun$',X3: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,'comp$i'(X1,X2)),X3)
| ~ 'fun_app$a'('case_option$e'(X0,X1),'fun_app$s'('map_option$b'(X2),X3)) ),
inference(cnf_transformation,[],[f1918]) ).
tff(f11344,plain,
spl249_968,
inference(avatar_split_clause,[],[f3234,f11342]) ).
tff(f11342,plain,
( spl249_968
<=> ! [X0: tlbool,X3: 'A_option$',X2: 'A_b_fun$',X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$av'('map_option$e'(X2),X3))
| ~ 'fun_app$aw'('case_option$g'(X0,'comp$h'(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_968])]) ).
tff(f3234,plain,
! [X2: 'A_b_fun$',X3: 'A_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$av'('map_option$e'(X2),X3))
| ~ 'fun_app$aw'('case_option$g'(X0,'comp$h'(X1,X2)),X3) ),
inference(cnf_transformation,[],[f1917]) ).
tff(f1917,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'A_b_fun$',X3: 'A_option$'] :
( ( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$av'('map_option$e'(X2),X3))
| ~ 'fun_app$aw'('case_option$g'(X0,'comp$h'(X1,X2)),X3) )
& ( 'fun_app$aw'('case_option$g'(X0,'comp$h'(X1,X2)),X3)
| ~ 'fun_app$a'('case_option$e'(X0,X1),'fun_app$av'('map_option$e'(X2),X3)) ) ),
inference(nnf_transformation,[],[f493]) ).
tff(f493,axiom,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'A_b_fun$',X3: 'A_option$'] :
( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$av'('map_option$e'(X2),X3))
<=> 'fun_app$aw'('case_option$g'(X0,'comp$h'(X1,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom491) ).
tff(f11340,plain,
spl249_967,
inference(avatar_split_clause,[],[f3233,f11338]) ).
tff(f11338,plain,
( spl249_967
<=> ! [X0: tlbool,X3: 'A_option$',X2: 'A_b_fun$',X1: 'B_bool_fun$'] :
( 'fun_app$aw'('case_option$g'(X0,'comp$h'(X1,X2)),X3)
| ~ 'fun_app$a'('case_option$e'(X0,X1),'fun_app$av'('map_option$e'(X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_967])]) ).
tff(f3233,plain,
! [X2: 'A_b_fun$',X3: 'A_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$aw'('case_option$g'(X0,'comp$h'(X1,X2)),X3)
| ~ 'fun_app$a'('case_option$e'(X0,X1),'fun_app$av'('map_option$e'(X2),X3)) ),
inference(cnf_transformation,[],[f1917]) ).
tff(f11336,plain,
( spl249_966
| ~ spl249_23
| ~ spl249_699 ),
inference(avatar_split_clause,[],[f8942,f8254,f3704,f11334]) ).
tff(f11334,plain,
( spl249_966
<=> ! [X2: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ~ sP43(X0,X1,'uwf$',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_966])]) ).
tff(f3704,plain,
( spl249_23
<=> ! [X0: 'B_option$'] : ~ 'fun_app$a'('uwf$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_23])]) ).
tff(f8942,plain,
( ! [X2: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ~ sP43(X0,X1,'uwf$',X2)
| ~ spl249_23
| ~ spl249_699 ),
inference(resolution,[],[f8255,f3705]) ).
tff(f3705,plain,
( ! [X0: 'B_option$'] : ~ 'fun_app$a'('uwf$',X0)
| ~ spl249_23 ),
inference(avatar_component_clause,[],[f3704]) ).
tff(f11332,plain,
spl249_965,
inference(avatar_split_clause,[],[f3232,f11330]) ).
tff(f11330,plain,
( spl249_965
<=> ! [X0: tlbool,X3: 'C_option$',X2: 'C_b_fun$',X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$bg'('map_option$'(X2),X3))
| ~ 'fun_app$'('case_option$f'(X0,'comp$j'(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_965])]) ).
tff(f3232,plain,
! [X2: 'C_b_fun$',X3: 'C_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$bg'('map_option$'(X2),X3))
| ~ 'fun_app$'('case_option$f'(X0,'comp$j'(X1,X2)),X3) ),
inference(cnf_transformation,[],[f1916]) ).
tff(f1916,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'C_b_fun$',X3: 'C_option$'] :
( ( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$bg'('map_option$'(X2),X3))
| ~ 'fun_app$'('case_option$f'(X0,'comp$j'(X1,X2)),X3) )
& ( 'fun_app$'('case_option$f'(X0,'comp$j'(X1,X2)),X3)
| ~ 'fun_app$a'('case_option$e'(X0,X1),'fun_app$bg'('map_option$'(X2),X3)) ) ),
inference(nnf_transformation,[],[f495]) ).
tff(f495,axiom,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'C_b_fun$',X3: 'C_option$'] :
( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$bg'('map_option$'(X2),X3))
<=> 'fun_app$'('case_option$f'(X0,'comp$j'(X1,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom493) ).
tff(f11328,plain,
spl249_964,
inference(avatar_split_clause,[],[f3231,f11326]) ).
tff(f11326,plain,
( spl249_964
<=> ! [X0: tlbool,X3: 'C_option$',X2: 'C_b_fun$',X1: 'B_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,'comp$j'(X1,X2)),X3)
| ~ 'fun_app$a'('case_option$e'(X0,X1),'fun_app$bg'('map_option$'(X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_964])]) ).
tff(f3231,plain,
! [X2: 'C_b_fun$',X3: 'C_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,'comp$j'(X1,X2)),X3)
| ~ 'fun_app$a'('case_option$e'(X0,X1),'fun_app$bg'('map_option$'(X2),X3)) ),
inference(cnf_transformation,[],[f1916]) ).
tff(f11324,plain,
spl249_963,
inference(avatar_split_clause,[],[f3230,f11322]) ).
tff(f11322,plain,
( spl249_963
<=> ! [X0: tlbool,X3: 'B_option$',X2: 'B_c_fun$',X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),'fun_app$an'('map_option$d'(X2),X3))
| ~ 'fun_app$a'('case_option$e'(X0,'comp$k'(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_963])]) ).
tff(f3230,plain,
! [X2: 'B_c_fun$',X3: 'B_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),'fun_app$an'('map_option$d'(X2),X3))
| ~ 'fun_app$a'('case_option$e'(X0,'comp$k'(X1,X2)),X3) ),
inference(cnf_transformation,[],[f1915]) ).
tff(f1915,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'B_c_fun$',X3: 'B_option$'] :
( ( 'fun_app$'('case_option$f'(X0,X1),'fun_app$an'('map_option$d'(X2),X3))
| ~ 'fun_app$a'('case_option$e'(X0,'comp$k'(X1,X2)),X3) )
& ( 'fun_app$a'('case_option$e'(X0,'comp$k'(X1,X2)),X3)
| ~ 'fun_app$'('case_option$f'(X0,X1),'fun_app$an'('map_option$d'(X2),X3)) ) ),
inference(nnf_transformation,[],[f496]) ).
tff(f496,axiom,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'B_c_fun$',X3: 'B_option$'] :
( 'fun_app$'('case_option$f'(X0,X1),'fun_app$an'('map_option$d'(X2),X3))
<=> 'fun_app$a'('case_option$e'(X0,'comp$k'(X1,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom494) ).
tff(f11320,plain,
spl249_962,
inference(avatar_split_clause,[],[f3229,f11318]) ).
tff(f11318,plain,
( spl249_962
<=> ! [X0: tlbool,X3: 'B_option$',X2: 'B_c_fun$',X1: 'C_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,'comp$k'(X1,X2)),X3)
| ~ 'fun_app$'('case_option$f'(X0,X1),'fun_app$an'('map_option$d'(X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_962])]) ).
tff(f3229,plain,
! [X2: 'B_c_fun$',X3: 'B_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,'comp$k'(X1,X2)),X3)
| ~ 'fun_app$'('case_option$f'(X0,X1),'fun_app$an'('map_option$d'(X2),X3)) ),
inference(cnf_transformation,[],[f1915]) ).
tff(f11316,plain,
spl249_961,
inference(avatar_split_clause,[],[f3228,f11314]) ).
tff(f11314,plain,
( spl249_961
<=> ! [X0: tlbool,X3: 'C_option$',X2: 'C_c_fun$',X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),'fun_app$u'('map_option$c'(X2),X3))
| ~ 'fun_app$'('case_option$f'(X0,'comp$l'(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_961])]) ).
tff(f3228,plain,
! [X2: 'C_c_fun$',X3: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),'fun_app$u'('map_option$c'(X2),X3))
| ~ 'fun_app$'('case_option$f'(X0,'comp$l'(X1,X2)),X3) ),
inference(cnf_transformation,[],[f1914]) ).
tff(f1914,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_c_fun$',X3: 'C_option$'] :
( ( 'fun_app$'('case_option$f'(X0,X1),'fun_app$u'('map_option$c'(X2),X3))
| ~ 'fun_app$'('case_option$f'(X0,'comp$l'(X1,X2)),X3) )
& ( 'fun_app$'('case_option$f'(X0,'comp$l'(X1,X2)),X3)
| ~ 'fun_app$'('case_option$f'(X0,X1),'fun_app$u'('map_option$c'(X2),X3)) ) ),
inference(nnf_transformation,[],[f497]) ).
tff(f497,axiom,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_c_fun$',X3: 'C_option$'] :
( 'fun_app$'('case_option$f'(X0,X1),'fun_app$u'('map_option$c'(X2),X3))
<=> 'fun_app$'('case_option$f'(X0,'comp$l'(X1,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom495) ).
tff(f11312,plain,
spl249_960,
inference(avatar_split_clause,[],[f3227,f11310]) ).
tff(f11310,plain,
( spl249_960
<=> ! [X0: tlbool,X3: 'C_option$',X2: 'C_c_fun$',X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,'comp$l'(X1,X2)),X3)
| ~ 'fun_app$'('case_option$f'(X0,X1),'fun_app$u'('map_option$c'(X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_960])]) ).
tff(f3227,plain,
! [X2: 'C_c_fun$',X3: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,'comp$l'(X1,X2)),X3)
| ~ 'fun_app$'('case_option$f'(X0,X1),'fun_app$u'('map_option$c'(X2),X3)) ),
inference(cnf_transformation,[],[f1914]) ).
tff(f11308,plain,
spl249_959,
inference(avatar_split_clause,[],[f3224,f11306]) ).
tff(f11306,plain,
( spl249_959
<=> ! [X0: 'B_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'B_b_option_fun$'] :
( sP43(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
| ~ 'fun_app$a'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_959])]) ).
tff(f3224,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( sP43(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
| ~ 'fun_app$a'(X2,X3) ),
inference(cnf_transformation,[],[f1912]) ).
tff(f11304,plain,
spl249_958,
inference(avatar_split_clause,[],[f3223,f11302]) ).
tff(f11302,plain,
( spl249_958
<=> ! [X0: 'B_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'B_b_option_fun$'] :
( sP43(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_958])]) ).
tff(f3223,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( sP43(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f1912]) ).
tff(f11300,plain,
spl249_957,
inference(avatar_split_clause,[],[f3222,f11298]) ).
tff(f11298,plain,
( spl249_957
<=> ! [X0: 'B_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'B_b_option_fun$'] :
( sP43(X0,X1,X2,X3)
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ~ 'fun_app$a'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_957])]) ).
tff(f3222,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( sP43(X0,X1,X2,X3)
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ~ 'fun_app$a'(X2,X3) ),
inference(cnf_transformation,[],[f1912]) ).
tff(f11296,plain,
spl249_956,
inference(avatar_split_clause,[],[f3216,f11294]) ).
tff(f11294,plain,
( spl249_956
<=> ! [X0: 'B_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'B_b_option_fun$'] :
( sP42(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
| ~ 'fun_app$a'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_956])]) ).
tff(f3216,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( sP42(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
| ~ 'fun_app$a'(X2,X3) ),
inference(cnf_transformation,[],[f1908]) ).
tff(f11292,plain,
( spl249_955
| ~ spl249_23
| ~ spl249_697 ),
inference(avatar_split_clause,[],[f8908,f8246,f3704,f11290]) ).
tff(f11290,plain,
( spl249_955
<=> ! [X2: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ~ sP42(X0,X1,'uwf$',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_955])]) ).
tff(f8908,plain,
( ! [X2: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ~ sP42(X0,X1,'uwf$',X2)
| ~ spl249_23
| ~ spl249_697 ),
inference(resolution,[],[f8247,f3705]) ).
tff(f11288,plain,
spl249_954,
inference(avatar_split_clause,[],[f3215,f11286]) ).
tff(f11286,plain,
( spl249_954
<=> ! [X0: 'B_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'B_b_option_fun$'] :
( sP42(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_954])]) ).
tff(f3215,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( sP42(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$g'(X1,'fun_app$al'('the$',X0)))
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f1908]) ).
tff(f11284,plain,
spl249_953,
inference(avatar_split_clause,[],[f3214,f11282]) ).
tff(f11282,plain,
( spl249_953
<=> ! [X0: 'B_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'B_b_option_fun$'] :
( sP42(X0,X1,X2,X3)
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ~ 'fun_app$a'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_953])]) ).
tff(f3214,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( sP42(X0,X1,X2,X3)
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ~ 'fun_app$a'(X2,X3) ),
inference(cnf_transformation,[],[f1908]) ).
tff(f11280,plain,
spl249_952,
inference(avatar_split_clause,[],[f3206,f11278]) ).
tff(f11278,plain,
( spl249_952
<=> ! [X0: 'A_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'A_b_option_fun$'] :
( sP41(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| ~ 'fun_app$a'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_952])]) ).
tff(f3206,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( sP41(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| ~ 'fun_app$a'(X2,X3) ),
inference(cnf_transformation,[],[f1903]) ).
tff(f11276,plain,
spl249_951,
inference(avatar_split_clause,[],[f3205,f11274]) ).
tff(f11274,plain,
( spl249_951
<=> ! [X0: 'A_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'A_b_option_fun$'] :
( sP41(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| ( 'none$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_951])]) ).
tff(f3205,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( sP41(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| ( 'none$b' = X0 ) ),
inference(cnf_transformation,[],[f1903]) ).
tff(f11272,plain,
spl249_950,
inference(avatar_split_clause,[],[f3204,f11270]) ).
tff(f11270,plain,
( spl249_950
<=> ! [X0: 'A_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'A_b_option_fun$'] :
( sP41(X0,X1,X2,X3)
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) = X0 )
| ~ 'fun_app$a'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_950])]) ).
tff(f3204,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( sP41(X0,X1,X2,X3)
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) = X0 )
| ~ 'fun_app$a'(X2,X3) ),
inference(cnf_transformation,[],[f1903]) ).
tff(f11268,plain,
spl249_949,
inference(avatar_split_clause,[],[f3198,f11266]) ).
tff(f11266,plain,
( spl249_949
<=> ! [X0: 'A_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'A_b_option_fun$'] :
( sP40(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| ~ 'fun_app$a'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_949])]) ).
tff(f3198,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( sP40(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| ~ 'fun_app$a'(X2,X3) ),
inference(cnf_transformation,[],[f1899]) ).
tff(f11264,plain,
spl249_948,
inference(avatar_split_clause,[],[f3197,f11262]) ).
tff(f11262,plain,
( spl249_948
<=> ! [X0: 'A_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'A_b_option_fun$'] :
( sP40(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| ( 'none$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_948])]) ).
tff(f3197,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( sP40(X0,X1,X2,X3)
| ~ 'fun_app$a'(X2,'fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| ( 'none$b' = X0 ) ),
inference(cnf_transformation,[],[f1899]) ).
tff(f11260,plain,
spl249_947,
inference(avatar_split_clause,[],[f3196,f11258]) ).
tff(f11258,plain,
( spl249_947
<=> ! [X0: 'A_option$',X3: 'B_option$',X2: 'B_option_bool_fun$',X1: 'A_b_option_fun$'] :
( sP40(X0,X1,X2,X3)
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) = X0 )
| ~ 'fun_app$a'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_947])]) ).
tff(f3196,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( sP40(X0,X1,X2,X3)
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) = X0 )
| ~ 'fun_app$a'(X2,X3) ),
inference(cnf_transformation,[],[f1899]) ).
tff(f11256,plain,
spl249_946,
inference(avatar_split_clause,[],[f3188,f11254]) ).
tff(f11254,plain,
( spl249_946
<=> ! [X0: 'B_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( sP39(X0,X1,X2,X3)
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ~ 'fun_app$'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_946])]) ).
tff(f3188,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( sP39(X0,X1,X2,X3)
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ~ 'fun_app$'(X2,X3) ),
inference(cnf_transformation,[],[f1895]) ).
tff(f11252,plain,
spl249_945,
inference(avatar_split_clause,[],[f3180,f11250]) ).
tff(f11250,plain,
( spl249_945
<=> ! [X0: 'B_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( sP38(X0,X1,X2,X3)
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ~ 'fun_app$'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_945])]) ).
tff(f3180,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( sP38(X0,X1,X2,X3)
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ~ 'fun_app$'(X2,X3) ),
inference(cnf_transformation,[],[f1891]) ).
tff(f11248,plain,
( spl249_944
| ~ spl249_23
| ~ spl249_695 ),
inference(avatar_split_clause,[],[f8873,f8236,f3704,f11246]) ).
tff(f11246,plain,
( spl249_944
<=> ! [X2: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] : ~ sP41(X0,X1,'uwf$',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_944])]) ).
tff(f8873,plain,
( ! [X2: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] : ~ sP41(X0,X1,'uwf$',X2)
| ~ spl249_23
| ~ spl249_695 ),
inference(resolution,[],[f8237,f3705]) ).
tff(f11244,plain,
spl249_943,
inference(avatar_split_clause,[],[f3172,f11242]) ).
tff(f11242,plain,
( spl249_943
<=> ! [X0: 'C_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'C_c_option_fun$'] :
( sP37(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| ~ 'fun_app$'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_943])]) ).
tff(f3172,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( sP37(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| ~ 'fun_app$'(X2,X3) ),
inference(cnf_transformation,[],[f1886]) ).
tff(f11240,plain,
spl249_942,
inference(avatar_split_clause,[],[f3171,f11238]) ).
tff(f11238,plain,
( spl249_942
<=> ! [X0: 'C_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'C_c_option_fun$'] :
( sP37(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_942])]) ).
tff(f3171,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( sP37(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f1886]) ).
tff(f11236,plain,
spl249_941,
inference(avatar_split_clause,[],[f3170,f11234]) ).
tff(f11234,plain,
( spl249_941
<=> ! [X0: 'C_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'C_c_option_fun$'] :
( sP37(X0,X1,X2,X3)
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 )
| ~ 'fun_app$'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_941])]) ).
tff(f3170,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( sP37(X0,X1,X2,X3)
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 )
| ~ 'fun_app$'(X2,X3) ),
inference(cnf_transformation,[],[f1886]) ).
tff(f11232,plain,
spl249_940,
inference(avatar_split_clause,[],[f3164,f11230]) ).
tff(f11230,plain,
( spl249_940
<=> ! [X0: 'C_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'C_c_option_fun$'] :
( sP36(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| ~ 'fun_app$'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_940])]) ).
tff(f3164,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( sP36(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| ~ 'fun_app$'(X2,X3) ),
inference(cnf_transformation,[],[f1882]) ).
tff(f11228,plain,
spl249_939,
inference(avatar_split_clause,[],[f3163,f11226]) ).
tff(f11226,plain,
( spl249_939
<=> ! [X0: 'C_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'C_c_option_fun$'] :
( sP36(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_939])]) ).
tff(f3163,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( sP36(X0,X1,X2,X3)
| ~ 'fun_app$'(X2,'fun_app$j'(X1,'fun_app$ak'('the$a',X0)))
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f1882]) ).
tff(f11224,plain,
spl249_938,
inference(avatar_split_clause,[],[f3162,f11222]) ).
tff(f11222,plain,
( spl249_938
<=> ! [X0: 'C_option$',X3: 'C_option$',X2: 'C_option_bool_fun$',X1: 'C_c_option_fun$'] :
( sP36(X0,X1,X2,X3)
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 )
| ~ 'fun_app$'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_938])]) ).
tff(f3162,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( sP36(X0,X1,X2,X3)
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 )
| ~ 'fun_app$'(X2,X3) ),
inference(cnf_transformation,[],[f1882]) ).
tff(f11220,plain,
spl249_937,
inference(avatar_split_clause,[],[f3152,f11218]) ).
tff(f11218,plain,
( spl249_937
<=> ! [X0: 'B_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'B_bool_fun$'] :
( sP35(X0,X1,X2,X3)
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ~ 'fun_app$ag'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_937])]) ).
tff(f3152,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( sP35(X0,X1,X2,X3)
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ~ 'fun_app$ag'(X2,X3) ),
inference(cnf_transformation,[],[f1877]) ).
tff(f11216,plain,
spl249_936,
inference(avatar_split_clause,[],[f3144,f11214]) ).
tff(f11214,plain,
( spl249_936
<=> ! [X0: 'C_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'C_bool_fun$'] :
( sP34(X0,X1,X2,X3)
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 )
| ~ 'fun_app$ag'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_936])]) ).
tff(f3144,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( sP34(X0,X1,X2,X3)
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 )
| ~ 'fun_app$ag'(X2,X3) ),
inference(cnf_transformation,[],[f1873]) ).
tff(f11212,plain,
spl249_935,
inference(avatar_split_clause,[],[f3136,f11210]) ).
tff(f11210,plain,
( spl249_935
<=> ! [X0: 'B_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'B_bool_fun$'] :
( sP33(X0,X1,X2,X3)
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ~ 'fun_app$ag'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_935])]) ).
tff(f3136,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( sP33(X0,X1,X2,X3)
| ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ~ 'fun_app$ag'(X2,X3) ),
inference(cnf_transformation,[],[f1869]) ).
tff(f11208,plain,
spl249_934,
inference(avatar_split_clause,[],[f3128,f11206]) ).
tff(f11206,plain,
( spl249_934
<=> ! [X0: 'C_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'C_bool_fun$'] :
( sP32(X0,X1,X2,X3)
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 )
| ~ 'fun_app$ag'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_934])]) ).
tff(f3128,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( sP32(X0,X1,X2,X3)
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 )
| ~ 'fun_app$ag'(X2,X3) ),
inference(cnf_transformation,[],[f1865]) ).
tff(f11204,plain,
( spl249_933
| ~ spl249_23
| ~ spl249_693 ),
inference(avatar_split_clause,[],[f8841,f8228,f3704,f11202]) ).
tff(f11202,plain,
( spl249_933
<=> ! [X2: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] : ~ sP40(X0,X1,'uwf$',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_933])]) ).
tff(f8841,plain,
( ! [X2: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] : ~ sP40(X0,X1,'uwf$',X2)
| ~ spl249_23
| ~ spl249_693 ),
inference(resolution,[],[f8229,f3705]) ).
tff(f11200,plain,
spl249_932,
inference(avatar_split_clause,[],[f3124,f11198]) ).
tff(f11198,plain,
( spl249_932
<=> ! [X0: 'Bool_bool_fun$',X3: 'B_option$',X2: 'B_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,def_6(X1,X2,X3))
| ~ 'fun_app$a'('case_option$e'(def_7(X0,X1),'uuj$'(X0,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_932])]) ).
tff(f3124,plain,
! [X2: 'B_bool_fun$',X3: 'B_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,def_6(X1,X2,X3))
| ~ 'fun_app$a'('case_option$e'(def_7(X0,X1),'uuj$'(X0,X2)),X3) ),
inference(cnf_transformation,[],[f1862]) ).
tff(f1862,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( ( 'fun_app$ag'(X0,def_6(X1,X2,X3))
| ~ 'fun_app$a'('case_option$e'(def_7(X0,X1),'uuj$'(X0,X2)),X3) )
& ( 'fun_app$a'('case_option$e'(def_7(X0,X1),'uuj$'(X0,X2)),X3)
| ~ 'fun_app$ag'(X0,def_6(X1,X2,X3)) ) ),
inference(nnf_transformation,[],[f145]) ).
tff(f145,axiom,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( 'fun_app$ag'(X0,def_6(X1,X2,X3))
<=> 'fun_app$a'('case_option$e'(def_7(X0,X1),'uuj$'(X0,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom143) ).
tff(f11196,plain,
spl249_931,
inference(avatar_split_clause,[],[f3123,f11194]) ).
tff(f11194,plain,
( spl249_931
<=> ! [X0: 'Bool_bool_fun$',X3: 'B_option$',X2: 'B_bool_fun$',X1: tlbool] :
( 'fun_app$a'('case_option$e'(def_7(X0,X1),'uuj$'(X0,X2)),X3)
| ~ 'fun_app$ag'(X0,def_6(X1,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_931])]) ).
tff(f3123,plain,
! [X2: 'B_bool_fun$',X3: 'B_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$a'('case_option$e'(def_7(X0,X1),'uuj$'(X0,X2)),X3)
| ~ 'fun_app$ag'(X0,def_6(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1862]) ).
tff(f11192,plain,
spl249_930,
inference(avatar_split_clause,[],[f3122,f11190]) ).
tff(f11190,plain,
( spl249_930
<=> ! [X0: 'Bool_bool_fun$',X3: 'C_option$',X2: 'C_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,def_8(X1,X2,X3))
| ~ 'fun_app$'('case_option$f'(def_9(X0,X1),'uuk$'(X0,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_930])]) ).
tff(f3122,plain,
! [X2: 'C_bool_fun$',X3: 'C_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,def_8(X1,X2,X3))
| ~ 'fun_app$'('case_option$f'(def_9(X0,X1),'uuk$'(X0,X2)),X3) ),
inference(cnf_transformation,[],[f1861]) ).
tff(f1861,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] :
( ( 'fun_app$ag'(X0,def_8(X1,X2,X3))
| ~ 'fun_app$'('case_option$f'(def_9(X0,X1),'uuk$'(X0,X2)),X3) )
& ( 'fun_app$'('case_option$f'(def_9(X0,X1),'uuk$'(X0,X2)),X3)
| ~ 'fun_app$ag'(X0,def_8(X1,X2,X3)) ) ),
inference(nnf_transformation,[],[f146]) ).
tff(f146,axiom,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] :
( 'fun_app$ag'(X0,def_8(X1,X2,X3))
<=> 'fun_app$'('case_option$f'(def_9(X0,X1),'uuk$'(X0,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom144) ).
tff(f11188,plain,
spl249_929,
inference(avatar_split_clause,[],[f3121,f11186]) ).
tff(f11186,plain,
( spl249_929
<=> ! [X0: 'Bool_bool_fun$',X3: 'C_option$',X2: 'C_bool_fun$',X1: tlbool] :
( 'fun_app$'('case_option$f'(def_9(X0,X1),'uuk$'(X0,X2)),X3)
| ~ 'fun_app$ag'(X0,def_8(X1,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_929])]) ).
tff(f3121,plain,
! [X2: 'C_bool_fun$',X3: 'C_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$'('case_option$f'(def_9(X0,X1),'uuk$'(X0,X2)),X3)
| ~ 'fun_app$ag'(X0,def_8(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1861]) ).
tff(f11184,plain,
spl249_928,
inference(avatar_split_clause,[],[f3035,f11182]) ).
tff(f3035,plain,
! [X2: 'B_c_fun$',X3: 'B_option$',X0: 'B_option$',X1: 'C_b_option_fun$'] : ( 'case_option$h'(X0,X1,'fun_app$an'('map_option$d'(X2),X3)) = 'fun_app$s'('case_option$'(X0,'comp$o'(X1,X2)),X3) ),
inference(cnf_transformation,[],[f500]) ).
tff(f500,axiom,
! [X0: 'B_option$',X1: 'C_b_option_fun$',X2: 'B_c_fun$',X3: 'B_option$'] : ( 'case_option$h'(X0,X1,'fun_app$an'('map_option$d'(X2),X3)) = 'fun_app$s'('case_option$'(X0,'comp$o'(X1,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom498) ).
tff(f11180,plain,
spl249_927,
inference(avatar_split_clause,[],[f2990,f11178]) ).
tff(f11178,plain,
( spl249_927
<=> ! [X2: 'B$',X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( 'fun_app$j'('some$a',sK192(X0,X1,X2)) = X0 )
| ( 'fun_app$g'('some$',X2) != 'bind$a'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_927])]) ).
tff(f2990,plain,
! [X2: 'B$',X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( 'fun_app$j'('some$a',sK192(X0,X1,X2)) = X0 )
| ( 'fun_app$g'('some$',X2) != 'bind$a'(X0,X1) ) ),
inference(cnf_transformation,[],[f1754]) ).
tff(f11176,plain,
spl249_926,
inference(avatar_split_clause,[],[f2987,f11174]) ).
tff(f11174,plain,
( spl249_926
<=> ! [X2: 'B$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( ( 'fun_app$q'('some$b',sK191(X0,X1,X2)) = X0 )
| ( 'fun_app$g'('some$',X2) != 'bind$e'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_926])]) ).
tff(f2987,plain,
! [X2: 'B$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( ( 'fun_app$q'('some$b',sK191(X0,X1,X2)) = X0 )
| ( 'fun_app$g'('some$',X2) != 'bind$e'(X0,X1) ) ),
inference(cnf_transformation,[],[f1750]) ).
tff(f11172,plain,
spl249_925,
inference(avatar_split_clause,[],[f2984,f11170]) ).
tff(f11170,plain,
( spl249_925
<=> ! [X2: 'C$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( 'fun_app$g'('some$',sK190(X0,X1,X2)) = X0 )
| ( 'fun_app$j'('some$a',X2) != 'bind$b'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_925])]) ).
tff(f2984,plain,
! [X2: 'C$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( 'fun_app$g'('some$',sK190(X0,X1,X2)) = X0 )
| ( 'fun_app$j'('some$a',X2) != 'bind$b'(X0,X1) ) ),
inference(cnf_transformation,[],[f1746]) ).
tff(f11168,plain,
spl249_924,
inference(avatar_split_clause,[],[f2981,f11166]) ).
tff(f11166,plain,
( spl249_924
<=> ! [X2: 'C$',X0: 'A_option$',X1: 'A_c_option_fun$'] :
( ( 'fun_app$q'('some$b',sK189(X0,X1,X2)) = X0 )
| ( 'fun_app$j'('some$a',X2) != 'bind$d'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_924])]) ).
tff(f2981,plain,
! [X2: 'C$',X0: 'A_option$',X1: 'A_c_option_fun$'] :
( ( 'fun_app$q'('some$b',sK189(X0,X1,X2)) = X0 )
| ( 'fun_app$j'('some$a',X2) != 'bind$d'(X0,X1) ) ),
inference(cnf_transformation,[],[f1742]) ).
tff(f11164,plain,
spl249_923,
inference(avatar_split_clause,[],[f2978,f11162]) ).
tff(f11162,plain,
( spl249_923
<=> ! [X2: 'A$',X0: 'B_option$',X1: 'B_a_option_fun$'] :
( ( 'fun_app$g'('some$',sK188(X0,X1,X2)) = X0 )
| ( 'fun_app$q'('some$b',X2) != 'bind$g'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_923])]) ).
tff(f2978,plain,
! [X2: 'A$',X0: 'B_option$',X1: 'B_a_option_fun$'] :
( ( 'fun_app$g'('some$',sK188(X0,X1,X2)) = X0 )
| ( 'fun_app$q'('some$b',X2) != 'bind$g'(X0,X1) ) ),
inference(cnf_transformation,[],[f1738]) ).
tff(f11160,plain,
( spl249_922
| ~ spl249_22
| ~ spl249_691 ),
inference(avatar_split_clause,[],[f8803,f8220,f3700,f11158]) ).
tff(f11158,plain,
( spl249_922
<=> ! [X2: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] : ~ sP39(X0,X1,'uwg$',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_922])]) ).
tff(f8803,plain,
( ! [X2: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] : ~ sP39(X0,X1,'uwg$',X2)
| ~ spl249_22
| ~ spl249_691 ),
inference(resolution,[],[f8221,f3701]) ).
tff(f11156,plain,
spl249_921,
inference(avatar_split_clause,[],[f2975,f11154]) ).
tff(f11154,plain,
( spl249_921
<=> ! [X2: 'A$',X0: 'C_option$',X1: 'C_a_option_fun$'] :
( ( 'fun_app$j'('some$a',sK187(X0,X1,X2)) = X0 )
| ( 'fun_app$q'('some$b',X2) != 'bind$f'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_921])]) ).
tff(f2975,plain,
! [X2: 'A$',X0: 'C_option$',X1: 'C_a_option_fun$'] :
( ( 'fun_app$j'('some$a',sK187(X0,X1,X2)) = X0 )
| ( 'fun_app$q'('some$b',X2) != 'bind$f'(X0,X1) ) ),
inference(cnf_transformation,[],[f1734]) ).
tff(f11152,plain,
spl249_920,
inference(avatar_split_clause,[],[f2972,f11150]) ).
tff(f11150,plain,
( spl249_920
<=> ! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP31(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$g'(X0,sK186(X0,X1,X2)))
| ~ 'fun_app$a'(X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_920])]) ).
tff(f2972,plain,
! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP31(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$g'(X0,sK186(X0,X1,X2)))
| ~ 'fun_app$a'(X1,'none$a') ),
inference(cnf_transformation,[],[f1729]) ).
tff(f1729,plain,
! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'B_option$'] :
( ( sP31(X0,X1,X2)
| ( ~ 'fun_app$a'(X1,'fun_app$g'(X0,sK186(X0,X1,X2)))
& ( 'fun_app$g'('some$',sK186(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$a'(X1,'none$a')
& ( 'none$a' = X2 ) ) )
& ( ( ! [X4: 'B$'] :
( 'fun_app$a'(X1,'fun_app$g'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 ) )
& ( 'fun_app$a'(X1,'none$a')
| ( 'none$a' != X2 ) ) )
| ~ sP31(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK186])],[f1727,f1728]) ).
tff(f1728,plain,
! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'B_option$'] :
( ? [X3: 'B$'] :
( ~ 'fun_app$a'(X1,'fun_app$g'(X0,X3))
& ( 'fun_app$g'('some$',X3) = X2 ) )
=> ( ~ 'fun_app$a'(X1,'fun_app$g'(X0,sK186(X0,X1,X2)))
& ( 'fun_app$g'('some$',sK186(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1727,plain,
! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'B_option$'] :
( ( sP31(X0,X1,X2)
| ? [X3: 'B$'] :
( ~ 'fun_app$a'(X1,'fun_app$g'(X0,X3))
& ( 'fun_app$g'('some$',X3) = X2 ) )
| ( ~ 'fun_app$a'(X1,'none$a')
& ( 'none$a' = X2 ) ) )
& ( ( ! [X4: 'B$'] :
( 'fun_app$a'(X1,'fun_app$g'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 ) )
& ( 'fun_app$a'(X1,'none$a')
| ( 'none$a' != X2 ) ) )
| ~ sP31(X0,X1,X2) ) ),
inference(rectify,[],[f1726]) ).
tff(f1726,plain,
! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( sP31(X2,X0,X1)
| ? [X3: 'B$'] :
( ~ 'fun_app$a'(X0,'fun_app$g'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$a' = X1 ) ) )
& ( ( ! [X3: 'B$'] :
( 'fun_app$a'(X0,'fun_app$g'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$a' != X1 ) ) )
| ~ sP31(X2,X0,X1) ) ),
inference(flattening,[],[f1725]) ).
tff(f1725,plain,
! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( sP31(X2,X0,X1)
| ? [X3: 'B$'] :
( ~ 'fun_app$a'(X0,'fun_app$g'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$a' = X1 ) ) )
& ( ( ! [X3: 'B$'] :
( 'fun_app$a'(X0,'fun_app$g'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$a' != X1 ) ) )
| ~ sP31(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1161]) ).
tff(f1161,plain,
! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( sP31(X2,X0,X1)
<=> ( ! [X3: 'B$'] :
( 'fun_app$a'(X0,'fun_app$g'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$a' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP31])]) ).
tff(f11148,plain,
spl249_919,
inference(avatar_split_clause,[],[f2971,f11146]) ).
tff(f11146,plain,
( spl249_919
<=> ! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP31(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$g'(X0,sK186(X0,X1,X2)))
| ( 'none$a' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_919])]) ).
tff(f2971,plain,
! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP31(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$g'(X0,sK186(X0,X1,X2)))
| ( 'none$a' = X2 ) ),
inference(cnf_transformation,[],[f1729]) ).
tff(f11144,plain,
spl249_918,
inference(avatar_split_clause,[],[f2970,f11142]) ).
tff(f11142,plain,
( spl249_918
<=> ! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP31(X0,X1,X2)
| ( 'fun_app$g'('some$',sK186(X0,X1,X2)) = X2 )
| ~ 'fun_app$a'(X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_918])]) ).
tff(f2970,plain,
! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP31(X0,X1,X2)
| ( 'fun_app$g'('some$',sK186(X0,X1,X2)) = X2 )
| ~ 'fun_app$a'(X1,'none$a') ),
inference(cnf_transformation,[],[f1729]) ).
tff(f11140,plain,
spl249_917,
inference(avatar_split_clause,[],[f2969,f11138]) ).
tff(f11138,plain,
( spl249_917
<=> ! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP31(X0,X1,X2)
| ( 'fun_app$g'('some$',sK186(X0,X1,X2)) = X2 )
| ( 'none$a' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_917])]) ).
tff(f2969,plain,
! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP31(X0,X1,X2)
| ( 'fun_app$g'('some$',sK186(X0,X1,X2)) = X2 )
| ( 'none$a' = X2 ) ),
inference(cnf_transformation,[],[f1729]) ).
tff(f11136,plain,
spl249_916,
inference(avatar_split_clause,[],[f2964,f11134]) ).
tff(f11134,plain,
( spl249_916
<=> ! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP30(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$g'(X0,sK185(X0,X1,X2)))
| ~ 'fun_app$a'(X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_916])]) ).
tff(f2964,plain,
! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP30(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$g'(X0,sK185(X0,X1,X2)))
| ~ 'fun_app$a'(X1,'none$a') ),
inference(cnf_transformation,[],[f1723]) ).
tff(f1723,plain,
! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'B_option$'] :
( ( sP30(X0,X1,X2)
| ( ~ 'fun_app$a'(X1,'fun_app$g'(X0,sK185(X0,X1,X2)))
& ( 'fun_app$g'('some$',sK185(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$a'(X1,'none$a')
& ( 'none$a' = X2 ) ) )
& ( ( ! [X4: 'B$'] :
( 'fun_app$a'(X1,'fun_app$g'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 ) )
& ( 'fun_app$a'(X1,'none$a')
| ( 'none$a' != X2 ) ) )
| ~ sP30(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK185])],[f1721,f1722]) ).
tff(f1722,plain,
! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'B_option$'] :
( ? [X3: 'B$'] :
( ~ 'fun_app$a'(X1,'fun_app$g'(X0,X3))
& ( 'fun_app$g'('some$',X3) = X2 ) )
=> ( ~ 'fun_app$a'(X1,'fun_app$g'(X0,sK185(X0,X1,X2)))
& ( 'fun_app$g'('some$',sK185(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1721,plain,
! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'B_option$'] :
( ( sP30(X0,X1,X2)
| ? [X3: 'B$'] :
( ~ 'fun_app$a'(X1,'fun_app$g'(X0,X3))
& ( 'fun_app$g'('some$',X3) = X2 ) )
| ( ~ 'fun_app$a'(X1,'none$a')
& ( 'none$a' = X2 ) ) )
& ( ( ! [X4: 'B$'] :
( 'fun_app$a'(X1,'fun_app$g'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 ) )
& ( 'fun_app$a'(X1,'none$a')
| ( 'none$a' != X2 ) ) )
| ~ sP30(X0,X1,X2) ) ),
inference(rectify,[],[f1720]) ).
tff(f1720,plain,
! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( sP30(X2,X0,X1)
| ? [X3: 'B$'] :
( ~ 'fun_app$a'(X0,'fun_app$g'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$a' = X1 ) ) )
& ( ( ! [X3: 'B$'] :
( 'fun_app$a'(X0,'fun_app$g'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$a' != X1 ) ) )
| ~ sP30(X2,X0,X1) ) ),
inference(flattening,[],[f1719]) ).
tff(f1719,plain,
! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( sP30(X2,X0,X1)
| ? [X3: 'B$'] :
( ~ 'fun_app$a'(X0,'fun_app$g'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$a' = X1 ) ) )
& ( ( ! [X3: 'B$'] :
( 'fun_app$a'(X0,'fun_app$g'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$a' != X1 ) ) )
| ~ sP30(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1159]) ).
tff(f1159,plain,
! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( sP30(X2,X0,X1)
<=> ( ! [X3: 'B$'] :
( 'fun_app$a'(X0,'fun_app$g'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$a' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP30])]) ).
tff(f11132,plain,
spl249_915,
inference(avatar_split_clause,[],[f2963,f11130]) ).
tff(f11130,plain,
( spl249_915
<=> ! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP30(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$g'(X0,sK185(X0,X1,X2)))
| ( 'none$a' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_915])]) ).
tff(f2963,plain,
! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP30(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$g'(X0,sK185(X0,X1,X2)))
| ( 'none$a' = X2 ) ),
inference(cnf_transformation,[],[f1723]) ).
tff(f11128,plain,
spl249_914,
inference(avatar_split_clause,[],[f2962,f11126]) ).
tff(f11126,plain,
( spl249_914
<=> ! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP30(X0,X1,X2)
| ( 'fun_app$g'('some$',sK185(X0,X1,X2)) = X2 )
| ~ 'fun_app$a'(X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_914])]) ).
tff(f2962,plain,
! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP30(X0,X1,X2)
| ( 'fun_app$g'('some$',sK185(X0,X1,X2)) = X2 )
| ~ 'fun_app$a'(X1,'none$a') ),
inference(cnf_transformation,[],[f1723]) ).
tff(f11124,plain,
spl249_913,
inference(avatar_split_clause,[],[f2961,f11122]) ).
tff(f11122,plain,
( spl249_913
<=> ! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP30(X0,X1,X2)
| ( 'fun_app$g'('some$',sK185(X0,X1,X2)) = X2 )
| ( 'none$a' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_913])]) ).
tff(f2961,plain,
! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP30(X0,X1,X2)
| ( 'fun_app$g'('some$',sK185(X0,X1,X2)) = X2 )
| ( 'none$a' = X2 ) ),
inference(cnf_transformation,[],[f1723]) ).
tff(f11120,plain,
spl249_912,
inference(avatar_split_clause,[],[f2956,f11118]) ).
tff(f11118,plain,
( spl249_912
<=> ! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP29(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$j'(X0,sK184(X0,X1,X2)))
| ~ 'fun_app$'(X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_912])]) ).
tff(f2956,plain,
! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP29(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$j'(X0,sK184(X0,X1,X2)))
| ~ 'fun_app$'(X1,'none$') ),
inference(cnf_transformation,[],[f1717]) ).
tff(f1717,plain,
! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'C_option$'] :
( ( sP29(X0,X1,X2)
| ( ~ 'fun_app$'(X1,'fun_app$j'(X0,sK184(X0,X1,X2)))
& ( 'fun_app$j'('some$a',sK184(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$'(X1,'none$')
& ( 'none$' = X2 ) ) )
& ( ( ! [X4: 'C$'] :
( 'fun_app$'(X1,'fun_app$j'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 ) )
& ( 'fun_app$'(X1,'none$')
| ( 'none$' != X2 ) ) )
| ~ sP29(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK184])],[f1715,f1716]) ).
tff(f1716,plain,
! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'C_option$'] :
( ? [X3: 'C$'] :
( ~ 'fun_app$'(X1,'fun_app$j'(X0,X3))
& ( 'fun_app$j'('some$a',X3) = X2 ) )
=> ( ~ 'fun_app$'(X1,'fun_app$j'(X0,sK184(X0,X1,X2)))
& ( 'fun_app$j'('some$a',sK184(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1715,plain,
! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'C_option$'] :
( ( sP29(X0,X1,X2)
| ? [X3: 'C$'] :
( ~ 'fun_app$'(X1,'fun_app$j'(X0,X3))
& ( 'fun_app$j'('some$a',X3) = X2 ) )
| ( ~ 'fun_app$'(X1,'none$')
& ( 'none$' = X2 ) ) )
& ( ( ! [X4: 'C$'] :
( 'fun_app$'(X1,'fun_app$j'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 ) )
& ( 'fun_app$'(X1,'none$')
| ( 'none$' != X2 ) ) )
| ~ sP29(X0,X1,X2) ) ),
inference(rectify,[],[f1714]) ).
tff(f1714,plain,
! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( sP29(X2,X0,X1)
| ? [X3: 'C$'] :
( ~ 'fun_app$'(X0,'fun_app$j'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$' = X1 ) ) )
& ( ( ! [X3: 'C$'] :
( 'fun_app$'(X0,'fun_app$j'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$' != X1 ) ) )
| ~ sP29(X2,X0,X1) ) ),
inference(flattening,[],[f1713]) ).
tff(f1713,plain,
! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( sP29(X2,X0,X1)
| ? [X3: 'C$'] :
( ~ 'fun_app$'(X0,'fun_app$j'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$' = X1 ) ) )
& ( ( ! [X3: 'C$'] :
( 'fun_app$'(X0,'fun_app$j'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$' != X1 ) ) )
| ~ sP29(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1157]) ).
tff(f1157,plain,
! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( sP29(X2,X0,X1)
<=> ( ! [X3: 'C$'] :
( 'fun_app$'(X0,'fun_app$j'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP29])]) ).
tff(f11116,plain,
( spl249_911
| ~ spl249_22
| ~ spl249_689 ),
inference(avatar_split_clause,[],[f8773,f8212,f3700,f11114]) ).
tff(f11114,plain,
( spl249_911
<=> ! [X2: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] : ~ sP38(X0,X1,'uwg$',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_911])]) ).
tff(f8773,plain,
( ! [X2: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] : ~ sP38(X0,X1,'uwg$',X2)
| ~ spl249_22
| ~ spl249_689 ),
inference(resolution,[],[f8213,f3701]) ).
tff(f11112,plain,
spl249_910,
inference(avatar_split_clause,[],[f2955,f11110]) ).
tff(f11110,plain,
( spl249_910
<=> ! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP29(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$j'(X0,sK184(X0,X1,X2)))
| ( 'none$' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_910])]) ).
tff(f2955,plain,
! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP29(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$j'(X0,sK184(X0,X1,X2)))
| ( 'none$' = X2 ) ),
inference(cnf_transformation,[],[f1717]) ).
tff(f11108,plain,
spl249_909,
inference(avatar_split_clause,[],[f2954,f11106]) ).
tff(f11106,plain,
( spl249_909
<=> ! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP29(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK184(X0,X1,X2)) = X2 )
| ~ 'fun_app$'(X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_909])]) ).
tff(f2954,plain,
! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP29(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK184(X0,X1,X2)) = X2 )
| ~ 'fun_app$'(X1,'none$') ),
inference(cnf_transformation,[],[f1717]) ).
tff(f11104,plain,
spl249_908,
inference(avatar_split_clause,[],[f2953,f11102]) ).
tff(f11102,plain,
( spl249_908
<=> ! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP29(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK184(X0,X1,X2)) = X2 )
| ( 'none$' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_908])]) ).
tff(f2953,plain,
! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP29(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK184(X0,X1,X2)) = X2 )
| ( 'none$' = X2 ) ),
inference(cnf_transformation,[],[f1717]) ).
tff(f11100,plain,
spl249_907,
inference(avatar_split_clause,[],[f2948,f11098]) ).
tff(f11098,plain,
( spl249_907
<=> ! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP28(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$j'(X0,sK183(X0,X1,X2)))
| ~ 'fun_app$'(X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_907])]) ).
tff(f2948,plain,
! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP28(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$j'(X0,sK183(X0,X1,X2)))
| ~ 'fun_app$'(X1,'none$') ),
inference(cnf_transformation,[],[f1711]) ).
tff(f1711,plain,
! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'C_option$'] :
( ( sP28(X0,X1,X2)
| ( ~ 'fun_app$'(X1,'fun_app$j'(X0,sK183(X0,X1,X2)))
& ( 'fun_app$j'('some$a',sK183(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$'(X1,'none$')
& ( 'none$' = X2 ) ) )
& ( ( ! [X4: 'C$'] :
( 'fun_app$'(X1,'fun_app$j'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 ) )
& ( 'fun_app$'(X1,'none$')
| ( 'none$' != X2 ) ) )
| ~ sP28(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK183])],[f1709,f1710]) ).
tff(f1710,plain,
! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'C_option$'] :
( ? [X3: 'C$'] :
( ~ 'fun_app$'(X1,'fun_app$j'(X0,X3))
& ( 'fun_app$j'('some$a',X3) = X2 ) )
=> ( ~ 'fun_app$'(X1,'fun_app$j'(X0,sK183(X0,X1,X2)))
& ( 'fun_app$j'('some$a',sK183(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1709,plain,
! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'C_option$'] :
( ( sP28(X0,X1,X2)
| ? [X3: 'C$'] :
( ~ 'fun_app$'(X1,'fun_app$j'(X0,X3))
& ( 'fun_app$j'('some$a',X3) = X2 ) )
| ( ~ 'fun_app$'(X1,'none$')
& ( 'none$' = X2 ) ) )
& ( ( ! [X4: 'C$'] :
( 'fun_app$'(X1,'fun_app$j'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 ) )
& ( 'fun_app$'(X1,'none$')
| ( 'none$' != X2 ) ) )
| ~ sP28(X0,X1,X2) ) ),
inference(rectify,[],[f1708]) ).
tff(f1708,plain,
! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( sP28(X2,X0,X1)
| ? [X3: 'C$'] :
( ~ 'fun_app$'(X0,'fun_app$j'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$' = X1 ) ) )
& ( ( ! [X3: 'C$'] :
( 'fun_app$'(X0,'fun_app$j'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$' != X1 ) ) )
| ~ sP28(X2,X0,X1) ) ),
inference(flattening,[],[f1707]) ).
tff(f1707,plain,
! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( sP28(X2,X0,X1)
| ? [X3: 'C$'] :
( ~ 'fun_app$'(X0,'fun_app$j'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$' = X1 ) ) )
& ( ( ! [X3: 'C$'] :
( 'fun_app$'(X0,'fun_app$j'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$' != X1 ) ) )
| ~ sP28(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1155]) ).
tff(f1155,plain,
! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( sP28(X2,X0,X1)
<=> ( ! [X3: 'C$'] :
( 'fun_app$'(X0,'fun_app$j'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP28])]) ).
tff(f11096,plain,
spl249_906,
inference(avatar_split_clause,[],[f2947,f11094]) ).
tff(f11094,plain,
( spl249_906
<=> ! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP28(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$j'(X0,sK183(X0,X1,X2)))
| ( 'none$' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_906])]) ).
tff(f2947,plain,
! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP28(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$j'(X0,sK183(X0,X1,X2)))
| ( 'none$' = X2 ) ),
inference(cnf_transformation,[],[f1711]) ).
tff(f11092,plain,
spl249_905,
inference(avatar_split_clause,[],[f2946,f11090]) ).
tff(f11090,plain,
( spl249_905
<=> ! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP28(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK183(X0,X1,X2)) = X2 )
| ~ 'fun_app$'(X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_905])]) ).
tff(f2946,plain,
! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP28(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK183(X0,X1,X2)) = X2 )
| ~ 'fun_app$'(X1,'none$') ),
inference(cnf_transformation,[],[f1711]) ).
tff(f11088,plain,
spl249_904,
inference(avatar_split_clause,[],[f2945,f11086]) ).
tff(f11086,plain,
( spl249_904
<=> ! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP28(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK183(X0,X1,X2)) = X2 )
| ( 'none$' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_904])]) ).
tff(f2945,plain,
! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP28(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK183(X0,X1,X2)) = X2 )
| ( 'none$' = X2 ) ),
inference(cnf_transformation,[],[f1711]) ).
tff(f11084,plain,
spl249_903,
inference(avatar_split_clause,[],[f2940,f11082]) ).
tff(f11082,plain,
( spl249_903
<=> ! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP27(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$q'(X0,sK182(X0,X1,X2)))
| ~ 'fun_app$aw'(X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_903])]) ).
tff(f2940,plain,
! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP27(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$q'(X0,sK182(X0,X1,X2)))
| ~ 'fun_app$aw'(X1,'none$b') ),
inference(cnf_transformation,[],[f1705]) ).
tff(f1705,plain,
! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'A_option$'] :
( ( sP27(X0,X1,X2)
| ( ~ 'fun_app$aw'(X1,'fun_app$q'(X0,sK182(X0,X1,X2)))
& ( 'fun_app$q'('some$b',sK182(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$aw'(X1,'none$b')
& ( 'none$b' = X2 ) ) )
& ( ( ! [X4: 'A$'] :
( 'fun_app$aw'(X1,'fun_app$q'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 ) )
& ( 'fun_app$aw'(X1,'none$b')
| ( 'none$b' != X2 ) ) )
| ~ sP27(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK182])],[f1703,f1704]) ).
tff(f1704,plain,
! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'A_option$'] :
( ? [X3: 'A$'] :
( ~ 'fun_app$aw'(X1,'fun_app$q'(X0,X3))
& ( 'fun_app$q'('some$b',X3) = X2 ) )
=> ( ~ 'fun_app$aw'(X1,'fun_app$q'(X0,sK182(X0,X1,X2)))
& ( 'fun_app$q'('some$b',sK182(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1703,plain,
! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'A_option$'] :
( ( sP27(X0,X1,X2)
| ? [X3: 'A$'] :
( ~ 'fun_app$aw'(X1,'fun_app$q'(X0,X3))
& ( 'fun_app$q'('some$b',X3) = X2 ) )
| ( ~ 'fun_app$aw'(X1,'none$b')
& ( 'none$b' = X2 ) ) )
& ( ( ! [X4: 'A$'] :
( 'fun_app$aw'(X1,'fun_app$q'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 ) )
& ( 'fun_app$aw'(X1,'none$b')
| ( 'none$b' != X2 ) ) )
| ~ sP27(X0,X1,X2) ) ),
inference(rectify,[],[f1702]) ).
tff(f1702,plain,
! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( ( sP27(X2,X0,X1)
| ? [X3: 'A$'] :
( ~ 'fun_app$aw'(X0,'fun_app$q'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$b' = X1 ) ) )
& ( ( ! [X3: 'A$'] :
( 'fun_app$aw'(X0,'fun_app$q'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$b' != X1 ) ) )
| ~ sP27(X2,X0,X1) ) ),
inference(flattening,[],[f1701]) ).
tff(f1701,plain,
! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( ( sP27(X2,X0,X1)
| ? [X3: 'A$'] :
( ~ 'fun_app$aw'(X0,'fun_app$q'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$b' = X1 ) ) )
& ( ( ! [X3: 'A$'] :
( 'fun_app$aw'(X0,'fun_app$q'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$b' != X1 ) ) )
| ~ sP27(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1153]) ).
tff(f1153,plain,
! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( sP27(X2,X0,X1)
<=> ( ! [X3: 'A$'] :
( 'fun_app$aw'(X0,'fun_app$q'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$b' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP27])]) ).
tff(f11080,plain,
spl249_902,
inference(avatar_split_clause,[],[f2939,f11078]) ).
tff(f11078,plain,
( spl249_902
<=> ! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP27(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$q'(X0,sK182(X0,X1,X2)))
| ( 'none$b' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_902])]) ).
tff(f2939,plain,
! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP27(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$q'(X0,sK182(X0,X1,X2)))
| ( 'none$b' = X2 ) ),
inference(cnf_transformation,[],[f1705]) ).
tff(f11076,plain,
spl249_901,
inference(avatar_split_clause,[],[f2938,f11074]) ).
tff(f11074,plain,
( spl249_901
<=> ! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP27(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK182(X0,X1,X2)) = X2 )
| ~ 'fun_app$aw'(X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_901])]) ).
tff(f2938,plain,
! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP27(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK182(X0,X1,X2)) = X2 )
| ~ 'fun_app$aw'(X1,'none$b') ),
inference(cnf_transformation,[],[f1705]) ).
tff(f11072,plain,
( spl249_900
| ~ spl249_22
| ~ spl249_687 ),
inference(avatar_split_clause,[],[f8744,f8204,f3700,f11070]) ).
tff(f11070,plain,
( spl249_900
<=> ! [X2: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ~ sP37(X0,X1,'uwg$',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_900])]) ).
tff(f8744,plain,
( ! [X2: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ~ sP37(X0,X1,'uwg$',X2)
| ~ spl249_22
| ~ spl249_687 ),
inference(resolution,[],[f8205,f3701]) ).
tff(f11068,plain,
spl249_899,
inference(avatar_split_clause,[],[f2937,f11066]) ).
tff(f11066,plain,
( spl249_899
<=> ! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP27(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK182(X0,X1,X2)) = X2 )
| ( 'none$b' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_899])]) ).
tff(f2937,plain,
! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP27(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK182(X0,X1,X2)) = X2 )
| ( 'none$b' = X2 ) ),
inference(cnf_transformation,[],[f1705]) ).
tff(f11064,plain,
spl249_898,
inference(avatar_split_clause,[],[f2932,f11062]) ).
tff(f11062,plain,
( spl249_898
<=> ! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP26(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$q'(X0,sK181(X0,X1,X2)))
| ~ 'fun_app$aw'(X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_898])]) ).
tff(f2932,plain,
! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP26(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$q'(X0,sK181(X0,X1,X2)))
| ~ 'fun_app$aw'(X1,'none$b') ),
inference(cnf_transformation,[],[f1699]) ).
tff(f1699,plain,
! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'A_option$'] :
( ( sP26(X0,X1,X2)
| ( ~ 'fun_app$aw'(X1,'fun_app$q'(X0,sK181(X0,X1,X2)))
& ( 'fun_app$q'('some$b',sK181(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$aw'(X1,'none$b')
& ( 'none$b' = X2 ) ) )
& ( ( ! [X4: 'A$'] :
( 'fun_app$aw'(X1,'fun_app$q'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 ) )
& ( 'fun_app$aw'(X1,'none$b')
| ( 'none$b' != X2 ) ) )
| ~ sP26(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK181])],[f1697,f1698]) ).
tff(f1698,plain,
! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'A_option$'] :
( ? [X3: 'A$'] :
( ~ 'fun_app$aw'(X1,'fun_app$q'(X0,X3))
& ( 'fun_app$q'('some$b',X3) = X2 ) )
=> ( ~ 'fun_app$aw'(X1,'fun_app$q'(X0,sK181(X0,X1,X2)))
& ( 'fun_app$q'('some$b',sK181(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1697,plain,
! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'A_option$'] :
( ( sP26(X0,X1,X2)
| ? [X3: 'A$'] :
( ~ 'fun_app$aw'(X1,'fun_app$q'(X0,X3))
& ( 'fun_app$q'('some$b',X3) = X2 ) )
| ( ~ 'fun_app$aw'(X1,'none$b')
& ( 'none$b' = X2 ) ) )
& ( ( ! [X4: 'A$'] :
( 'fun_app$aw'(X1,'fun_app$q'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 ) )
& ( 'fun_app$aw'(X1,'none$b')
| ( 'none$b' != X2 ) ) )
| ~ sP26(X0,X1,X2) ) ),
inference(rectify,[],[f1696]) ).
tff(f1696,plain,
! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( ( sP26(X2,X0,X1)
| ? [X3: 'A$'] :
( ~ 'fun_app$aw'(X0,'fun_app$q'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$b' = X1 ) ) )
& ( ( ! [X3: 'A$'] :
( 'fun_app$aw'(X0,'fun_app$q'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$b' != X1 ) ) )
| ~ sP26(X2,X0,X1) ) ),
inference(flattening,[],[f1695]) ).
tff(f1695,plain,
! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( ( sP26(X2,X0,X1)
| ? [X3: 'A$'] :
( ~ 'fun_app$aw'(X0,'fun_app$q'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$b' = X1 ) ) )
& ( ( ! [X3: 'A$'] :
( 'fun_app$aw'(X0,'fun_app$q'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$b' != X1 ) ) )
| ~ sP26(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1151]) ).
tff(f1151,plain,
! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( sP26(X2,X0,X1)
<=> ( ! [X3: 'A$'] :
( 'fun_app$aw'(X0,'fun_app$q'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$b' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP26])]) ).
tff(f11060,plain,
spl249_897,
inference(avatar_split_clause,[],[f2931,f11058]) ).
tff(f11058,plain,
( spl249_897
<=> ! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP26(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$q'(X0,sK181(X0,X1,X2)))
| ( 'none$b' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_897])]) ).
tff(f2931,plain,
! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP26(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$q'(X0,sK181(X0,X1,X2)))
| ( 'none$b' = X2 ) ),
inference(cnf_transformation,[],[f1699]) ).
tff(f11056,plain,
spl249_896,
inference(avatar_split_clause,[],[f2930,f11054]) ).
tff(f11054,plain,
( spl249_896
<=> ! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP26(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK181(X0,X1,X2)) = X2 )
| ~ 'fun_app$aw'(X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_896])]) ).
tff(f2930,plain,
! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP26(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK181(X0,X1,X2)) = X2 )
| ~ 'fun_app$aw'(X1,'none$b') ),
inference(cnf_transformation,[],[f1699]) ).
tff(f11052,plain,
spl249_895,
inference(avatar_split_clause,[],[f2929,f11050]) ).
tff(f11050,plain,
( spl249_895
<=> ! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP26(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK181(X0,X1,X2)) = X2 )
| ( 'none$b' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_895])]) ).
tff(f2929,plain,
! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP26(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK181(X0,X1,X2)) = X2 )
| ( 'none$b' = X2 ) ),
inference(cnf_transformation,[],[f1699]) ).
tff(f11048,plain,
spl249_894,
inference(avatar_split_clause,[],[f2896,f11046]) ).
tff(f11046,plain,
( spl249_894
<=> ! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP24(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK180(X0,X1,X2)) = X2 )
| ~ 'fun_app$a'(X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_894])]) ).
tff(f2896,plain,
! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP24(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK180(X0,X1,X2)) = X2 )
| ~ 'fun_app$a'(X1,'none$a') ),
inference(cnf_transformation,[],[f1680]) ).
tff(f11044,plain,
spl249_893,
inference(avatar_split_clause,[],[f2895,f11042]) ).
tff(f11042,plain,
( spl249_893
<=> ! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP24(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK180(X0,X1,X2)) = X2 )
| ( 'none$' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_893])]) ).
tff(f2895,plain,
! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP24(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK180(X0,X1,X2)) = X2 )
| ( 'none$' = X2 ) ),
inference(cnf_transformation,[],[f1680]) ).
tff(f11040,plain,
spl249_892,
inference(avatar_split_clause,[],[f2888,f11038]) ).
tff(f11038,plain,
( spl249_892
<=> ! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP23(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK179(X0,X1,X2)) = X2 )
| ~ 'fun_app$a'(X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_892])]) ).
tff(f2888,plain,
! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP23(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK179(X0,X1,X2)) = X2 )
| ~ 'fun_app$a'(X1,'none$a') ),
inference(cnf_transformation,[],[f1674]) ).
tff(f11036,plain,
spl249_891,
inference(avatar_split_clause,[],[f2887,f11034]) ).
tff(f11034,plain,
( spl249_891
<=> ! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP23(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK179(X0,X1,X2)) = X2 )
| ( 'none$' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_891])]) ).
tff(f2887,plain,
! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP23(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK179(X0,X1,X2)) = X2 )
| ( 'none$' = X2 ) ),
inference(cnf_transformation,[],[f1674]) ).
tff(f11032,plain,
spl249_890,
inference(avatar_split_clause,[],[f2882,f11030]) ).
tff(f11030,plain,
( spl249_890
<=> ! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP22(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$f'(X0,sK178(X0,X1,X2)))
| ~ 'fun_app$a'(X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_890])]) ).
tff(f2882,plain,
! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP22(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$f'(X0,sK178(X0,X1,X2)))
| ~ 'fun_app$a'(X1,'none$a') ),
inference(cnf_transformation,[],[f1668]) ).
tff(f1668,plain,
! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'A_option$'] :
( ( sP22(X0,X1,X2)
| ( ~ 'fun_app$a'(X1,'fun_app$f'(X0,sK178(X0,X1,X2)))
& ( 'fun_app$q'('some$b',sK178(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$a'(X1,'none$a')
& ( 'none$b' = X2 ) ) )
& ( ( ! [X4: 'A$'] :
( 'fun_app$a'(X1,'fun_app$f'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 ) )
& ( 'fun_app$a'(X1,'none$a')
| ( 'none$b' != X2 ) ) )
| ~ sP22(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK178])],[f1666,f1667]) ).
tff(f1667,plain,
! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'A_option$'] :
( ? [X3: 'A$'] :
( ~ 'fun_app$a'(X1,'fun_app$f'(X0,X3))
& ( 'fun_app$q'('some$b',X3) = X2 ) )
=> ( ~ 'fun_app$a'(X1,'fun_app$f'(X0,sK178(X0,X1,X2)))
& ( 'fun_app$q'('some$b',sK178(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1666,plain,
! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'A_option$'] :
( ( sP22(X0,X1,X2)
| ? [X3: 'A$'] :
( ~ 'fun_app$a'(X1,'fun_app$f'(X0,X3))
& ( 'fun_app$q'('some$b',X3) = X2 ) )
| ( ~ 'fun_app$a'(X1,'none$a')
& ( 'none$b' = X2 ) ) )
& ( ( ! [X4: 'A$'] :
( 'fun_app$a'(X1,'fun_app$f'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 ) )
& ( 'fun_app$a'(X1,'none$a')
| ( 'none$b' != X2 ) ) )
| ~ sP22(X0,X1,X2) ) ),
inference(rectify,[],[f1665]) ).
tff(f1665,plain,
! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( ( sP22(X2,X0,X1)
| ? [X3: 'A$'] :
( ~ 'fun_app$a'(X0,'fun_app$f'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$b' = X1 ) ) )
& ( ( ! [X3: 'A$'] :
( 'fun_app$a'(X0,'fun_app$f'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$b' != X1 ) ) )
| ~ sP22(X2,X0,X1) ) ),
inference(flattening,[],[f1664]) ).
tff(f1664,plain,
! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( ( sP22(X2,X0,X1)
| ? [X3: 'A$'] :
( ~ 'fun_app$a'(X0,'fun_app$f'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$b' = X1 ) ) )
& ( ( ! [X3: 'A$'] :
( 'fun_app$a'(X0,'fun_app$f'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$b' != X1 ) ) )
| ~ sP22(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1143]) ).
tff(f1143,plain,
! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( sP22(X2,X0,X1)
<=> ( ! [X3: 'A$'] :
( 'fun_app$a'(X0,'fun_app$f'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$b' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
tff(f11028,plain,
( spl249_889
| ~ spl249_22
| ~ spl249_685 ),
inference(avatar_split_clause,[],[f8708,f8194,f3700,f11026]) ).
tff(f11026,plain,
( spl249_889
<=> ! [X2: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ~ sP36(X0,X1,'uwg$',X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_889])]) ).
tff(f8708,plain,
( ! [X2: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ~ sP36(X0,X1,'uwg$',X2)
| ~ spl249_22
| ~ spl249_685 ),
inference(resolution,[],[f8195,f3701]) ).
tff(f11024,plain,
spl249_888,
inference(avatar_split_clause,[],[f2881,f11022]) ).
tff(f11022,plain,
( spl249_888
<=> ! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP22(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$f'(X0,sK178(X0,X1,X2)))
| ( 'none$b' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_888])]) ).
tff(f2881,plain,
! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP22(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$f'(X0,sK178(X0,X1,X2)))
| ( 'none$b' = X2 ) ),
inference(cnf_transformation,[],[f1668]) ).
tff(f11020,plain,
spl249_887,
inference(avatar_split_clause,[],[f2880,f11018]) ).
tff(f11018,plain,
( spl249_887
<=> ! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP22(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK178(X0,X1,X2)) = X2 )
| ~ 'fun_app$a'(X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_887])]) ).
tff(f2880,plain,
! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP22(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK178(X0,X1,X2)) = X2 )
| ~ 'fun_app$a'(X1,'none$a') ),
inference(cnf_transformation,[],[f1668]) ).
tff(f11016,plain,
spl249_886,
inference(avatar_split_clause,[],[f2879,f11014]) ).
tff(f11014,plain,
( spl249_886
<=> ! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP22(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK178(X0,X1,X2)) = X2 )
| ( 'none$b' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_886])]) ).
tff(f2879,plain,
! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP22(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK178(X0,X1,X2)) = X2 )
| ( 'none$b' = X2 ) ),
inference(cnf_transformation,[],[f1668]) ).
tff(f11012,plain,
spl249_885,
inference(avatar_split_clause,[],[f2874,f11010]) ).
tff(f11010,plain,
( spl249_885
<=> ! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP21(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$f'(X0,sK177(X0,X1,X2)))
| ~ 'fun_app$a'(X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_885])]) ).
tff(f2874,plain,
! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP21(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$f'(X0,sK177(X0,X1,X2)))
| ~ 'fun_app$a'(X1,'none$a') ),
inference(cnf_transformation,[],[f1662]) ).
tff(f1662,plain,
! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'A_option$'] :
( ( sP21(X0,X1,X2)
| ( ~ 'fun_app$a'(X1,'fun_app$f'(X0,sK177(X0,X1,X2)))
& ( 'fun_app$q'('some$b',sK177(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$a'(X1,'none$a')
& ( 'none$b' = X2 ) ) )
& ( ( ! [X4: 'A$'] :
( 'fun_app$a'(X1,'fun_app$f'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 ) )
& ( 'fun_app$a'(X1,'none$a')
| ( 'none$b' != X2 ) ) )
| ~ sP21(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK177])],[f1660,f1661]) ).
tff(f1661,plain,
! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'A_option$'] :
( ? [X3: 'A$'] :
( ~ 'fun_app$a'(X1,'fun_app$f'(X0,X3))
& ( 'fun_app$q'('some$b',X3) = X2 ) )
=> ( ~ 'fun_app$a'(X1,'fun_app$f'(X0,sK177(X0,X1,X2)))
& ( 'fun_app$q'('some$b',sK177(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1660,plain,
! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$',X2: 'A_option$'] :
( ( sP21(X0,X1,X2)
| ? [X3: 'A$'] :
( ~ 'fun_app$a'(X1,'fun_app$f'(X0,X3))
& ( 'fun_app$q'('some$b',X3) = X2 ) )
| ( ~ 'fun_app$a'(X1,'none$a')
& ( 'none$b' = X2 ) ) )
& ( ( ! [X4: 'A$'] :
( 'fun_app$a'(X1,'fun_app$f'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 ) )
& ( 'fun_app$a'(X1,'none$a')
| ( 'none$b' != X2 ) ) )
| ~ sP21(X0,X1,X2) ) ),
inference(rectify,[],[f1659]) ).
tff(f1659,plain,
! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( ( sP21(X2,X0,X1)
| ? [X3: 'A$'] :
( ~ 'fun_app$a'(X0,'fun_app$f'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$b' = X1 ) ) )
& ( ( ! [X3: 'A$'] :
( 'fun_app$a'(X0,'fun_app$f'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$b' != X1 ) ) )
| ~ sP21(X2,X0,X1) ) ),
inference(flattening,[],[f1658]) ).
tff(f1658,plain,
! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( ( sP21(X2,X0,X1)
| ? [X3: 'A$'] :
( ~ 'fun_app$a'(X0,'fun_app$f'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$b' = X1 ) ) )
& ( ( ! [X3: 'A$'] :
( 'fun_app$a'(X0,'fun_app$f'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$b' != X1 ) ) )
| ~ sP21(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1141]) ).
tff(f1141,plain,
! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( sP21(X2,X0,X1)
<=> ( ! [X3: 'A$'] :
( 'fun_app$a'(X0,'fun_app$f'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$b' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
tff(f11008,plain,
spl249_884,
inference(avatar_split_clause,[],[f2873,f11006]) ).
tff(f11006,plain,
( spl249_884
<=> ! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP21(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$f'(X0,sK177(X0,X1,X2)))
| ( 'none$b' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_884])]) ).
tff(f2873,plain,
! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP21(X0,X1,X2)
| ~ 'fun_app$a'(X1,'fun_app$f'(X0,sK177(X0,X1,X2)))
| ( 'none$b' = X2 ) ),
inference(cnf_transformation,[],[f1662]) ).
tff(f11004,plain,
spl249_883,
inference(avatar_split_clause,[],[f2872,f11002]) ).
tff(f11002,plain,
( spl249_883
<=> ! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP21(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK177(X0,X1,X2)) = X2 )
| ~ 'fun_app$a'(X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_883])]) ).
tff(f2872,plain,
! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP21(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK177(X0,X1,X2)) = X2 )
| ~ 'fun_app$a'(X1,'none$a') ),
inference(cnf_transformation,[],[f1662]) ).
tff(f11000,plain,
spl249_882,
inference(avatar_split_clause,[],[f2871,f10998]) ).
tff(f10998,plain,
( spl249_882
<=> ! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP21(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK177(X0,X1,X2)) = X2 )
| ( 'none$b' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_882])]) ).
tff(f2871,plain,
! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( sP21(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK177(X0,X1,X2)) = X2 )
| ( 'none$b' = X2 ) ),
inference(cnf_transformation,[],[f1662]) ).
tff(f10996,plain,
spl249_881,
inference(avatar_split_clause,[],[f2856,f10994]) ).
tff(f10994,plain,
( spl249_881
<=> ! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP19(X0,X1,X2)
| ( 'fun_app$g'('some$',sK176(X0,X1,X2)) = X2 )
| ~ 'fun_app$'(X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_881])]) ).
tff(f2856,plain,
! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP19(X0,X1,X2)
| ( 'fun_app$g'('some$',sK176(X0,X1,X2)) = X2 )
| ~ 'fun_app$'(X1,'none$') ),
inference(cnf_transformation,[],[f1652]) ).
tff(f10992,plain,
spl249_880,
inference(avatar_split_clause,[],[f2855,f10990]) ).
tff(f10990,plain,
( spl249_880
<=> ! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP19(X0,X1,X2)
| ( 'fun_app$g'('some$',sK176(X0,X1,X2)) = X2 )
| ( 'none$a' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_880])]) ).
tff(f2855,plain,
! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP19(X0,X1,X2)
| ( 'fun_app$g'('some$',sK176(X0,X1,X2)) = X2 )
| ( 'none$a' = X2 ) ),
inference(cnf_transformation,[],[f1652]) ).
tff(f10988,plain,
spl249_879,
inference(avatar_split_clause,[],[f2848,f10986]) ).
tff(f10986,plain,
( spl249_879
<=> ! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP18(X0,X1,X2)
| ( 'fun_app$g'('some$',sK175(X0,X1,X2)) = X2 )
| ~ 'fun_app$'(X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_879])]) ).
tff(f2848,plain,
! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP18(X0,X1,X2)
| ( 'fun_app$g'('some$',sK175(X0,X1,X2)) = X2 )
| ~ 'fun_app$'(X1,'none$') ),
inference(cnf_transformation,[],[f1646]) ).
tff(f10984,plain,
( spl249_878
| ~ spl249_63
| ~ spl249_156
| ~ spl249_559 ),
inference(avatar_split_clause,[],[f7615,f7203,f4293,f3891,f10982]) ).
tff(f10982,plain,
( spl249_878
<=> ! [X0: 'B$'] : ( 'fun_app$h'('id$b',X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_878])]) ).
tff(f4293,plain,
( spl249_156
<=> ! [X0: 'B$'] : ( 'fun_app$al'('the$','fun_app$g'('some$',X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_156])]) ).
tff(f7203,plain,
( spl249_559
<=> ! [X2: 'B$',X0: 'B_option_b_fun$',X1: 'B_b_option_fun$'] : ( 'fun_app$h'('comp$m'(X0,X1),X2) = 'fun_app$al'(X0,'fun_app$g'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_559])]) ).
tff(f7615,plain,
( ! [X0: 'B$'] : ( 'fun_app$h'('id$b',X0) = X0 )
| ~ spl249_63
| ~ spl249_156
| ~ spl249_559 ),
inference(forward_demodulation,[],[f7600,f3893]) ).
tff(f7600,plain,
( ! [X0: 'B$'] : ( 'fun_app$h'('comp$m'('the$','some$'),X0) = X0 )
| ~ spl249_156
| ~ spl249_559 ),
inference(superposition,[],[f7204,f4294]) ).
tff(f4294,plain,
( ! [X0: 'B$'] : ( 'fun_app$al'('the$','fun_app$g'('some$',X0)) = X0 )
| ~ spl249_156 ),
inference(avatar_component_clause,[],[f4293]) ).
tff(f7204,plain,
( ! [X2: 'B$',X0: 'B_option_b_fun$',X1: 'B_b_option_fun$'] : ( 'fun_app$h'('comp$m'(X0,X1),X2) = 'fun_app$al'(X0,'fun_app$g'(X1,X2)) )
| ~ spl249_559 ),
inference(avatar_component_clause,[],[f7203]) ).
tff(f10980,plain,
spl249_877,
inference(avatar_split_clause,[],[f2847,f10978]) ).
tff(f10978,plain,
( spl249_877
<=> ! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP18(X0,X1,X2)
| ( 'fun_app$g'('some$',sK175(X0,X1,X2)) = X2 )
| ( 'none$a' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_877])]) ).
tff(f2847,plain,
! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP18(X0,X1,X2)
| ( 'fun_app$g'('some$',sK175(X0,X1,X2)) = X2 )
| ( 'none$a' = X2 ) ),
inference(cnf_transformation,[],[f1646]) ).
tff(f10976,plain,
spl249_876,
inference(avatar_split_clause,[],[f2842,f10974]) ).
tff(f10974,plain,
( spl249_876
<=> ! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP17(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$bm'(X0,sK174(X0,X1,X2)))
| ~ 'fun_app$'(X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_876])]) ).
tff(f2842,plain,
! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP17(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$bm'(X0,sK174(X0,X1,X2)))
| ~ 'fun_app$'(X1,'none$') ),
inference(cnf_transformation,[],[f1640]) ).
tff(f1640,plain,
! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'A_option$'] :
( ( sP17(X0,X1,X2)
| ( ~ 'fun_app$'(X1,'fun_app$bm'(X0,sK174(X0,X1,X2)))
& ( 'fun_app$q'('some$b',sK174(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$'(X1,'none$')
& ( 'none$b' = X2 ) ) )
& ( ( ! [X4: 'A$'] :
( 'fun_app$'(X1,'fun_app$bm'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 ) )
& ( 'fun_app$'(X1,'none$')
| ( 'none$b' != X2 ) ) )
| ~ sP17(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK174])],[f1638,f1639]) ).
tff(f1639,plain,
! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'A_option$'] :
( ? [X3: 'A$'] :
( ~ 'fun_app$'(X1,'fun_app$bm'(X0,X3))
& ( 'fun_app$q'('some$b',X3) = X2 ) )
=> ( ~ 'fun_app$'(X1,'fun_app$bm'(X0,sK174(X0,X1,X2)))
& ( 'fun_app$q'('some$b',sK174(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1638,plain,
! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'A_option$'] :
( ( sP17(X0,X1,X2)
| ? [X3: 'A$'] :
( ~ 'fun_app$'(X1,'fun_app$bm'(X0,X3))
& ( 'fun_app$q'('some$b',X3) = X2 ) )
| ( ~ 'fun_app$'(X1,'none$')
& ( 'none$b' = X2 ) ) )
& ( ( ! [X4: 'A$'] :
( 'fun_app$'(X1,'fun_app$bm'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 ) )
& ( 'fun_app$'(X1,'none$')
| ( 'none$b' != X2 ) ) )
| ~ sP17(X0,X1,X2) ) ),
inference(rectify,[],[f1637]) ).
tff(f1637,plain,
! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( ( sP17(X2,X0,X1)
| ? [X3: 'A$'] :
( ~ 'fun_app$'(X0,'fun_app$bm'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$b' = X1 ) ) )
& ( ( ! [X3: 'A$'] :
( 'fun_app$'(X0,'fun_app$bm'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$b' != X1 ) ) )
| ~ sP17(X2,X0,X1) ) ),
inference(flattening,[],[f1636]) ).
tff(f1636,plain,
! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( ( sP17(X2,X0,X1)
| ? [X3: 'A$'] :
( ~ 'fun_app$'(X0,'fun_app$bm'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$b' = X1 ) ) )
& ( ( ! [X3: 'A$'] :
( 'fun_app$'(X0,'fun_app$bm'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$b' != X1 ) ) )
| ~ sP17(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1133]) ).
tff(f1133,plain,
! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( sP17(X2,X0,X1)
<=> ( ! [X3: 'A$'] :
( 'fun_app$'(X0,'fun_app$bm'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$b' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
tff(f10972,plain,
spl249_875,
inference(avatar_split_clause,[],[f2841,f10970]) ).
tff(f10970,plain,
( spl249_875
<=> ! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP17(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$bm'(X0,sK174(X0,X1,X2)))
| ( 'none$b' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_875])]) ).
tff(f2841,plain,
! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP17(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$bm'(X0,sK174(X0,X1,X2)))
| ( 'none$b' = X2 ) ),
inference(cnf_transformation,[],[f1640]) ).
tff(f10968,plain,
spl249_874,
inference(avatar_split_clause,[],[f2840,f10966]) ).
tff(f10966,plain,
( spl249_874
<=> ! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP17(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK174(X0,X1,X2)) = X2 )
| ~ 'fun_app$'(X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_874])]) ).
tff(f2840,plain,
! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP17(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK174(X0,X1,X2)) = X2 )
| ~ 'fun_app$'(X1,'none$') ),
inference(cnf_transformation,[],[f1640]) ).
tff(f10964,plain,
spl249_873,
inference(avatar_split_clause,[],[f2839,f10962]) ).
tff(f10962,plain,
( spl249_873
<=> ! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP17(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK174(X0,X1,X2)) = X2 )
| ( 'none$b' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_873])]) ).
tff(f2839,plain,
! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP17(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK174(X0,X1,X2)) = X2 )
| ( 'none$b' = X2 ) ),
inference(cnf_transformation,[],[f1640]) ).
tff(f10960,plain,
spl249_872,
inference(avatar_split_clause,[],[f2834,f10958]) ).
tff(f10958,plain,
( spl249_872
<=> ! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP16(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$bm'(X0,sK173(X0,X1,X2)))
| ~ 'fun_app$'(X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_872])]) ).
tff(f2834,plain,
! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP16(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$bm'(X0,sK173(X0,X1,X2)))
| ~ 'fun_app$'(X1,'none$') ),
inference(cnf_transformation,[],[f1634]) ).
tff(f1634,plain,
! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'A_option$'] :
( ( sP16(X0,X1,X2)
| ( ~ 'fun_app$'(X1,'fun_app$bm'(X0,sK173(X0,X1,X2)))
& ( 'fun_app$q'('some$b',sK173(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$'(X1,'none$')
& ( 'none$b' = X2 ) ) )
& ( ( ! [X4: 'A$'] :
( 'fun_app$'(X1,'fun_app$bm'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 ) )
& ( 'fun_app$'(X1,'none$')
| ( 'none$b' != X2 ) ) )
| ~ sP16(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK173])],[f1632,f1633]) ).
tff(f1633,plain,
! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'A_option$'] :
( ? [X3: 'A$'] :
( ~ 'fun_app$'(X1,'fun_app$bm'(X0,X3))
& ( 'fun_app$q'('some$b',X3) = X2 ) )
=> ( ~ 'fun_app$'(X1,'fun_app$bm'(X0,sK173(X0,X1,X2)))
& ( 'fun_app$q'('some$b',sK173(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1632,plain,
! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$',X2: 'A_option$'] :
( ( sP16(X0,X1,X2)
| ? [X3: 'A$'] :
( ~ 'fun_app$'(X1,'fun_app$bm'(X0,X3))
& ( 'fun_app$q'('some$b',X3) = X2 ) )
| ( ~ 'fun_app$'(X1,'none$')
& ( 'none$b' = X2 ) ) )
& ( ( ! [X4: 'A$'] :
( 'fun_app$'(X1,'fun_app$bm'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 ) )
& ( 'fun_app$'(X1,'none$')
| ( 'none$b' != X2 ) ) )
| ~ sP16(X0,X1,X2) ) ),
inference(rectify,[],[f1631]) ).
tff(f1631,plain,
! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( ( sP16(X2,X0,X1)
| ? [X3: 'A$'] :
( ~ 'fun_app$'(X0,'fun_app$bm'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$b' = X1 ) ) )
& ( ( ! [X3: 'A$'] :
( 'fun_app$'(X0,'fun_app$bm'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$b' != X1 ) ) )
| ~ sP16(X2,X0,X1) ) ),
inference(flattening,[],[f1630]) ).
tff(f1630,plain,
! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( ( sP16(X2,X0,X1)
| ? [X3: 'A$'] :
( ~ 'fun_app$'(X0,'fun_app$bm'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$b' = X1 ) ) )
& ( ( ! [X3: 'A$'] :
( 'fun_app$'(X0,'fun_app$bm'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$b' != X1 ) ) )
| ~ sP16(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1131]) ).
tff(f1131,plain,
! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( sP16(X2,X0,X1)
<=> ( ! [X3: 'A$'] :
( 'fun_app$'(X0,'fun_app$bm'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$b' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
tff(f10956,plain,
spl249_871,
inference(avatar_split_clause,[],[f2833,f10954]) ).
tff(f10954,plain,
( spl249_871
<=> ! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP16(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$bm'(X0,sK173(X0,X1,X2)))
| ( 'none$b' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_871])]) ).
tff(f2833,plain,
! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP16(X0,X1,X2)
| ~ 'fun_app$'(X1,'fun_app$bm'(X0,sK173(X0,X1,X2)))
| ( 'none$b' = X2 ) ),
inference(cnf_transformation,[],[f1634]) ).
tff(f10952,plain,
spl249_870,
inference(avatar_split_clause,[],[f2832,f10950]) ).
tff(f10950,plain,
( spl249_870
<=> ! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP16(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK173(X0,X1,X2)) = X2 )
| ~ 'fun_app$'(X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_870])]) ).
tff(f2832,plain,
! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP16(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK173(X0,X1,X2)) = X2 )
| ~ 'fun_app$'(X1,'none$') ),
inference(cnf_transformation,[],[f1634]) ).
tff(f10948,plain,
spl249_869,
inference(avatar_split_clause,[],[f2831,f10946]) ).
tff(f10946,plain,
( spl249_869
<=> ! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP16(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK173(X0,X1,X2)) = X2 )
| ( 'none$b' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_869])]) ).
tff(f2831,plain,
! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( sP16(X0,X1,X2)
| ( 'fun_app$q'('some$b',sK173(X0,X1,X2)) = X2 )
| ( 'none$b' = X2 ) ),
inference(cnf_transformation,[],[f1634]) ).
tff(f10944,plain,
spl249_868,
inference(avatar_split_clause,[],[f2826,f10942]) ).
tff(f10942,plain,
( spl249_868
<=> ! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP15(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,sK172(X0,X1,X2)))
| ~ 'fun_app$aw'(X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_868])]) ).
tff(f2826,plain,
! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP15(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,sK172(X0,X1,X2)))
| ~ 'fun_app$aw'(X1,'none$b') ),
inference(cnf_transformation,[],[f1628]) ).
tff(f1628,plain,
! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'B_option$'] :
( ( sP15(X0,X1,X2)
| ( ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,sK172(X0,X1,X2)))
& ( 'fun_app$g'('some$',sK172(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$aw'(X1,'none$b')
& ( 'none$a' = X2 ) ) )
& ( ( ! [X4: 'B$'] :
( 'fun_app$aw'(X1,'fun_app$bo'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 ) )
& ( 'fun_app$aw'(X1,'none$b')
| ( 'none$a' != X2 ) ) )
| ~ sP15(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK172])],[f1626,f1627]) ).
tff(f1627,plain,
! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'B_option$'] :
( ? [X3: 'B$'] :
( ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,X3))
& ( 'fun_app$g'('some$',X3) = X2 ) )
=> ( ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,sK172(X0,X1,X2)))
& ( 'fun_app$g'('some$',sK172(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1626,plain,
! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'B_option$'] :
( ( sP15(X0,X1,X2)
| ? [X3: 'B$'] :
( ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,X3))
& ( 'fun_app$g'('some$',X3) = X2 ) )
| ( ~ 'fun_app$aw'(X1,'none$b')
& ( 'none$a' = X2 ) ) )
& ( ( ! [X4: 'B$'] :
( 'fun_app$aw'(X1,'fun_app$bo'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 ) )
& ( 'fun_app$aw'(X1,'none$b')
| ( 'none$a' != X2 ) ) )
| ~ sP15(X0,X1,X2) ) ),
inference(rectify,[],[f1625]) ).
tff(f1625,plain,
! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( ( sP15(X2,X0,X1)
| ? [X3: 'B$'] :
( ~ 'fun_app$aw'(X0,'fun_app$bo'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$a' = X1 ) ) )
& ( ( ! [X3: 'B$'] :
( 'fun_app$aw'(X0,'fun_app$bo'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$a' != X1 ) ) )
| ~ sP15(X2,X0,X1) ) ),
inference(flattening,[],[f1624]) ).
tff(f1624,plain,
! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( ( sP15(X2,X0,X1)
| ? [X3: 'B$'] :
( ~ 'fun_app$aw'(X0,'fun_app$bo'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$a' = X1 ) ) )
& ( ( ! [X3: 'B$'] :
( 'fun_app$aw'(X0,'fun_app$bo'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$a' != X1 ) ) )
| ~ sP15(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1129]) ).
tff(f1129,plain,
! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( sP15(X2,X0,X1)
<=> ( ! [X3: 'B$'] :
( 'fun_app$aw'(X0,'fun_app$bo'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$a' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
tff(f10940,plain,
( spl249_867
| ~ spl249_62
| ~ spl249_155
| ~ spl249_558 ),
inference(avatar_split_clause,[],[f7588,f7199,f4289,f3886,f10938]) ).
tff(f10938,plain,
( spl249_867
<=> ! [X0: 'C$'] : ( 'fun_app$k'('id$a',X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_867])]) ).
tff(f3886,plain,
( spl249_62
<=> ( 'comp$n'('the$a','some$a') = 'id$a' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_62])]) ).
tff(f4289,plain,
( spl249_155
<=> ! [X0: 'C$'] : ( 'fun_app$ak'('the$a','fun_app$j'('some$a',X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_155])]) ).
tff(f7199,plain,
( spl249_558
<=> ! [X2: 'C$',X0: 'C_option_c_fun$',X1: 'C_c_option_fun$'] : ( 'fun_app$k'('comp$n'(X0,X1),X2) = 'fun_app$ak'(X0,'fun_app$j'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_558])]) ).
tff(f7588,plain,
( ! [X0: 'C$'] : ( 'fun_app$k'('id$a',X0) = X0 )
| ~ spl249_62
| ~ spl249_155
| ~ spl249_558 ),
inference(forward_demodulation,[],[f7573,f3888]) ).
tff(f3888,plain,
( ( 'comp$n'('the$a','some$a') = 'id$a' )
| ~ spl249_62 ),
inference(avatar_component_clause,[],[f3886]) ).
tff(f7573,plain,
( ! [X0: 'C$'] : ( 'fun_app$k'('comp$n'('the$a','some$a'),X0) = X0 )
| ~ spl249_155
| ~ spl249_558 ),
inference(superposition,[],[f7200,f4290]) ).
tff(f4290,plain,
( ! [X0: 'C$'] : ( 'fun_app$ak'('the$a','fun_app$j'('some$a',X0)) = X0 )
| ~ spl249_155 ),
inference(avatar_component_clause,[],[f4289]) ).
tff(f7200,plain,
( ! [X2: 'C$',X0: 'C_option_c_fun$',X1: 'C_c_option_fun$'] : ( 'fun_app$k'('comp$n'(X0,X1),X2) = 'fun_app$ak'(X0,'fun_app$j'(X1,X2)) )
| ~ spl249_558 ),
inference(avatar_component_clause,[],[f7199]) ).
tff(f10936,plain,
spl249_866,
inference(avatar_split_clause,[],[f2825,f10934]) ).
tff(f10934,plain,
( spl249_866
<=> ! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP15(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,sK172(X0,X1,X2)))
| ( 'none$a' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_866])]) ).
tff(f2825,plain,
! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP15(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,sK172(X0,X1,X2)))
| ( 'none$a' = X2 ) ),
inference(cnf_transformation,[],[f1628]) ).
tff(f10932,plain,
spl249_865,
inference(avatar_split_clause,[],[f2824,f10930]) ).
tff(f10930,plain,
( spl249_865
<=> ! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP15(X0,X1,X2)
| ( 'fun_app$g'('some$',sK172(X0,X1,X2)) = X2 )
| ~ 'fun_app$aw'(X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_865])]) ).
tff(f2824,plain,
! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP15(X0,X1,X2)
| ( 'fun_app$g'('some$',sK172(X0,X1,X2)) = X2 )
| ~ 'fun_app$aw'(X1,'none$b') ),
inference(cnf_transformation,[],[f1628]) ).
tff(f10928,plain,
spl249_864,
inference(avatar_split_clause,[],[f2823,f10926]) ).
tff(f10926,plain,
( spl249_864
<=> ! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP15(X0,X1,X2)
| ( 'fun_app$g'('some$',sK172(X0,X1,X2)) = X2 )
| ( 'none$a' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_864])]) ).
tff(f2823,plain,
! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP15(X0,X1,X2)
| ( 'fun_app$g'('some$',sK172(X0,X1,X2)) = X2 )
| ( 'none$a' = X2 ) ),
inference(cnf_transformation,[],[f1628]) ).
tff(f10924,plain,
spl249_863,
inference(avatar_split_clause,[],[f2818,f10922]) ).
tff(f10922,plain,
( spl249_863
<=> ! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP14(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,sK171(X0,X1,X2)))
| ~ 'fun_app$aw'(X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_863])]) ).
tff(f2818,plain,
! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP14(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,sK171(X0,X1,X2)))
| ~ 'fun_app$aw'(X1,'none$b') ),
inference(cnf_transformation,[],[f1622]) ).
tff(f1622,plain,
! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'C_option$'] :
( ( sP14(X0,X1,X2)
| ( ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,sK171(X0,X1,X2)))
& ( 'fun_app$j'('some$a',sK171(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$aw'(X1,'none$b')
& ( 'none$' = X2 ) ) )
& ( ( ! [X4: 'C$'] :
( 'fun_app$aw'(X1,'fun_app$bn'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 ) )
& ( 'fun_app$aw'(X1,'none$b')
| ( 'none$' != X2 ) ) )
| ~ sP14(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK171])],[f1620,f1621]) ).
tff(f1621,plain,
! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'C_option$'] :
( ? [X3: 'C$'] :
( ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,X3))
& ( 'fun_app$j'('some$a',X3) = X2 ) )
=> ( ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,sK171(X0,X1,X2)))
& ( 'fun_app$j'('some$a',sK171(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1620,plain,
! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'C_option$'] :
( ( sP14(X0,X1,X2)
| ? [X3: 'C$'] :
( ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,X3))
& ( 'fun_app$j'('some$a',X3) = X2 ) )
| ( ~ 'fun_app$aw'(X1,'none$b')
& ( 'none$' = X2 ) ) )
& ( ( ! [X4: 'C$'] :
( 'fun_app$aw'(X1,'fun_app$bn'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 ) )
& ( 'fun_app$aw'(X1,'none$b')
| ( 'none$' != X2 ) ) )
| ~ sP14(X0,X1,X2) ) ),
inference(rectify,[],[f1619]) ).
tff(f1619,plain,
! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( ( sP14(X2,X0,X1)
| ? [X3: 'C$'] :
( ~ 'fun_app$aw'(X0,'fun_app$bn'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$' = X1 ) ) )
& ( ( ! [X3: 'C$'] :
( 'fun_app$aw'(X0,'fun_app$bn'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$' != X1 ) ) )
| ~ sP14(X2,X0,X1) ) ),
inference(flattening,[],[f1618]) ).
tff(f1618,plain,
! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( ( sP14(X2,X0,X1)
| ? [X3: 'C$'] :
( ~ 'fun_app$aw'(X0,'fun_app$bn'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$' = X1 ) ) )
& ( ( ! [X3: 'C$'] :
( 'fun_app$aw'(X0,'fun_app$bn'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$' != X1 ) ) )
| ~ sP14(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1127]) ).
tff(f1127,plain,
! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( sP14(X2,X0,X1)
<=> ( ! [X3: 'C$'] :
( 'fun_app$aw'(X0,'fun_app$bn'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
tff(f10920,plain,
spl249_862,
inference(avatar_split_clause,[],[f2817,f10918]) ).
tff(f10918,plain,
( spl249_862
<=> ! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP14(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,sK171(X0,X1,X2)))
| ( 'none$' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_862])]) ).
tff(f2817,plain,
! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP14(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,sK171(X0,X1,X2)))
| ( 'none$' = X2 ) ),
inference(cnf_transformation,[],[f1622]) ).
tff(f10916,plain,
spl249_861,
inference(avatar_split_clause,[],[f2816,f10914]) ).
tff(f10914,plain,
( spl249_861
<=> ! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP14(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK171(X0,X1,X2)) = X2 )
| ~ 'fun_app$aw'(X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_861])]) ).
tff(f2816,plain,
! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP14(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK171(X0,X1,X2)) = X2 )
| ~ 'fun_app$aw'(X1,'none$b') ),
inference(cnf_transformation,[],[f1622]) ).
tff(f10912,plain,
spl249_860,
inference(avatar_split_clause,[],[f2815,f10910]) ).
tff(f10910,plain,
( spl249_860
<=> ! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP14(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK171(X0,X1,X2)) = X2 )
| ( 'none$' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_860])]) ).
tff(f2815,plain,
! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP14(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK171(X0,X1,X2)) = X2 )
| ( 'none$' = X2 ) ),
inference(cnf_transformation,[],[f1622]) ).
tff(f10908,plain,
spl249_859,
inference(avatar_split_clause,[],[f2810,f10906]) ).
tff(f10906,plain,
( spl249_859
<=> ! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP13(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,sK170(X0,X1,X2)))
| ~ 'fun_app$aw'(X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_859])]) ).
tff(f2810,plain,
! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP13(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,sK170(X0,X1,X2)))
| ~ 'fun_app$aw'(X1,'none$b') ),
inference(cnf_transformation,[],[f1616]) ).
tff(f1616,plain,
! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'B_option$'] :
( ( sP13(X0,X1,X2)
| ( ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,sK170(X0,X1,X2)))
& ( 'fun_app$g'('some$',sK170(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$aw'(X1,'none$b')
& ( 'none$a' = X2 ) ) )
& ( ( ! [X4: 'B$'] :
( 'fun_app$aw'(X1,'fun_app$bo'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 ) )
& ( 'fun_app$aw'(X1,'none$b')
| ( 'none$a' != X2 ) ) )
| ~ sP13(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK170])],[f1614,f1615]) ).
tff(f1615,plain,
! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'B_option$'] :
( ? [X3: 'B$'] :
( ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,X3))
& ( 'fun_app$g'('some$',X3) = X2 ) )
=> ( ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,sK170(X0,X1,X2)))
& ( 'fun_app$g'('some$',sK170(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1614,plain,
! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'B_option$'] :
( ( sP13(X0,X1,X2)
| ? [X3: 'B$'] :
( ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,X3))
& ( 'fun_app$g'('some$',X3) = X2 ) )
| ( ~ 'fun_app$aw'(X1,'none$b')
& ( 'none$a' = X2 ) ) )
& ( ( ! [X4: 'B$'] :
( 'fun_app$aw'(X1,'fun_app$bo'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 ) )
& ( 'fun_app$aw'(X1,'none$b')
| ( 'none$a' != X2 ) ) )
| ~ sP13(X0,X1,X2) ) ),
inference(rectify,[],[f1613]) ).
tff(f1613,plain,
! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( ( sP13(X2,X0,X1)
| ? [X3: 'B$'] :
( ~ 'fun_app$aw'(X0,'fun_app$bo'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$a' = X1 ) ) )
& ( ( ! [X3: 'B$'] :
( 'fun_app$aw'(X0,'fun_app$bo'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$a' != X1 ) ) )
| ~ sP13(X2,X0,X1) ) ),
inference(flattening,[],[f1612]) ).
tff(f1612,plain,
! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( ( sP13(X2,X0,X1)
| ? [X3: 'B$'] :
( ~ 'fun_app$aw'(X0,'fun_app$bo'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$a' = X1 ) ) )
& ( ( ! [X3: 'B$'] :
( 'fun_app$aw'(X0,'fun_app$bo'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$a' != X1 ) ) )
| ~ sP13(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1125]) ).
tff(f1125,plain,
! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( sP13(X2,X0,X1)
<=> ( ! [X3: 'B$'] :
( 'fun_app$aw'(X0,'fun_app$bo'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$a' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
tff(f10904,plain,
spl249_858,
inference(avatar_split_clause,[],[f2809,f10902]) ).
tff(f10902,plain,
( spl249_858
<=> ! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP13(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,sK170(X0,X1,X2)))
| ( 'none$a' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_858])]) ).
tff(f2809,plain,
! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP13(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bo'(X0,sK170(X0,X1,X2)))
| ( 'none$a' = X2 ) ),
inference(cnf_transformation,[],[f1616]) ).
tff(f10900,plain,
spl249_857,
inference(avatar_split_clause,[],[f2808,f10898]) ).
tff(f10898,plain,
( spl249_857
<=> ! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP13(X0,X1,X2)
| ( 'fun_app$g'('some$',sK170(X0,X1,X2)) = X2 )
| ~ 'fun_app$aw'(X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_857])]) ).
tff(f2808,plain,
! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP13(X0,X1,X2)
| ( 'fun_app$g'('some$',sK170(X0,X1,X2)) = X2 )
| ~ 'fun_app$aw'(X1,'none$b') ),
inference(cnf_transformation,[],[f1616]) ).
tff(f10896,plain,
( spl249_856
| ~ spl249_20
| ~ spl249_487 ),
inference(avatar_split_clause,[],[f6793,f6493,f3692,f10894]) ).
tff(f10894,plain,
( spl249_856
<=> ! [X0: 'B_option$'] : ( tltrue = def_21('uug$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_856])]) ).
tff(f6493,plain,
( spl249_487
<=> ! [X0: 'B_bool_fun$',X1: 'B_option$'] :
( ( tltrue = def_21(X0,X1) )
| ~ 'fun_app$c'(X0,'fun_app$al'('the$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_487])]) ).
tff(f6793,plain,
( ! [X0: 'B_option$'] : ( tltrue = def_21('uug$',X0) )
| ~ spl249_20
| ~ spl249_487 ),
inference(resolution,[],[f6494,f3693]) ).
tff(f6494,plain,
( ! [X0: 'B_bool_fun$',X1: 'B_option$'] :
( ~ 'fun_app$c'(X0,'fun_app$al'('the$',X1))
| ( tltrue = def_21(X0,X1) ) )
| ~ spl249_487 ),
inference(avatar_component_clause,[],[f6493]) ).
tff(f10892,plain,
spl249_855,
inference(avatar_split_clause,[],[f2807,f10890]) ).
tff(f10890,plain,
( spl249_855
<=> ! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP13(X0,X1,X2)
| ( 'fun_app$g'('some$',sK170(X0,X1,X2)) = X2 )
| ( 'none$a' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_855])]) ).
tff(f2807,plain,
! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP13(X0,X1,X2)
| ( 'fun_app$g'('some$',sK170(X0,X1,X2)) = X2 )
| ( 'none$a' = X2 ) ),
inference(cnf_transformation,[],[f1616]) ).
tff(f10888,plain,
spl249_854,
inference(avatar_split_clause,[],[f2802,f10886]) ).
tff(f10886,plain,
( spl249_854
<=> ! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP12(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,sK169(X0,X1,X2)))
| ~ 'fun_app$aw'(X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_854])]) ).
tff(f2802,plain,
! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP12(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,sK169(X0,X1,X2)))
| ~ 'fun_app$aw'(X1,'none$b') ),
inference(cnf_transformation,[],[f1610]) ).
tff(f1610,plain,
! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'C_option$'] :
( ( sP12(X0,X1,X2)
| ( ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,sK169(X0,X1,X2)))
& ( 'fun_app$j'('some$a',sK169(X0,X1,X2)) = X2 ) )
| ( ~ 'fun_app$aw'(X1,'none$b')
& ( 'none$' = X2 ) ) )
& ( ( ! [X4: 'C$'] :
( 'fun_app$aw'(X1,'fun_app$bn'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 ) )
& ( 'fun_app$aw'(X1,'none$b')
| ( 'none$' != X2 ) ) )
| ~ sP12(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK169])],[f1608,f1609]) ).
tff(f1609,plain,
! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'C_option$'] :
( ? [X3: 'C$'] :
( ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,X3))
& ( 'fun_app$j'('some$a',X3) = X2 ) )
=> ( ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,sK169(X0,X1,X2)))
& ( 'fun_app$j'('some$a',sK169(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1608,plain,
! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$',X2: 'C_option$'] :
( ( sP12(X0,X1,X2)
| ? [X3: 'C$'] :
( ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,X3))
& ( 'fun_app$j'('some$a',X3) = X2 ) )
| ( ~ 'fun_app$aw'(X1,'none$b')
& ( 'none$' = X2 ) ) )
& ( ( ! [X4: 'C$'] :
( 'fun_app$aw'(X1,'fun_app$bn'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 ) )
& ( 'fun_app$aw'(X1,'none$b')
| ( 'none$' != X2 ) ) )
| ~ sP12(X0,X1,X2) ) ),
inference(rectify,[],[f1607]) ).
tff(f1607,plain,
! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( ( sP12(X2,X0,X1)
| ? [X3: 'C$'] :
( ~ 'fun_app$aw'(X0,'fun_app$bn'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$' = X1 ) ) )
& ( ( ! [X3: 'C$'] :
( 'fun_app$aw'(X0,'fun_app$bn'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$' != X1 ) ) )
| ~ sP12(X2,X0,X1) ) ),
inference(flattening,[],[f1606]) ).
tff(f1606,plain,
! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( ( sP12(X2,X0,X1)
| ? [X3: 'C$'] :
( ~ 'fun_app$aw'(X0,'fun_app$bn'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$' = X1 ) ) )
& ( ( ! [X3: 'C$'] :
( 'fun_app$aw'(X0,'fun_app$bn'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$' != X1 ) ) )
| ~ sP12(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f1123]) ).
tff(f1123,plain,
! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( sP12(X2,X0,X1)
<=> ( ! [X3: 'C$'] :
( 'fun_app$aw'(X0,'fun_app$bn'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$' != X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
tff(f10884,plain,
spl249_853,
inference(avatar_split_clause,[],[f2801,f10882]) ).
tff(f10882,plain,
( spl249_853
<=> ! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP12(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,sK169(X0,X1,X2)))
| ( 'none$' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_853])]) ).
tff(f2801,plain,
! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP12(X0,X1,X2)
| ~ 'fun_app$aw'(X1,'fun_app$bn'(X0,sK169(X0,X1,X2)))
| ( 'none$' = X2 ) ),
inference(cnf_transformation,[],[f1610]) ).
tff(f10880,plain,
spl249_852,
inference(avatar_split_clause,[],[f2800,f10878]) ).
tff(f10878,plain,
( spl249_852
<=> ! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP12(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK169(X0,X1,X2)) = X2 )
| ~ 'fun_app$aw'(X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_852])]) ).
tff(f2800,plain,
! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP12(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK169(X0,X1,X2)) = X2 )
| ~ 'fun_app$aw'(X1,'none$b') ),
inference(cnf_transformation,[],[f1610]) ).
tff(f10876,plain,
spl249_851,
inference(avatar_split_clause,[],[f2799,f10874]) ).
tff(f10874,plain,
( spl249_851
<=> ! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP12(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK169(X0,X1,X2)) = X2 )
| ( 'none$' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_851])]) ).
tff(f2799,plain,
! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( sP12(X0,X1,X2)
| ( 'fun_app$j'('some$a',sK169(X0,X1,X2)) = X2 )
| ( 'none$' = X2 ) ),
inference(cnf_transformation,[],[f1610]) ).
tff(f10872,plain,
spl249_850,
inference(avatar_split_clause,[],[f2757,f10870]) ).
tff(f10870,plain,
( spl249_850
<=> ! [X2: 'B_option$',X0: 'B_option$',X1: 'B_option_b_option_bool_fun_fun$'] :
( 'fun_app$a'('fun_app$e'(X1,X0),X2)
| sP11(X2,X0,X1)
| ( 'none$a' = X2 )
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_850])]) ).
tff(f2757,plain,
! [X2: 'B_option$',X0: 'B_option$',X1: 'B_option_b_option_bool_fun_fun$'] :
( 'fun_app$a'('fun_app$e'(X1,X0),X2)
| sP11(X2,X0,X1)
| ( 'none$a' = X2 )
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f1122]) ).
tff(f1122,plain,
! [X0: 'B_option$',X1: 'B_option_b_option_bool_fun_fun$',X2: 'B_option$'] :
( 'fun_app$a'('fun_app$e'(X1,X0),X2)
| sP11(X2,X0,X1)
| ( ~ 'fun_app$a'('fun_app$e'(X1,X0),X2)
& ( 'none$a' = X2 ) )
| ( ~ 'fun_app$a'('fun_app$e'(X1,X0),X2)
& ( 'none$a' = X0 ) ) ),
inference(definition_folding,[],[f981,f1121]) ).
tff(f1121,plain,
! [X2: 'B_option$',X0: 'B_option$',X1: 'B_option_b_option_bool_fun_fun$'] :
( ? [X3: 'B$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$e'(X1,X0),X2)
& ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ~ sP11(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
tff(f981,plain,
! [X0: 'B_option$',X1: 'B_option_b_option_bool_fun_fun$',X2: 'B_option$'] :
( 'fun_app$a'('fun_app$e'(X1,X0),X2)
| ? [X3: 'B$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$e'(X1,X0),X2)
& ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ( ~ 'fun_app$a'('fun_app$e'(X1,X0),X2)
& ( 'none$a' = X2 ) )
| ( ~ 'fun_app$a'('fun_app$e'(X1,X0),X2)
& ( 'none$a' = X0 ) ) ),
inference(flattening,[],[f980]) ).
tff(f980,plain,
! [X0: 'B_option$',X1: 'B_option_b_option_bool_fun_fun$',X2: 'B_option$'] :
( 'fun_app$a'('fun_app$e'(X1,X0),X2)
| ? [X3: 'B$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$e'(X1,X0),X2)
& ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ( ~ 'fun_app$a'('fun_app$e'(X1,X0),X2)
& ( 'none$a' = X2 ) )
| ( ~ 'fun_app$a'('fun_app$e'(X1,X0),X2)
& ( 'none$a' = X0 ) ) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,axiom,
! [X0: 'B_option$',X1: 'B_option_b_option_bool_fun_fun$',X2: 'B_option$'] :
( ( ! [X3: 'B$',X4: 'B$'] :
( ( ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
=> 'fun_app$a'('fun_app$e'(X1,X0),X2) )
& ( ( 'none$a' = X2 )
=> 'fun_app$a'('fun_app$e'(X1,X0),X2) )
& ( ( 'none$a' = X0 )
=> 'fun_app$a'('fun_app$e'(X1,X0),X2) ) )
=> 'fun_app$a'('fun_app$e'(X1,X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom159) ).
tff(f10868,plain,
spl249_849,
inference(avatar_split_clause,[],[f2750,f10866]) ).
tff(f10866,plain,
( spl249_849
<=> ! [X2: 'C_option$',X0: 'B_option$',X1: 'B_option_c_option_bool_fun_fun$'] :
( 'fun_app$'('fun_app$bd'(X1,X0),X2)
| sP10(X2,X0,X1)
| ( 'none$' = X2 )
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_849])]) ).
tff(f2750,plain,
! [X2: 'C_option$',X0: 'B_option$',X1: 'B_option_c_option_bool_fun_fun$'] :
( 'fun_app$'('fun_app$bd'(X1,X0),X2)
| sP10(X2,X0,X1)
| ( 'none$' = X2 )
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f1120]) ).
tff(f1120,plain,
! [X0: 'B_option$',X1: 'B_option_c_option_bool_fun_fun$',X2: 'C_option$'] :
( 'fun_app$'('fun_app$bd'(X1,X0),X2)
| sP10(X2,X0,X1)
| ( ~ 'fun_app$'('fun_app$bd'(X1,X0),X2)
& ( 'none$' = X2 ) )
| ( ~ 'fun_app$'('fun_app$bd'(X1,X0),X2)
& ( 'none$a' = X0 ) ) ),
inference(definition_folding,[],[f979,f1119]) ).
tff(f1119,plain,
! [X2: 'C_option$',X0: 'B_option$',X1: 'B_option_c_option_bool_fun_fun$'] :
( ? [X3: 'B$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$bd'(X1,X0),X2)
& ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ~ sP10(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
tff(f979,plain,
! [X0: 'B_option$',X1: 'B_option_c_option_bool_fun_fun$',X2: 'C_option$'] :
( 'fun_app$'('fun_app$bd'(X1,X0),X2)
| ? [X3: 'B$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$bd'(X1,X0),X2)
& ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ( ~ 'fun_app$'('fun_app$bd'(X1,X0),X2)
& ( 'none$' = X2 ) )
| ( ~ 'fun_app$'('fun_app$bd'(X1,X0),X2)
& ( 'none$a' = X0 ) ) ),
inference(flattening,[],[f978]) ).
tff(f978,plain,
! [X0: 'B_option$',X1: 'B_option_c_option_bool_fun_fun$',X2: 'C_option$'] :
( 'fun_app$'('fun_app$bd'(X1,X0),X2)
| ? [X3: 'B$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$bd'(X1,X0),X2)
& ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ( ~ 'fun_app$'('fun_app$bd'(X1,X0),X2)
& ( 'none$' = X2 ) )
| ( ~ 'fun_app$'('fun_app$bd'(X1,X0),X2)
& ( 'none$a' = X0 ) ) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,axiom,
! [X0: 'B_option$',X1: 'B_option_c_option_bool_fun_fun$',X2: 'C_option$'] :
( ( ! [X3: 'B$',X4: 'C$'] :
( ( ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
=> 'fun_app$'('fun_app$bd'(X1,X0),X2) )
& ( ( 'none$' = X2 )
=> 'fun_app$'('fun_app$bd'(X1,X0),X2) )
& ( ( 'none$a' = X0 )
=> 'fun_app$'('fun_app$bd'(X1,X0),X2) ) )
=> 'fun_app$'('fun_app$bd'(X1,X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom158) ).
tff(f10864,plain,
spl249_848,
inference(avatar_split_clause,[],[f2743,f10862]) ).
tff(f10862,plain,
( spl249_848
<=> ! [X2: 'A_option$',X0: 'B_option$',X1: 'B_option_a_option_bool_fun_fun$'] :
( 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
| sP9(X2,X0,X1)
| ( 'none$b' = X2 )
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_848])]) ).
tff(f2743,plain,
! [X2: 'A_option$',X0: 'B_option$',X1: 'B_option_a_option_bool_fun_fun$'] :
( 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
| sP9(X2,X0,X1)
| ( 'none$b' = X2 )
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f1118]) ).
tff(f1118,plain,
! [X0: 'B_option$',X1: 'B_option_a_option_bool_fun_fun$',X2: 'A_option$'] :
( 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
| sP9(X2,X0,X1)
| ( ~ 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
& ( 'none$b' = X2 ) )
| ( ~ 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
& ( 'none$a' = X0 ) ) ),
inference(definition_folding,[],[f977,f1117]) ).
tff(f1117,plain,
! [X2: 'A_option$',X0: 'B_option$',X1: 'B_option_a_option_bool_fun_fun$'] :
( ? [X3: 'B$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
& ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ~ sP9(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
tff(f977,plain,
! [X0: 'B_option$',X1: 'B_option_a_option_bool_fun_fun$',X2: 'A_option$'] :
( 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
| ? [X3: 'B$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
& ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ( ~ 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
& ( 'none$b' = X2 ) )
| ( ~ 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
& ( 'none$a' = X0 ) ) ),
inference(flattening,[],[f976]) ).
tff(f976,plain,
! [X0: 'B_option$',X1: 'B_option_a_option_bool_fun_fun$',X2: 'A_option$'] :
( 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
| ? [X3: 'B$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
& ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ( ~ 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
& ( 'none$b' = X2 ) )
| ( ~ 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
& ( 'none$a' = X0 ) ) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,axiom,
! [X0: 'B_option$',X1: 'B_option_a_option_bool_fun_fun$',X2: 'A_option$'] :
( ( ! [X3: 'B$',X4: 'A$'] :
( ( ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
=> 'fun_app$aw'('fun_app$ay'(X1,X0),X2) )
& ( ( 'none$b' = X2 )
=> 'fun_app$aw'('fun_app$ay'(X1,X0),X2) )
& ( ( 'none$a' = X0 )
=> 'fun_app$aw'('fun_app$ay'(X1,X0),X2) ) )
=> 'fun_app$aw'('fun_app$ay'(X1,X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom152) ).
tff(f10860,plain,
spl249_847,
inference(avatar_split_clause,[],[f2736,f10858]) ).
tff(f10858,plain,
( spl249_847
<=> ! [X2: 'B_option$',X0: 'C_option$',X1: 'C_option_b_option_bool_fun_fun$'] :
( 'fun_app$a'('fun_app$bc'(X1,X0),X2)
| sP8(X2,X0,X1)
| ( 'none$a' = X2 )
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_847])]) ).
tff(f2736,plain,
! [X2: 'B_option$',X0: 'C_option$',X1: 'C_option_b_option_bool_fun_fun$'] :
( 'fun_app$a'('fun_app$bc'(X1,X0),X2)
| sP8(X2,X0,X1)
| ( 'none$a' = X2 )
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f1116]) ).
tff(f1116,plain,
! [X0: 'C_option$',X1: 'C_option_b_option_bool_fun_fun$',X2: 'B_option$'] :
( 'fun_app$a'('fun_app$bc'(X1,X0),X2)
| sP8(X2,X0,X1)
| ( ~ 'fun_app$a'('fun_app$bc'(X1,X0),X2)
& ( 'none$a' = X2 ) )
| ( ~ 'fun_app$a'('fun_app$bc'(X1,X0),X2)
& ( 'none$' = X0 ) ) ),
inference(definition_folding,[],[f975,f1115]) ).
tff(f1115,plain,
! [X2: 'B_option$',X0: 'C_option$',X1: 'C_option_b_option_bool_fun_fun$'] :
( ? [X3: 'C$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$bc'(X1,X0),X2)
& ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ~ sP8(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
tff(f975,plain,
! [X0: 'C_option$',X1: 'C_option_b_option_bool_fun_fun$',X2: 'B_option$'] :
( 'fun_app$a'('fun_app$bc'(X1,X0),X2)
| ? [X3: 'C$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$bc'(X1,X0),X2)
& ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ( ~ 'fun_app$a'('fun_app$bc'(X1,X0),X2)
& ( 'none$a' = X2 ) )
| ( ~ 'fun_app$a'('fun_app$bc'(X1,X0),X2)
& ( 'none$' = X0 ) ) ),
inference(flattening,[],[f974]) ).
tff(f974,plain,
! [X0: 'C_option$',X1: 'C_option_b_option_bool_fun_fun$',X2: 'B_option$'] :
( 'fun_app$a'('fun_app$bc'(X1,X0),X2)
| ? [X3: 'C$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$bc'(X1,X0),X2)
& ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ( ~ 'fun_app$a'('fun_app$bc'(X1,X0),X2)
& ( 'none$a' = X2 ) )
| ( ~ 'fun_app$a'('fun_app$bc'(X1,X0),X2)
& ( 'none$' = X0 ) ) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,axiom,
! [X0: 'C_option$',X1: 'C_option_b_option_bool_fun_fun$',X2: 'B_option$'] :
( ( ! [X3: 'C$',X4: 'B$'] :
( ( ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
=> 'fun_app$a'('fun_app$bc'(X1,X0),X2) )
& ( ( 'none$a' = X2 )
=> 'fun_app$a'('fun_app$bc'(X1,X0),X2) )
& ( ( 'none$' = X0 )
=> 'fun_app$a'('fun_app$bc'(X1,X0),X2) ) )
=> 'fun_app$a'('fun_app$bc'(X1,X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom157) ).
tff(f10856,plain,
spl249_846,
inference(avatar_split_clause,[],[f2729,f10854]) ).
tff(f10854,plain,
( spl249_846
<=> ! [X2: 'C_option$',X0: 'C_option$',X1: 'C_option_c_option_bool_fun_fun$'] :
( 'fun_app$'('fun_app$d'(X1,X0),X2)
| sP7(X2,X0,X1)
| ( 'none$' = X2 )
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_846])]) ).
tff(f2729,plain,
! [X2: 'C_option$',X0: 'C_option$',X1: 'C_option_c_option_bool_fun_fun$'] :
( 'fun_app$'('fun_app$d'(X1,X0),X2)
| sP7(X2,X0,X1)
| ( 'none$' = X2 )
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f1114]) ).
tff(f1114,plain,
! [X0: 'C_option$',X1: 'C_option_c_option_bool_fun_fun$',X2: 'C_option$'] :
( 'fun_app$'('fun_app$d'(X1,X0),X2)
| sP7(X2,X0,X1)
| ( ~ 'fun_app$'('fun_app$d'(X1,X0),X2)
& ( 'none$' = X2 ) )
| ( ~ 'fun_app$'('fun_app$d'(X1,X0),X2)
& ( 'none$' = X0 ) ) ),
inference(definition_folding,[],[f973,f1113]) ).
tff(f1113,plain,
! [X2: 'C_option$',X0: 'C_option$',X1: 'C_option_c_option_bool_fun_fun$'] :
( ? [X3: 'C$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$d'(X1,X0),X2)
& ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ~ sP7(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
tff(f973,plain,
! [X0: 'C_option$',X1: 'C_option_c_option_bool_fun_fun$',X2: 'C_option$'] :
( 'fun_app$'('fun_app$d'(X1,X0),X2)
| ? [X3: 'C$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$d'(X1,X0),X2)
& ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ( ~ 'fun_app$'('fun_app$d'(X1,X0),X2)
& ( 'none$' = X2 ) )
| ( ~ 'fun_app$'('fun_app$d'(X1,X0),X2)
& ( 'none$' = X0 ) ) ),
inference(flattening,[],[f972]) ).
tff(f972,plain,
! [X0: 'C_option$',X1: 'C_option_c_option_bool_fun_fun$',X2: 'C_option$'] :
( 'fun_app$'('fun_app$d'(X1,X0),X2)
| ? [X3: 'C$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$d'(X1,X0),X2)
& ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ( ~ 'fun_app$'('fun_app$d'(X1,X0),X2)
& ( 'none$' = X2 ) )
| ( ~ 'fun_app$'('fun_app$d'(X1,X0),X2)
& ( 'none$' = X0 ) ) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,axiom,
! [X0: 'C_option$',X1: 'C_option_c_option_bool_fun_fun$',X2: 'C_option$'] :
( ( ! [X3: 'C$',X4: 'C$'] :
( ( ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
=> 'fun_app$'('fun_app$d'(X1,X0),X2) )
& ( ( 'none$' = X2 )
=> 'fun_app$'('fun_app$d'(X1,X0),X2) )
& ( ( 'none$' = X0 )
=> 'fun_app$'('fun_app$d'(X1,X0),X2) ) )
=> 'fun_app$'('fun_app$d'(X1,X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom156) ).
tff(f10852,plain,
( spl249_845
| ~ spl249_20
| ~ spl249_484 ),
inference(avatar_split_clause,[],[f6782,f6481,f3692,f10850]) ).
tff(f10850,plain,
( spl249_845
<=> ! [X0: 'B_option$'] : ( tltrue = def_17('uug$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_845])]) ).
tff(f6481,plain,
( spl249_484
<=> ! [X0: 'B_bool_fun$',X1: 'B_option$'] :
( ( tltrue = def_17(X0,X1) )
| ~ 'fun_app$c'(X0,'fun_app$al'('the$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_484])]) ).
tff(f6782,plain,
( ! [X0: 'B_option$'] : ( tltrue = def_17('uug$',X0) )
| ~ spl249_20
| ~ spl249_484 ),
inference(resolution,[],[f6482,f3693]) ).
tff(f6482,plain,
( ! [X0: 'B_bool_fun$',X1: 'B_option$'] :
( ~ 'fun_app$c'(X0,'fun_app$al'('the$',X1))
| ( tltrue = def_17(X0,X1) ) )
| ~ spl249_484 ),
inference(avatar_component_clause,[],[f6481]) ).
tff(f10848,plain,
spl249_844,
inference(avatar_split_clause,[],[f2722,f10846]) ).
tff(f10846,plain,
( spl249_844
<=> ! [X2: 'A_option$',X0: 'C_option$',X1: 'C_option_a_option_bool_fun_fun$'] :
( 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
| sP6(X2,X0,X1)
| ( 'none$b' = X2 )
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_844])]) ).
tff(f2722,plain,
! [X2: 'A_option$',X0: 'C_option$',X1: 'C_option_a_option_bool_fun_fun$'] :
( 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
| sP6(X2,X0,X1)
| ( 'none$b' = X2 )
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f1112]) ).
tff(f1112,plain,
! [X0: 'C_option$',X1: 'C_option_a_option_bool_fun_fun$',X2: 'A_option$'] :
( 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
| sP6(X2,X0,X1)
| ( ~ 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
& ( 'none$b' = X2 ) )
| ( ~ 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
& ( 'none$' = X0 ) ) ),
inference(definition_folding,[],[f971,f1111]) ).
tff(f1111,plain,
! [X2: 'A_option$',X0: 'C_option$',X1: 'C_option_a_option_bool_fun_fun$'] :
( ? [X3: 'C$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
& ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ~ sP6(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
tff(f971,plain,
! [X0: 'C_option$',X1: 'C_option_a_option_bool_fun_fun$',X2: 'A_option$'] :
( 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
| ? [X3: 'C$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
& ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ( ~ 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
& ( 'none$b' = X2 ) )
| ( ~ 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
& ( 'none$' = X0 ) ) ),
inference(flattening,[],[f970]) ).
tff(f970,plain,
! [X0: 'C_option$',X1: 'C_option_a_option_bool_fun_fun$',X2: 'A_option$'] :
( 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
| ? [X3: 'C$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
& ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ( ~ 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
& ( 'none$b' = X2 ) )
| ( ~ 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
& ( 'none$' = X0 ) ) ),
inference(ennf_transformation,[],[f153]) ).
tff(f153,axiom,
! [X0: 'C_option$',X1: 'C_option_a_option_bool_fun_fun$',X2: 'A_option$'] :
( ( ! [X3: 'C$',X4: 'A$'] :
( ( ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
=> 'fun_app$aw'('fun_app$ax'(X1,X0),X2) )
& ( ( 'none$b' = X2 )
=> 'fun_app$aw'('fun_app$ax'(X1,X0),X2) )
& ( ( 'none$' = X0 )
=> 'fun_app$aw'('fun_app$ax'(X1,X0),X2) ) )
=> 'fun_app$aw'('fun_app$ax'(X1,X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom151) ).
tff(f10844,plain,
spl249_843,
inference(avatar_split_clause,[],[f2715,f10842]) ).
tff(f10842,plain,
( spl249_843
<=> ! [X2: 'B_option$',X0: 'A_option$',X1: 'A_option_b_option_bool_fun_fun$'] :
( 'fun_app$a'('fun_app$ba'(X1,X0),X2)
| sP5(X2,X0,X1)
| ( 'none$a' = X2 )
| ( 'none$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_843])]) ).
tff(f2715,plain,
! [X2: 'B_option$',X0: 'A_option$',X1: 'A_option_b_option_bool_fun_fun$'] :
( 'fun_app$a'('fun_app$ba'(X1,X0),X2)
| sP5(X2,X0,X1)
| ( 'none$a' = X2 )
| ( 'none$b' = X0 ) ),
inference(cnf_transformation,[],[f1110]) ).
tff(f1110,plain,
! [X0: 'A_option$',X1: 'A_option_b_option_bool_fun_fun$',X2: 'B_option$'] :
( 'fun_app$a'('fun_app$ba'(X1,X0),X2)
| sP5(X2,X0,X1)
| ( ~ 'fun_app$a'('fun_app$ba'(X1,X0),X2)
& ( 'none$a' = X2 ) )
| ( ~ 'fun_app$a'('fun_app$ba'(X1,X0),X2)
& ( 'none$b' = X0 ) ) ),
inference(definition_folding,[],[f969,f1109]) ).
tff(f1109,plain,
! [X2: 'B_option$',X0: 'A_option$',X1: 'A_option_b_option_bool_fun_fun$'] :
( ? [X3: 'A$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$ba'(X1,X0),X2)
& ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ~ sP5(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
tff(f969,plain,
! [X0: 'A_option$',X1: 'A_option_b_option_bool_fun_fun$',X2: 'B_option$'] :
( 'fun_app$a'('fun_app$ba'(X1,X0),X2)
| ? [X3: 'A$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$ba'(X1,X0),X2)
& ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ( ~ 'fun_app$a'('fun_app$ba'(X1,X0),X2)
& ( 'none$a' = X2 ) )
| ( ~ 'fun_app$a'('fun_app$ba'(X1,X0),X2)
& ( 'none$b' = X0 ) ) ),
inference(flattening,[],[f968]) ).
tff(f968,plain,
! [X0: 'A_option$',X1: 'A_option_b_option_bool_fun_fun$',X2: 'B_option$'] :
( 'fun_app$a'('fun_app$ba'(X1,X0),X2)
| ? [X3: 'A$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$ba'(X1,X0),X2)
& ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ( ~ 'fun_app$a'('fun_app$ba'(X1,X0),X2)
& ( 'none$a' = X2 ) )
| ( ~ 'fun_app$a'('fun_app$ba'(X1,X0),X2)
& ( 'none$b' = X0 ) ) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,axiom,
! [X0: 'A_option$',X1: 'A_option_b_option_bool_fun_fun$',X2: 'B_option$'] :
( ( ! [X3: 'A$',X4: 'B$'] :
( ( ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
=> 'fun_app$a'('fun_app$ba'(X1,X0),X2) )
& ( ( 'none$a' = X2 )
=> 'fun_app$a'('fun_app$ba'(X1,X0),X2) )
& ( ( 'none$b' = X0 )
=> 'fun_app$a'('fun_app$ba'(X1,X0),X2) ) )
=> 'fun_app$a'('fun_app$ba'(X1,X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom154) ).
tff(f10840,plain,
spl249_842,
inference(avatar_split_clause,[],[f2708,f10838]) ).
tff(f10838,plain,
( spl249_842
<=> ! [X2: 'C_option$',X0: 'A_option$',X1: 'A_option_c_option_bool_fun_fun$'] :
( 'fun_app$'('fun_app$az'(X1,X0),X2)
| sP4(X2,X0,X1)
| ( 'none$' = X2 )
| ( 'none$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_842])]) ).
tff(f2708,plain,
! [X2: 'C_option$',X0: 'A_option$',X1: 'A_option_c_option_bool_fun_fun$'] :
( 'fun_app$'('fun_app$az'(X1,X0),X2)
| sP4(X2,X0,X1)
| ( 'none$' = X2 )
| ( 'none$b' = X0 ) ),
inference(cnf_transformation,[],[f1108]) ).
tff(f1108,plain,
! [X0: 'A_option$',X1: 'A_option_c_option_bool_fun_fun$',X2: 'C_option$'] :
( 'fun_app$'('fun_app$az'(X1,X0),X2)
| sP4(X2,X0,X1)
| ( ~ 'fun_app$'('fun_app$az'(X1,X0),X2)
& ( 'none$' = X2 ) )
| ( ~ 'fun_app$'('fun_app$az'(X1,X0),X2)
& ( 'none$b' = X0 ) ) ),
inference(definition_folding,[],[f967,f1107]) ).
tff(f1107,plain,
! [X2: 'C_option$',X0: 'A_option$',X1: 'A_option_c_option_bool_fun_fun$'] :
( ? [X3: 'A$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$az'(X1,X0),X2)
& ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ~ sP4(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
tff(f967,plain,
! [X0: 'A_option$',X1: 'A_option_c_option_bool_fun_fun$',X2: 'C_option$'] :
( 'fun_app$'('fun_app$az'(X1,X0),X2)
| ? [X3: 'A$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$az'(X1,X0),X2)
& ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ( ~ 'fun_app$'('fun_app$az'(X1,X0),X2)
& ( 'none$' = X2 ) )
| ( ~ 'fun_app$'('fun_app$az'(X1,X0),X2)
& ( 'none$b' = X0 ) ) ),
inference(flattening,[],[f966]) ).
tff(f966,plain,
! [X0: 'A_option$',X1: 'A_option_c_option_bool_fun_fun$',X2: 'C_option$'] :
( 'fun_app$'('fun_app$az'(X1,X0),X2)
| ? [X3: 'A$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$az'(X1,X0),X2)
& ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ( ~ 'fun_app$'('fun_app$az'(X1,X0),X2)
& ( 'none$' = X2 ) )
| ( ~ 'fun_app$'('fun_app$az'(X1,X0),X2)
& ( 'none$b' = X0 ) ) ),
inference(ennf_transformation,[],[f155]) ).
tff(f155,axiom,
! [X0: 'A_option$',X1: 'A_option_c_option_bool_fun_fun$',X2: 'C_option$'] :
( ( ! [X3: 'A$',X4: 'C$'] :
( ( ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
=> 'fun_app$'('fun_app$az'(X1,X0),X2) )
& ( ( 'none$' = X2 )
=> 'fun_app$'('fun_app$az'(X1,X0),X2) )
& ( ( 'none$b' = X0 )
=> 'fun_app$'('fun_app$az'(X1,X0),X2) ) )
=> 'fun_app$'('fun_app$az'(X1,X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom153) ).
tff(f10836,plain,
spl249_841,
inference(avatar_split_clause,[],[f2701,f10834]) ).
tff(f10834,plain,
( spl249_841
<=> ! [X2: 'A_option$',X0: 'A_option$',X1: 'A_option_a_option_bool_fun_fun$'] :
( 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
| sP3(X2,X0,X1)
| ( 'none$b' = X2 )
| ( 'none$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_841])]) ).
tff(f2701,plain,
! [X2: 'A_option$',X0: 'A_option$',X1: 'A_option_a_option_bool_fun_fun$'] :
( 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
| sP3(X2,X0,X1)
| ( 'none$b' = X2 )
| ( 'none$b' = X0 ) ),
inference(cnf_transformation,[],[f1106]) ).
tff(f1106,plain,
! [X0: 'A_option$',X1: 'A_option_a_option_bool_fun_fun$',X2: 'A_option$'] :
( 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
| sP3(X2,X0,X1)
| ( ~ 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
& ( 'none$b' = X2 ) )
| ( ~ 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
& ( 'none$b' = X0 ) ) ),
inference(definition_folding,[],[f965,f1105]) ).
tff(f1105,plain,
! [X2: 'A_option$',X0: 'A_option$',X1: 'A_option_a_option_bool_fun_fun$'] :
( ? [X3: 'A$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
& ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ~ sP3(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
tff(f965,plain,
! [X0: 'A_option$',X1: 'A_option_a_option_bool_fun_fun$',X2: 'A_option$'] :
( 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
| ? [X3: 'A$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
& ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ( ~ 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
& ( 'none$b' = X2 ) )
| ( ~ 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
& ( 'none$b' = X0 ) ) ),
inference(flattening,[],[f964]) ).
tff(f964,plain,
! [X0: 'A_option$',X1: 'A_option_a_option_bool_fun_fun$',X2: 'A_option$'] :
( 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
| ? [X3: 'A$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
& ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ( ~ 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
& ( 'none$b' = X2 ) )
| ( ~ 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
& ( 'none$b' = X0 ) ) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,axiom,
! [X0: 'A_option$',X1: 'A_option_a_option_bool_fun_fun$',X2: 'A_option$'] :
( ( ! [X3: 'A$',X4: 'A$'] :
( ( ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
=> 'fun_app$aw'('fun_app$bb'(X1,X0),X2) )
& ( ( 'none$b' = X2 )
=> 'fun_app$aw'('fun_app$bb'(X1,X0),X2) )
& ( ( 'none$b' = X0 )
=> 'fun_app$aw'('fun_app$bb'(X1,X0),X2) ) )
=> 'fun_app$aw'('fun_app$bb'(X1,X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom155) ).
tff(f10832,plain,
spl249_840,
inference(avatar_split_clause,[],[f2695,f10830]) ).
tff(f10830,plain,
( spl249_840
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ( 'fun_app$g'('some$',sK136(X1,X2)) = X2 )
| ( tltrue = X0 )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_840])]) ).
tff(f2695,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ( 'fun_app$g'('some$',sK136(X1,X2)) = X2 )
| ( tltrue = X0 )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1538]) ).
tff(f1538,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( ( 'fun_app$c'(X1,sK136(X1,X2))
& ( 'fun_app$g'('some$',sK136(X1,X2)) = X2 ) )
| ( ( tltrue = X0 )
& ( 'none$a' = X2 ) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK136])],[f963,f1537]) ).
tff(f1537,plain,
! [X1: 'B_bool_fun$',X2: 'B_option$'] :
( ? [X3: 'B$'] :
( 'fun_app$c'(X1,X3)
& ( 'fun_app$g'('some$',X3) = X2 ) )
=> ( 'fun_app$c'(X1,sK136(X1,X2))
& ( 'fun_app$g'('some$',sK136(X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f963,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( ? [X3: 'B$'] :
( 'fun_app$c'(X1,X3)
& ( 'fun_app$g'('some$',X3) = X2 ) )
| ( ( tltrue = X0 )
& ( 'none$a' = X2 ) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(ennf_transformation,[],[f833]) ).
tff(f833,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
~ ( ! [X3: 'B$'] :
~ ( 'fun_app$c'(X1,X3)
& ( 'fun_app$g'('some$',X3) = X2 ) )
& ~ ( ( tltrue = X0 )
& ( 'none$a' = X2 ) )
& 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(true_and_false_elimination,[],[f134]) ).
tff(f134,axiom,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( ( ! [X3: 'B$'] :
( ( 'fun_app$c'(X1,X3)
& ( 'fun_app$g'('some$',X3) = X2 ) )
=> $false )
& ( ( ( tltrue = X0 )
& ( 'none$a' = X2 ) )
=> $false )
& 'fun_app$a'('case_option$e'(X0,X1),X2) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom132) ).
tff(f10828,plain,
spl249_839,
inference(avatar_split_clause,[],[f2694,f10826]) ).
tff(f10826,plain,
( spl249_839
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ( 'fun_app$g'('some$',sK136(X1,X2)) = X2 )
| ( 'none$a' = X2 )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_839])]) ).
tff(f2694,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ( 'fun_app$g'('some$',sK136(X1,X2)) = X2 )
| ( 'none$a' = X2 )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1538]) ).
tff(f10824,plain,
spl249_838,
inference(avatar_split_clause,[],[f2691,f10822]) ).
tff(f10822,plain,
( spl249_838
<=> ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ( 'fun_app$j'('some$a',sK135(X1,X2)) = X2 )
| ( tltrue = X0 )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_838])]) ).
tff(f2691,plain,
! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ( 'fun_app$j'('some$a',sK135(X1,X2)) = X2 )
| ( tltrue = X0 )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1536]) ).
tff(f1536,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( ( 'fun_app$b'(X1,sK135(X1,X2))
& ( 'fun_app$j'('some$a',sK135(X1,X2)) = X2 ) )
| ( ( tltrue = X0 )
& ( 'none$' = X2 ) )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK135])],[f962,f1535]) ).
tff(f1535,plain,
! [X1: 'C_bool_fun$',X2: 'C_option$'] :
( ? [X3: 'C$'] :
( 'fun_app$b'(X1,X3)
& ( 'fun_app$j'('some$a',X3) = X2 ) )
=> ( 'fun_app$b'(X1,sK135(X1,X2))
& ( 'fun_app$j'('some$a',sK135(X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f962,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( ? [X3: 'C$'] :
( 'fun_app$b'(X1,X3)
& ( 'fun_app$j'('some$a',X3) = X2 ) )
| ( ( tltrue = X0 )
& ( 'none$' = X2 ) )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(ennf_transformation,[],[f832]) ).
tff(f832,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
~ ( ! [X3: 'C$'] :
~ ( 'fun_app$b'(X1,X3)
& ( 'fun_app$j'('some$a',X3) = X2 ) )
& ~ ( ( tltrue = X0 )
& ( 'none$' = X2 ) )
& 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(true_and_false_elimination,[],[f133]) ).
tff(f133,axiom,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( ( ! [X3: 'C$'] :
( ( 'fun_app$b'(X1,X3)
& ( 'fun_app$j'('some$a',X3) = X2 ) )
=> $false )
& ( ( ( tltrue = X0 )
& ( 'none$' = X2 ) )
=> $false )
& 'fun_app$'('case_option$f'(X0,X1),X2) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom131) ).
tff(f10820,plain,
spl249_837,
inference(avatar_split_clause,[],[f2690,f10818]) ).
tff(f10818,plain,
( spl249_837
<=> ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ( 'fun_app$j'('some$a',sK135(X1,X2)) = X2 )
| ( 'none$' = X2 )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_837])]) ).
tff(f2690,plain,
! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ( 'fun_app$j'('some$a',sK135(X1,X2)) = X2 )
| ( 'none$' = X2 )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1536]) ).
tff(f10816,plain,
spl249_836,
inference(avatar_split_clause,[],[f2687,f10814]) ).
tff(f10814,plain,
( spl249_836
<=> ! [X2: 'A_option$',X0: tlbool,X1: 'A_bool_fun$'] :
( ( 'fun_app$q'('some$b',sK134(X1,X2)) = X2 )
| ( tltrue = X0 )
| ~ 'fun_app$aw'('case_option$g'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_836])]) ).
tff(f2687,plain,
! [X2: 'A_option$',X0: tlbool,X1: 'A_bool_fun$'] :
( ( 'fun_app$q'('some$b',sK134(X1,X2)) = X2 )
| ( tltrue = X0 )
| ~ 'fun_app$aw'('case_option$g'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1534]) ).
tff(f1534,plain,
! [X0: tlbool,X1: 'A_bool_fun$',X2: 'A_option$'] :
( ( 'fun_app$z'(X1,sK134(X1,X2))
& ( 'fun_app$q'('some$b',sK134(X1,X2)) = X2 ) )
| ( ( tltrue = X0 )
& ( 'none$b' = X2 ) )
| ~ 'fun_app$aw'('case_option$g'(X0,X1),X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK134])],[f961,f1533]) ).
tff(f1533,plain,
! [X1: 'A_bool_fun$',X2: 'A_option$'] :
( ? [X3: 'A$'] :
( 'fun_app$z'(X1,X3)
& ( 'fun_app$q'('some$b',X3) = X2 ) )
=> ( 'fun_app$z'(X1,sK134(X1,X2))
& ( 'fun_app$q'('some$b',sK134(X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f961,plain,
! [X0: tlbool,X1: 'A_bool_fun$',X2: 'A_option$'] :
( ? [X3: 'A$'] :
( 'fun_app$z'(X1,X3)
& ( 'fun_app$q'('some$b',X3) = X2 ) )
| ( ( tltrue = X0 )
& ( 'none$b' = X2 ) )
| ~ 'fun_app$aw'('case_option$g'(X0,X1),X2) ),
inference(ennf_transformation,[],[f831]) ).
tff(f831,plain,
! [X0: tlbool,X1: 'A_bool_fun$',X2: 'A_option$'] :
~ ( ! [X3: 'A$'] :
~ ( 'fun_app$z'(X1,X3)
& ( 'fun_app$q'('some$b',X3) = X2 ) )
& ~ ( ( tltrue = X0 )
& ( 'none$b' = X2 ) )
& 'fun_app$aw'('case_option$g'(X0,X1),X2) ),
inference(true_and_false_elimination,[],[f132]) ).
tff(f132,axiom,
! [X0: tlbool,X1: 'A_bool_fun$',X2: 'A_option$'] :
( ( ! [X3: 'A$'] :
( ( 'fun_app$z'(X1,X3)
& ( 'fun_app$q'('some$b',X3) = X2 ) )
=> $false )
& ( ( ( tltrue = X0 )
& ( 'none$b' = X2 ) )
=> $false )
& 'fun_app$aw'('case_option$g'(X0,X1),X2) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom130) ).
tff(f10812,plain,
spl249_835,
inference(avatar_split_clause,[],[f2686,f10810]) ).
tff(f10810,plain,
( spl249_835
<=> ! [X2: 'A_option$',X0: tlbool,X1: 'A_bool_fun$'] :
( ( 'fun_app$q'('some$b',sK134(X1,X2)) = X2 )
| ( 'none$b' = X2 )
| ~ 'fun_app$aw'('case_option$g'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_835])]) ).
tff(f2686,plain,
! [X2: 'A_option$',X0: tlbool,X1: 'A_bool_fun$'] :
( ( 'fun_app$q'('some$b',sK134(X1,X2)) = X2 )
| ( 'none$b' = X2 )
| ~ 'fun_app$aw'('case_option$g'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1534]) ).
tff(f10808,plain,
( spl249_834
| ~ spl249_18
| ~ spl249_482 ),
inference(avatar_split_clause,[],[f6775,f6473,f3684,f10806]) ).
tff(f10806,plain,
( spl249_834
<=> ! [X0: 'C_option$'] : ( tltrue = def_19('uuf$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_834])]) ).
tff(f6473,plain,
( spl249_482
<=> ! [X0: 'C_bool_fun$',X1: 'C_option$'] :
( ( tltrue = def_19(X0,X1) )
| ~ 'fun_app$b'(X0,'fun_app$ak'('the$a',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_482])]) ).
tff(f6775,plain,
( ! [X0: 'C_option$'] : ( tltrue = def_19('uuf$',X0) )
| ~ spl249_18
| ~ spl249_482 ),
inference(resolution,[],[f6474,f3685]) ).
tff(f6474,plain,
( ! [X0: 'C_bool_fun$',X1: 'C_option$'] :
( ~ 'fun_app$b'(X0,'fun_app$ak'('the$a',X1))
| ( tltrue = def_19(X0,X1) ) )
| ~ spl249_482 ),
inference(avatar_component_clause,[],[f6473]) ).
tff(f10804,plain,
spl249_833,
inference(avatar_split_clause,[],[f2658,f10802]) ).
tff(f10802,plain,
( spl249_833
<=> ! [X2: 'B_b_option_fun$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ( 'fun_app$ac'('bind$c'('fun_app$ac'('bind$c'(X0),X1)),X2) = 'fun_app$ac'('bind$c'(X0),'fun_app$ad'('uvt$'(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_833])]) ).
tff(f2658,plain,
! [X2: 'B_b_option_fun$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ( 'fun_app$ac'('bind$c'('fun_app$ac'('bind$c'(X0),X1)),X2) = 'fun_app$ac'('bind$c'(X0),'fun_app$ad'('uvt$'(X1),X2)) ),
inference(cnf_transformation,[],[f355]) ).
tff(f355,axiom,
! [X0: 'B_option$',X1: 'B_b_option_fun$',X2: 'B_b_option_fun$'] : ( 'fun_app$ac'('bind$c'('fun_app$ac'('bind$c'(X0),X1)),X2) = 'fun_app$ac'('bind$c'(X0),'fun_app$ad'('uvt$'(X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom353) ).
tff(f10800,plain,
spl249_832,
inference(avatar_split_clause,[],[f2657,f10798]) ).
tff(f10798,plain,
( spl249_832
<=> ! [X2: 'C_c_option_fun$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ( 'fun_app$ab'('bind$'('fun_app$ab'('bind$'(X0),X1)),X2) = 'fun_app$ab'('bind$'(X0),'fun_app$aa'('uwa$'(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_832])]) ).
tff(f2657,plain,
! [X2: 'C_c_option_fun$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ( 'fun_app$ab'('bind$'('fun_app$ab'('bind$'(X0),X1)),X2) = 'fun_app$ab'('bind$'(X0),'fun_app$aa'('uwa$'(X1),X2)) ),
inference(cnf_transformation,[],[f362]) ).
tff(f362,axiom,
! [X0: 'C_option$',X1: 'C_c_option_fun$',X2: 'C_c_option_fun$'] : ( 'fun_app$ab'('bind$'('fun_app$ab'('bind$'(X0),X1)),X2) = 'fun_app$ab'('bind$'(X0),'fun_app$aa'('uwa$'(X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom360) ).
tff(f10796,plain,
spl249_831,
inference(avatar_split_clause,[],[f2446,f10794]) ).
tff(f10794,plain,
( spl249_831
<=> ! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'('is_none$','fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| 'fun_app$aw'('is_none$b',X0)
| ~ 'fun_app$a'('is_none$','bind$e'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_831])]) ).
tff(f2446,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'('is_none$','fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| 'fun_app$aw'('is_none$b',X0)
| ~ 'fun_app$a'('is_none$','bind$e'(X0,X1)) ),
inference(cnf_transformation,[],[f1481]) ).
tff(f1481,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( ( 'fun_app$a'('is_none$','bind$e'(X0,X1))
| ( ~ 'fun_app$a'('is_none$','fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
& ~ 'fun_app$aw'('is_none$b',X0) ) )
& ( 'fun_app$a'('is_none$','fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| 'fun_app$aw'('is_none$b',X0)
| ~ 'fun_app$a'('is_none$','bind$e'(X0,X1)) ) ),
inference(flattening,[],[f1480]) ).
tff(f1480,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( ( 'fun_app$a'('is_none$','bind$e'(X0,X1))
| ( ~ 'fun_app$a'('is_none$','fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
& ~ 'fun_app$aw'('is_none$b',X0) ) )
& ( 'fun_app$a'('is_none$','fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| 'fun_app$aw'('is_none$b',X0)
| ~ 'fun_app$a'('is_none$','bind$e'(X0,X1)) ) ),
inference(nnf_transformation,[],[f395]) ).
tff(f395,axiom,
! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$e'(X0,X1))
<=> ( 'fun_app$a'('is_none$','fun_app$f'(X1,'fun_app$bf'('the$b',X0)))
| 'fun_app$aw'('is_none$b',X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom393) ).
tff(f10792,plain,
spl249_830,
inference(avatar_split_clause,[],[f2434,f10790]) ).
tff(f10790,plain,
( spl249_830
<=> ! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( 'fun_app$'('is_none$a','fun_app$bm'(X1,'fun_app$bf'('the$b',X0)))
| 'fun_app$aw'('is_none$b',X0)
| ~ 'fun_app$'('is_none$a','bind$d'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_830])]) ).
tff(f2434,plain,
! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( 'fun_app$'('is_none$a','fun_app$bm'(X1,'fun_app$bf'('the$b',X0)))
| 'fun_app$aw'('is_none$b',X0)
| ~ 'fun_app$'('is_none$a','bind$d'(X0,X1)) ),
inference(cnf_transformation,[],[f1474]) ).
tff(f1474,plain,
! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( ( 'fun_app$'('is_none$a','bind$d'(X0,X1))
| ( ~ 'fun_app$'('is_none$a','fun_app$bm'(X1,'fun_app$bf'('the$b',X0)))
& ~ 'fun_app$aw'('is_none$b',X0) ) )
& ( 'fun_app$'('is_none$a','fun_app$bm'(X1,'fun_app$bf'('the$b',X0)))
| 'fun_app$aw'('is_none$b',X0)
| ~ 'fun_app$'('is_none$a','bind$d'(X0,X1)) ) ),
inference(flattening,[],[f1473]) ).
tff(f1473,plain,
! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( ( 'fun_app$'('is_none$a','bind$d'(X0,X1))
| ( ~ 'fun_app$'('is_none$a','fun_app$bm'(X1,'fun_app$bf'('the$b',X0)))
& ~ 'fun_app$aw'('is_none$b',X0) ) )
& ( 'fun_app$'('is_none$a','fun_app$bm'(X1,'fun_app$bf'('the$b',X0)))
| 'fun_app$aw'('is_none$b',X0)
| ~ 'fun_app$'('is_none$a','bind$d'(X0,X1)) ) ),
inference(nnf_transformation,[],[f396]) ).
tff(f396,axiom,
! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$d'(X0,X1))
<=> ( 'fun_app$'('is_none$a','fun_app$bm'(X1,'fun_app$bf'('the$b',X0)))
| 'fun_app$aw'('is_none$b',X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom394) ).
tff(f10788,plain,
spl249_829,
inference(avatar_split_clause,[],[f2418,f10786]) ).
tff(f10786,plain,
( spl249_829
<=> ! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( ( 'none$a' = 'fun_app$f'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 )
| ( 'none$a' != 'bind$e'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_829])]) ).
tff(f2418,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( ( 'none$a' = 'fun_app$f'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 )
| ( 'none$a' != 'bind$e'(X0,X1) ) ),
inference(cnf_transformation,[],[f1465]) ).
tff(f1465,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( ( ( 'none$a' = 'bind$e'(X0,X1) )
| ( ( 'none$a' != 'fun_app$f'(X1,'fun_app$bf'('the$b',X0)) )
& ( 'none$b' != X0 ) ) )
& ( ( 'none$a' = 'fun_app$f'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 )
| ( 'none$a' != 'bind$e'(X0,X1) ) ) ),
inference(flattening,[],[f1464]) ).
tff(f1464,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( ( ( 'none$a' = 'bind$e'(X0,X1) )
| ( ( 'none$a' != 'fun_app$f'(X1,'fun_app$bf'('the$b',X0)) )
& ( 'none$b' != X0 ) ) )
& ( ( 'none$a' = 'fun_app$f'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 )
| ( 'none$a' != 'bind$e'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f338]) ).
tff(f338,axiom,
! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( ( 'none$a' = 'bind$e'(X0,X1) )
<=> ( ( 'none$a' = 'fun_app$f'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom336) ).
tff(f10784,plain,
spl249_828,
inference(avatar_split_clause,[],[f2412,f10782]) ).
tff(f10782,plain,
( spl249_828
<=> ! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( ( 'none$' = 'fun_app$bm'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 )
| ( 'none$' != 'bind$d'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_828])]) ).
tff(f2412,plain,
! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( ( 'none$' = 'fun_app$bm'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 )
| ( 'none$' != 'bind$d'(X0,X1) ) ),
inference(cnf_transformation,[],[f1461]) ).
tff(f1461,plain,
! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( ( ( 'none$' = 'bind$d'(X0,X1) )
| ( ( 'none$' != 'fun_app$bm'(X1,'fun_app$bf'('the$b',X0)) )
& ( 'none$b' != X0 ) ) )
& ( ( 'none$' = 'fun_app$bm'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 )
| ( 'none$' != 'bind$d'(X0,X1) ) ) ),
inference(flattening,[],[f1460]) ).
tff(f1460,plain,
! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( ( ( 'none$' = 'bind$d'(X0,X1) )
| ( ( 'none$' != 'fun_app$bm'(X1,'fun_app$bf'('the$b',X0)) )
& ( 'none$b' != X0 ) ) )
& ( ( 'none$' = 'fun_app$bm'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 )
| ( 'none$' != 'bind$d'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f337]) ).
tff(f337,axiom,
! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( ( 'none$' = 'bind$d'(X0,X1) )
<=> ( ( 'none$' = 'fun_app$bm'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom335) ).
tff(f10780,plain,
spl249_827,
inference(avatar_split_clause,[],[f2409,f10778]) ).
tff(f10778,plain,
( spl249_827
<=> ! [X0: 'B_option$',X1: 'B_a_option_fun$'] :
( ( 'none$b' = 'fun_app$bo'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 )
| ( 'none$b' != 'bind$g'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_827])]) ).
tff(f2409,plain,
! [X0: 'B_option$',X1: 'B_a_option_fun$'] :
( ( 'none$b' = 'fun_app$bo'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 )
| ( 'none$b' != 'bind$g'(X0,X1) ) ),
inference(cnf_transformation,[],[f1459]) ).
tff(f1459,plain,
! [X0: 'B_option$',X1: 'B_a_option_fun$'] :
( ( ( 'none$b' = 'bind$g'(X0,X1) )
| ( ( 'none$b' != 'fun_app$bo'(X1,'fun_app$al'('the$',X0)) )
& ( 'none$a' != X0 ) ) )
& ( ( 'none$b' = 'fun_app$bo'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 )
| ( 'none$b' != 'bind$g'(X0,X1) ) ) ),
inference(flattening,[],[f1458]) ).
tff(f1458,plain,
! [X0: 'B_option$',X1: 'B_a_option_fun$'] :
( ( ( 'none$b' = 'bind$g'(X0,X1) )
| ( ( 'none$b' != 'fun_app$bo'(X1,'fun_app$al'('the$',X0)) )
& ( 'none$a' != X0 ) ) )
& ( ( 'none$b' = 'fun_app$bo'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 )
| ( 'none$b' != 'bind$g'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f340]) ).
tff(f340,axiom,
! [X0: 'B_option$',X1: 'B_a_option_fun$'] :
( ( 'none$b' = 'bind$g'(X0,X1) )
<=> ( ( 'none$b' = 'fun_app$bo'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom338) ).
tff(f10776,plain,
spl249_826,
inference(avatar_split_clause,[],[f2406,f10774]) ).
tff(f10774,plain,
( spl249_826
<=> ! [X0: 'C_option$',X1: 'C_a_option_fun$'] :
( ( 'none$b' = 'fun_app$bn'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 )
| ( 'none$b' != 'bind$f'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_826])]) ).
tff(f2406,plain,
! [X0: 'C_option$',X1: 'C_a_option_fun$'] :
( ( 'none$b' = 'fun_app$bn'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 )
| ( 'none$b' != 'bind$f'(X0,X1) ) ),
inference(cnf_transformation,[],[f1457]) ).
tff(f1457,plain,
! [X0: 'C_option$',X1: 'C_a_option_fun$'] :
( ( ( 'none$b' = 'bind$f'(X0,X1) )
| ( ( 'none$b' != 'fun_app$bn'(X1,'fun_app$ak'('the$a',X0)) )
& ( 'none$' != X0 ) ) )
& ( ( 'none$b' = 'fun_app$bn'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 )
| ( 'none$b' != 'bind$f'(X0,X1) ) ) ),
inference(flattening,[],[f1456]) ).
tff(f1456,plain,
! [X0: 'C_option$',X1: 'C_a_option_fun$'] :
( ( ( 'none$b' = 'bind$f'(X0,X1) )
| ( ( 'none$b' != 'fun_app$bn'(X1,'fun_app$ak'('the$a',X0)) )
& ( 'none$' != X0 ) ) )
& ( ( 'none$b' = 'fun_app$bn'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 )
| ( 'none$b' != 'bind$f'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f339]) ).
tff(f339,axiom,
! [X0: 'C_option$',X1: 'C_a_option_fun$'] :
( ( 'none$b' = 'bind$f'(X0,X1) )
<=> ( ( 'none$b' = 'fun_app$bn'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom337) ).
tff(f10772,plain,
spl249_825,
inference(avatar_split_clause,[],[f2341,f10770]) ).
tff(f10770,plain,
( spl249_825
<=> ! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X1),X0) = X0 )
| ( sK121(X0,X1) != 'fun_app$h'(X1,sK121(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_825])]) ).
tff(f2341,plain,
! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X1),X0) = X0 )
| ( sK121(X0,X1) != 'fun_app$h'(X1,sK121(X0,X1)) ) ),
inference(cnf_transformation,[],[f1413]) ).
tff(f1413,plain,
! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X1),X0) = X0 )
| ( ( sK121(X0,X1) != 'fun_app$h'(X1,sK121(X0,X1)) )
& 'member$c'(sK121(X0,X1),'set_option$d'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK121])],[f947,f1412]) ).
tff(f1412,plain,
! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ? [X2: 'B$'] :
( ( 'fun_app$h'(X1,X2) != X2 )
& 'member$c'(X2,'set_option$d'(X0)) )
=> ( ( sK121(X0,X1) != 'fun_app$h'(X1,sK121(X0,X1)) )
& 'member$c'(sK121(X0,X1),'set_option$d'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f947,plain,
! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X1),X0) = X0 )
| ? [X2: 'B$'] :
( ( 'fun_app$h'(X1,X2) != X2 )
& 'member$c'(X2,'set_option$d'(X0)) ) ),
inference(ennf_transformation,[],[f445]) ).
tff(f445,axiom,
! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ! [X2: 'B$'] :
( 'member$c'(X2,'set_option$d'(X0))
=> ( 'fun_app$h'(X1,X2) = X2 ) )
=> ( 'fun_app$s'('map_option$b'(X1),X0) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom443) ).
tff(f10768,plain,
spl249_824,
inference(avatar_split_clause,[],[f2339,f10766]) ).
tff(f2339,plain,
! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ( 'fun_app$u'('map_option$c'(X1),X0) = X0 )
| ( sK120(X0,X1) != 'fun_app$k'(X1,sK120(X0,X1)) ) ),
inference(cnf_transformation,[],[f1411]) ).
tff(f1411,plain,
! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ( 'fun_app$u'('map_option$c'(X1),X0) = X0 )
| ( ( sK120(X0,X1) != 'fun_app$k'(X1,sK120(X0,X1)) )
& 'member$b'(sK120(X0,X1),'set_option$c'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK120])],[f946,f1410]) ).
tff(f1410,plain,
! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ? [X2: 'C$'] :
( ( 'fun_app$k'(X1,X2) != X2 )
& 'member$b'(X2,'set_option$c'(X0)) )
=> ( ( sK120(X0,X1) != 'fun_app$k'(X1,sK120(X0,X1)) )
& 'member$b'(sK120(X0,X1),'set_option$c'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f946,plain,
! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ( 'fun_app$u'('map_option$c'(X1),X0) = X0 )
| ? [X2: 'C$'] :
( ( 'fun_app$k'(X1,X2) != X2 )
& 'member$b'(X2,'set_option$c'(X0)) ) ),
inference(ennf_transformation,[],[f446]) ).
tff(f446,axiom,
! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ! [X2: 'C$'] :
( 'member$b'(X2,'set_option$c'(X0))
=> ( 'fun_app$k'(X1,X2) = X2 ) )
=> ( 'fun_app$u'('map_option$c'(X1),X0) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom444) ).
tff(f10764,plain,
( spl249_823
| ~ spl249_18
| ~ spl249_480 ),
inference(avatar_split_clause,[],[f6768,f6465,f3684,f10762]) ).
tff(f10762,plain,
( spl249_823
<=> ! [X0: 'C_option$'] : ( tltrue = def_23('uuf$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_823])]) ).
tff(f6465,plain,
( spl249_480
<=> ! [X0: 'C_bool_fun$',X1: 'C_option$'] :
( ( tltrue = def_23(X0,X1) )
| ~ 'fun_app$b'(X0,'fun_app$ak'('the$a',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_480])]) ).
tff(f6768,plain,
( ! [X0: 'C_option$'] : ( tltrue = def_23('uuf$',X0) )
| ~ spl249_18
| ~ spl249_480 ),
inference(resolution,[],[f6466,f3685]) ).
tff(f6466,plain,
( ! [X0: 'C_bool_fun$',X1: 'C_option$'] :
( ~ 'fun_app$b'(X0,'fun_app$ak'('the$a',X1))
| ( tltrue = def_23(X0,X1) ) )
| ~ spl249_480 ),
inference(avatar_component_clause,[],[f6465]) ).
tff(f10760,plain,
spl249_822,
inference(avatar_split_clause,[],[f2337,f10758]) ).
tff(f10758,plain,
( spl249_822
<=> ! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X1),X0) = X0 )
| ( sK119(X0,X1) != 'fun_app$r'(X1,sK119(X0,X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_822])]) ).
tff(f2337,plain,
! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X1),X0) = X0 )
| ( sK119(X0,X1) != 'fun_app$r'(X1,sK119(X0,X1)) ) ),
inference(cnf_transformation,[],[f1409]) ).
tff(f1409,plain,
! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X1),X0) = X0 )
| ( ( sK119(X0,X1) != 'fun_app$r'(X1,sK119(X0,X1)) )
& 'member$d'(sK119(X0,X1),'set_option$b'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK119])],[f945,f1408]) ).
tff(f1408,plain,
! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ? [X2: 'A$'] :
( ( 'fun_app$r'(X1,X2) != X2 )
& 'member$d'(X2,'set_option$b'(X0)) )
=> ( ( sK119(X0,X1) != 'fun_app$r'(X1,sK119(X0,X1)) )
& 'member$d'(sK119(X0,X1),'set_option$b'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f945,plain,
! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X1),X0) = X0 )
| ? [X2: 'A$'] :
( ( 'fun_app$r'(X1,X2) != X2 )
& 'member$d'(X2,'set_option$b'(X0)) ) ),
inference(ennf_transformation,[],[f444]) ).
tff(f444,axiom,
! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ! [X2: 'A$'] :
( 'member$d'(X2,'set_option$b'(X0))
=> ( 'fun_app$r'(X1,X2) = X2 ) )
=> ( 'fun_app$be'('map_option$a'(X1),X0) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom442) ).
tff(f10756,plain,
spl249_821,
inference(avatar_split_clause,[],[f2295,f10754]) ).
tff(f10754,plain,
( spl249_821
<=> ! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$s'('map_option$b'(X1),X0)) = 'fun_app$h'(X1,'fun_app$al'('the$',X0)) )
| 'fun_app$a'('is_none$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_821])]) ).
tff(f2295,plain,
! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$s'('map_option$b'(X1),X0)) = 'fun_app$h'(X1,'fun_app$al'('the$',X0)) )
| 'fun_app$a'('is_none$',X0) ),
inference(cnf_transformation,[],[f910]) ).
tff(f910,plain,
! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$s'('map_option$b'(X1),X0)) = 'fun_app$h'(X1,'fun_app$al'('the$',X0)) )
| 'fun_app$a'('is_none$',X0) ),
inference(ennf_transformation,[],[f326]) ).
tff(f326,axiom,
! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ~ 'fun_app$a'('is_none$',X0)
=> ( 'fun_app$al'('the$','fun_app$s'('map_option$b'(X1),X0)) = 'fun_app$h'(X1,'fun_app$al'('the$',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom324) ).
tff(f10752,plain,
spl249_820,
inference(avatar_split_clause,[],[f2294,f10750]) ).
tff(f10750,plain,
( spl249_820
<=> ! [X0: 'B_option$',X1: 'B_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$an'('map_option$d'(X1),X0)) = 'fun_app$o'(X1,'fun_app$al'('the$',X0)) )
| 'fun_app$a'('is_none$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_820])]) ).
tff(f2294,plain,
! [X0: 'B_option$',X1: 'B_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$an'('map_option$d'(X1),X0)) = 'fun_app$o'(X1,'fun_app$al'('the$',X0)) )
| 'fun_app$a'('is_none$',X0) ),
inference(cnf_transformation,[],[f909]) ).
tff(f909,plain,
! [X0: 'B_option$',X1: 'B_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$an'('map_option$d'(X1),X0)) = 'fun_app$o'(X1,'fun_app$al'('the$',X0)) )
| 'fun_app$a'('is_none$',X0) ),
inference(ennf_transformation,[],[f325]) ).
tff(f325,axiom,
! [X0: 'B_option$',X1: 'B_c_fun$'] :
( ~ 'fun_app$a'('is_none$',X0)
=> ( 'fun_app$ak'('the$a','fun_app$an'('map_option$d'(X1),X0)) = 'fun_app$o'(X1,'fun_app$al'('the$',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom323) ).
tff(f10748,plain,
spl249_819,
inference(avatar_split_clause,[],[f2293,f10746]) ).
tff(f10746,plain,
( spl249_819
<=> ! [X0: 'B_option$',X1: 'B_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$bj'('map_option$h'(X1),X0)) = 'fun_app$ao'(X1,'fun_app$al'('the$',X0)) )
| 'fun_app$a'('is_none$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_819])]) ).
tff(f2293,plain,
! [X0: 'B_option$',X1: 'B_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$bj'('map_option$h'(X1),X0)) = 'fun_app$ao'(X1,'fun_app$al'('the$',X0)) )
| 'fun_app$a'('is_none$',X0) ),
inference(cnf_transformation,[],[f908]) ).
tff(f908,plain,
! [X0: 'B_option$',X1: 'B_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$bj'('map_option$h'(X1),X0)) = 'fun_app$ao'(X1,'fun_app$al'('the$',X0)) )
| 'fun_app$a'('is_none$',X0) ),
inference(ennf_transformation,[],[f320]) ).
tff(f320,axiom,
! [X0: 'B_option$',X1: 'B_a_fun$'] :
( ~ 'fun_app$a'('is_none$',X0)
=> ( 'fun_app$bf'('the$b','fun_app$bj'('map_option$h'(X1),X0)) = 'fun_app$ao'(X1,'fun_app$al'('the$',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom318) ).
tff(f10744,plain,
spl249_818,
inference(avatar_split_clause,[],[f2292,f10742]) ).
tff(f10742,plain,
( spl249_818
<=> ! [X0: 'C_option$',X1: 'C_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$bg'('map_option$'(X1),X0)) = 'fun_app$m'(X1,'fun_app$ak'('the$a',X0)) )
| 'fun_app$'('is_none$a',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_818])]) ).
tff(f2292,plain,
! [X0: 'C_option$',X1: 'C_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$bg'('map_option$'(X1),X0)) = 'fun_app$m'(X1,'fun_app$ak'('the$a',X0)) )
| 'fun_app$'('is_none$a',X0) ),
inference(cnf_transformation,[],[f907]) ).
tff(f907,plain,
! [X0: 'C_option$',X1: 'C_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$bg'('map_option$'(X1),X0)) = 'fun_app$m'(X1,'fun_app$ak'('the$a',X0)) )
| 'fun_app$'('is_none$a',X0) ),
inference(ennf_transformation,[],[f324]) ).
tff(f324,axiom,
! [X0: 'C_option$',X1: 'C_b_fun$'] :
( ~ 'fun_app$'('is_none$a',X0)
=> ( 'fun_app$al'('the$','fun_app$bg'('map_option$'(X1),X0)) = 'fun_app$m'(X1,'fun_app$ak'('the$a',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom322) ).
tff(f10740,plain,
spl249_817,
inference(avatar_split_clause,[],[f2291,f10738]) ).
tff(f10738,plain,
( spl249_817
<=> ! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$u'('map_option$c'(X1),X0)) = 'fun_app$k'(X1,'fun_app$ak'('the$a',X0)) )
| 'fun_app$'('is_none$a',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_817])]) ).
tff(f2291,plain,
! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$u'('map_option$c'(X1),X0)) = 'fun_app$k'(X1,'fun_app$ak'('the$a',X0)) )
| 'fun_app$'('is_none$a',X0) ),
inference(cnf_transformation,[],[f906]) ).
tff(f906,plain,
! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$u'('map_option$c'(X1),X0)) = 'fun_app$k'(X1,'fun_app$ak'('the$a',X0)) )
| 'fun_app$'('is_none$a',X0) ),
inference(ennf_transformation,[],[f323]) ).
tff(f323,axiom,
! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ~ 'fun_app$'('is_none$a',X0)
=> ( 'fun_app$ak'('the$a','fun_app$u'('map_option$c'(X1),X0)) = 'fun_app$k'(X1,'fun_app$ak'('the$a',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom321) ).
tff(f10736,plain,
spl249_816,
inference(avatar_split_clause,[],[f2290,f10734]) ).
tff(f10734,plain,
( spl249_816
<=> ! [X0: 'C_option$',X1: 'C_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$bi'('map_option$g'(X1),X0)) = 'fun_app$bl'(X1,'fun_app$ak'('the$a',X0)) )
| 'fun_app$'('is_none$a',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_816])]) ).
tff(f2290,plain,
! [X0: 'C_option$',X1: 'C_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$bi'('map_option$g'(X1),X0)) = 'fun_app$bl'(X1,'fun_app$ak'('the$a',X0)) )
| 'fun_app$'('is_none$a',X0) ),
inference(cnf_transformation,[],[f905]) ).
tff(f905,plain,
! [X0: 'C_option$',X1: 'C_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$bi'('map_option$g'(X1),X0)) = 'fun_app$bl'(X1,'fun_app$ak'('the$a',X0)) )
| 'fun_app$'('is_none$a',X0) ),
inference(ennf_transformation,[],[f321]) ).
tff(f321,axiom,
! [X0: 'C_option$',X1: 'C_a_fun$'] :
( ~ 'fun_app$'('is_none$a',X0)
=> ( 'fun_app$bf'('the$b','fun_app$bi'('map_option$g'(X1),X0)) = 'fun_app$bl'(X1,'fun_app$ak'('the$a',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom319) ).
tff(f10732,plain,
spl249_815,
inference(avatar_split_clause,[],[f2289,f10730]) ).
tff(f10730,plain,
( spl249_815
<=> ! [X0: 'A_option$',X1: 'A_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$av'('map_option$e'(X1),X0)) = 'fun_app$p'(X1,'fun_app$bf'('the$b',X0)) )
| 'fun_app$aw'('is_none$b',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_815])]) ).
tff(f2289,plain,
! [X0: 'A_option$',X1: 'A_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$av'('map_option$e'(X1),X0)) = 'fun_app$p'(X1,'fun_app$bf'('the$b',X0)) )
| 'fun_app$aw'('is_none$b',X0) ),
inference(cnf_transformation,[],[f904]) ).
tff(f904,plain,
! [X0: 'A_option$',X1: 'A_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$av'('map_option$e'(X1),X0)) = 'fun_app$p'(X1,'fun_app$bf'('the$b',X0)) )
| 'fun_app$aw'('is_none$b',X0) ),
inference(ennf_transformation,[],[f327]) ).
tff(f327,axiom,
! [X0: 'A_option$',X1: 'A_b_fun$'] :
( ~ 'fun_app$aw'('is_none$b',X0)
=> ( 'fun_app$al'('the$','fun_app$av'('map_option$e'(X1),X0)) = 'fun_app$p'(X1,'fun_app$bf'('the$b',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom325) ).
tff(f10728,plain,
spl249_814,
inference(avatar_split_clause,[],[f2288,f10726]) ).
tff(f10726,plain,
( spl249_814
<=> ! [X0: 'A_option$',X1: 'A_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$bh'('map_option$f'(X1),X0)) = 'fun_app$bk'(X1,'fun_app$bf'('the$b',X0)) )
| 'fun_app$aw'('is_none$b',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_814])]) ).
tff(f2288,plain,
! [X0: 'A_option$',X1: 'A_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$bh'('map_option$f'(X1),X0)) = 'fun_app$bk'(X1,'fun_app$bf'('the$b',X0)) )
| 'fun_app$aw'('is_none$b',X0) ),
inference(cnf_transformation,[],[f903]) ).
tff(f903,plain,
! [X0: 'A_option$',X1: 'A_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$bh'('map_option$f'(X1),X0)) = 'fun_app$bk'(X1,'fun_app$bf'('the$b',X0)) )
| 'fun_app$aw'('is_none$b',X0) ),
inference(ennf_transformation,[],[f322]) ).
tff(f322,axiom,
! [X0: 'A_option$',X1: 'A_c_fun$'] :
( ~ 'fun_app$aw'('is_none$b',X0)
=> ( 'fun_app$ak'('the$a','fun_app$bh'('map_option$f'(X1),X0)) = 'fun_app$bk'(X1,'fun_app$bf'('the$b',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom320) ).
tff(f10724,plain,
spl249_813,
inference(avatar_split_clause,[],[f2287,f10722]) ).
tff(f10722,plain,
( spl249_813
<=> ! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$be'('map_option$a'(X1),X0)) = 'fun_app$r'(X1,'fun_app$bf'('the$b',X0)) )
| 'fun_app$aw'('is_none$b',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_813])]) ).
tff(f2287,plain,
! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$be'('map_option$a'(X1),X0)) = 'fun_app$r'(X1,'fun_app$bf'('the$b',X0)) )
| 'fun_app$aw'('is_none$b',X0) ),
inference(cnf_transformation,[],[f902]) ).
tff(f902,plain,
! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$be'('map_option$a'(X1),X0)) = 'fun_app$r'(X1,'fun_app$bf'('the$b',X0)) )
| 'fun_app$aw'('is_none$b',X0) ),
inference(ennf_transformation,[],[f328]) ).
tff(f328,axiom,
! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ~ 'fun_app$aw'('is_none$b',X0)
=> ( 'fun_app$bf'('the$b','fun_app$be'('map_option$a'(X1),X0)) = 'fun_app$r'(X1,'fun_app$bf'('the$b',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom326) ).
tff(f10720,plain,
spl249_812,
inference(avatar_split_clause,[],[f2286,f10718]) ).
tff(f10718,plain,
( spl249_812
<=> ! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$s'('map_option$b'(X1),X0)) = 'fun_app$h'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_812])]) ).
tff(f2286,plain,
! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$s'('map_option$b'(X1),X0)) = 'fun_app$h'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f901]) ).
tff(f901,plain,
! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$s'('map_option$b'(X1),X0)) = 'fun_app$h'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 ) ),
inference(ennf_transformation,[],[f270]) ).
tff(f270,axiom,
! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'none$a' != X0 )
=> ( 'fun_app$al'('the$','fun_app$s'('map_option$b'(X1),X0)) = 'fun_app$h'(X1,'fun_app$al'('the$',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom268) ).
tff(f10716,plain,
spl249_811,
inference(avatar_split_clause,[],[f2285,f10714]) ).
tff(f10714,plain,
( spl249_811
<=> ! [X0: 'B_option$',X1: 'B_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$an'('map_option$d'(X1),X0)) = 'fun_app$o'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_811])]) ).
tff(f2285,plain,
! [X0: 'B_option$',X1: 'B_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$an'('map_option$d'(X1),X0)) = 'fun_app$o'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f900]) ).
tff(f900,plain,
! [X0: 'B_option$',X1: 'B_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$an'('map_option$d'(X1),X0)) = 'fun_app$o'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 ) ),
inference(ennf_transformation,[],[f269]) ).
tff(f269,axiom,
! [X0: 'B_option$',X1: 'B_c_fun$'] :
( ( 'none$a' != X0 )
=> ( 'fun_app$ak'('the$a','fun_app$an'('map_option$d'(X1),X0)) = 'fun_app$o'(X1,'fun_app$al'('the$',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom267) ).
tff(f10712,plain,
spl249_810,
inference(avatar_split_clause,[],[f2284,f10710]) ).
tff(f10710,plain,
( spl249_810
<=> ! [X0: 'B_option$',X1: 'B_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$bj'('map_option$h'(X1),X0)) = 'fun_app$ao'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_810])]) ).
tff(f2284,plain,
! [X0: 'B_option$',X1: 'B_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$bj'('map_option$h'(X1),X0)) = 'fun_app$ao'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f899]) ).
tff(f899,plain,
! [X0: 'B_option$',X1: 'B_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$bj'('map_option$h'(X1),X0)) = 'fun_app$ao'(X1,'fun_app$al'('the$',X0)) )
| ( 'none$a' = X0 ) ),
inference(ennf_transformation,[],[f266]) ).
tff(f266,axiom,
! [X0: 'B_option$',X1: 'B_a_fun$'] :
( ( 'none$a' != X0 )
=> ( 'fun_app$bf'('the$b','fun_app$bj'('map_option$h'(X1),X0)) = 'fun_app$ao'(X1,'fun_app$al'('the$',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom264) ).
tff(f10708,plain,
spl249_809,
inference(avatar_split_clause,[],[f2283,f10706]) ).
tff(f10706,plain,
( spl249_809
<=> ! [X0: 'C_option$',X1: 'C_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$bg'('map_option$'(X1),X0)) = 'fun_app$m'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_809])]) ).
tff(f2283,plain,
! [X0: 'C_option$',X1: 'C_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$bg'('map_option$'(X1),X0)) = 'fun_app$m'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f898]) ).
tff(f898,plain,
! [X0: 'C_option$',X1: 'C_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$bg'('map_option$'(X1),X0)) = 'fun_app$m'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 ) ),
inference(ennf_transformation,[],[f268]) ).
tff(f268,axiom,
! [X0: 'C_option$',X1: 'C_b_fun$'] :
( ( 'none$' != X0 )
=> ( 'fun_app$al'('the$','fun_app$bg'('map_option$'(X1),X0)) = 'fun_app$m'(X1,'fun_app$ak'('the$a',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom266) ).
tff(f10704,plain,
spl249_808,
inference(avatar_split_clause,[],[f2282,f10702]) ).
tff(f10702,plain,
( spl249_808
<=> ! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$u'('map_option$c'(X1),X0)) = 'fun_app$k'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_808])]) ).
tff(f2282,plain,
! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$u'('map_option$c'(X1),X0)) = 'fun_app$k'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f897]) ).
tff(f897,plain,
! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$u'('map_option$c'(X1),X0)) = 'fun_app$k'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 ) ),
inference(ennf_transformation,[],[f265]) ).
tff(f265,axiom,
! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ( 'none$' != X0 )
=> ( 'fun_app$ak'('the$a','fun_app$u'('map_option$c'(X1),X0)) = 'fun_app$k'(X1,'fun_app$ak'('the$a',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom263) ).
tff(f10700,plain,
spl249_807,
inference(avatar_split_clause,[],[f2281,f10698]) ).
tff(f10698,plain,
( spl249_807
<=> ! [X0: 'C_option$',X1: 'C_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$bi'('map_option$g'(X1),X0)) = 'fun_app$bl'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_807])]) ).
tff(f2281,plain,
! [X0: 'C_option$',X1: 'C_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$bi'('map_option$g'(X1),X0)) = 'fun_app$bl'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f896]) ).
tff(f896,plain,
! [X0: 'C_option$',X1: 'C_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$bi'('map_option$g'(X1),X0)) = 'fun_app$bl'(X1,'fun_app$ak'('the$a',X0)) )
| ( 'none$' = X0 ) ),
inference(ennf_transformation,[],[f264]) ).
tff(f264,axiom,
! [X0: 'C_option$',X1: 'C_a_fun$'] :
( ( 'none$' != X0 )
=> ( 'fun_app$bf'('the$b','fun_app$bi'('map_option$g'(X1),X0)) = 'fun_app$bl'(X1,'fun_app$ak'('the$a',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom262) ).
tff(f10696,plain,
spl249_806,
inference(avatar_split_clause,[],[f2280,f10694]) ).
tff(f10694,plain,
( spl249_806
<=> ! [X0: 'A_option$',X1: 'A_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$av'('map_option$e'(X1),X0)) = 'fun_app$p'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_806])]) ).
tff(f2280,plain,
! [X0: 'A_option$',X1: 'A_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$av'('map_option$e'(X1),X0)) = 'fun_app$p'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 ) ),
inference(cnf_transformation,[],[f895]) ).
tff(f895,plain,
! [X0: 'A_option$',X1: 'A_b_fun$'] :
( ( 'fun_app$al'('the$','fun_app$av'('map_option$e'(X1),X0)) = 'fun_app$p'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 ) ),
inference(ennf_transformation,[],[f271]) ).
tff(f271,axiom,
! [X0: 'A_option$',X1: 'A_b_fun$'] :
( ( 'none$b' != X0 )
=> ( 'fun_app$al'('the$','fun_app$av'('map_option$e'(X1),X0)) = 'fun_app$p'(X1,'fun_app$bf'('the$b',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom269) ).
tff(f10692,plain,
spl249_805,
inference(avatar_split_clause,[],[f2279,f10690]) ).
tff(f10690,plain,
( spl249_805
<=> ! [X0: 'A_option$',X1: 'A_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$bh'('map_option$f'(X1),X0)) = 'fun_app$bk'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_805])]) ).
tff(f2279,plain,
! [X0: 'A_option$',X1: 'A_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$bh'('map_option$f'(X1),X0)) = 'fun_app$bk'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 ) ),
inference(cnf_transformation,[],[f894]) ).
tff(f894,plain,
! [X0: 'A_option$',X1: 'A_c_fun$'] :
( ( 'fun_app$ak'('the$a','fun_app$bh'('map_option$f'(X1),X0)) = 'fun_app$bk'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 ) ),
inference(ennf_transformation,[],[f267]) ).
tff(f267,axiom,
! [X0: 'A_option$',X1: 'A_c_fun$'] :
( ( 'none$b' != X0 )
=> ( 'fun_app$ak'('the$a','fun_app$bh'('map_option$f'(X1),X0)) = 'fun_app$bk'(X1,'fun_app$bf'('the$b',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom265) ).
tff(f10688,plain,
spl249_804,
inference(avatar_split_clause,[],[f2278,f10686]) ).
tff(f10686,plain,
( spl249_804
<=> ! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$be'('map_option$a'(X1),X0)) = 'fun_app$r'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_804])]) ).
tff(f2278,plain,
! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$be'('map_option$a'(X1),X0)) = 'fun_app$r'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 ) ),
inference(cnf_transformation,[],[f893]) ).
tff(f893,plain,
! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$bf'('the$b','fun_app$be'('map_option$a'(X1),X0)) = 'fun_app$r'(X1,'fun_app$bf'('the$b',X0)) )
| ( 'none$b' = X0 ) ),
inference(ennf_transformation,[],[f272]) ).
tff(f272,axiom,
! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'none$b' != X0 )
=> ( 'fun_app$bf'('the$b','fun_app$be'('map_option$a'(X1),X0)) = 'fun_app$r'(X1,'fun_app$bf'('the$b',X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom270) ).
tff(f10010,plain,
spl249_803,
inference(avatar_split_clause,[],[f3584,f10008]) ).
tff(f10008,plain,
( spl249_803
<=> ! [X2: 'B$',X0: 'B_c_c_fun_fun$',X1: 'C$'] : ( 'bind$b'('fun_app$g'('some$',X2),'uu$'(X0,X1)) = 'fun_app$j'('uvf$'('fun_app$y'(X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_803])]) ).
tff(f3584,plain,
! [X2: 'B$',X0: 'B_c_c_fun_fun$',X1: 'C$'] : ( 'bind$b'('fun_app$g'('some$',X2),'uu$'(X0,X1)) = 'fun_app$j'('uvf$'('fun_app$y'(X0,X2)),X1) ),
inference(forward_demodulation,[],[f3267,f2244]) ).
tff(f3267,plain,
! [X2: 'B$',X0: 'B_c_c_fun_fun$',X1: 'C$'] : ( 'fun_app$j'('some$a','fun_app$k'('fun_app$y'(X0,X2),X1)) = 'bind$b'('fun_app$g'('some$',X2),'uu$'(X0,X1)) ),
inference(definition_unfolding,[],[f2611,f2234]) ).
tff(f2611,plain,
! [X2: 'B$',X0: 'B_c_c_fun_fun$',X1: 'C$'] : ( 'fun_app$n'('uu$'(X0,X1),X2) = 'fun_app$j'('some$a','fun_app$k'('fun_app$y'(X0,X2),X1)) ),
inference(cnf_transformation,[],[f50]) ).
tff(f50,axiom,
! [X0: 'B_c_c_fun_fun$',X1: 'C$',X2: 'B$'] : ( 'fun_app$n'('uu$'(X0,X1),X2) = 'fun_app$j'('some$a','fun_app$k'('fun_app$y'(X0,X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom49) ).
tff(f10006,plain,
spl249_802,
inference(avatar_split_clause,[],[f3582,f10004]) ).
tff(f10004,plain,
( spl249_802
<=> ! [X2: 'B$',X0: 'B_c_option_fun$',X1: 'B_b_fun$'] : ( 'bind$b'('fun_app$g'('some$',X2),'comp$f'(X0,X1)) = 'bind$b'('fun_app$g'('uve$'(X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_802])]) ).
tff(f3582,plain,
! [X2: 'B$',X0: 'B_c_option_fun$',X1: 'B_b_fun$'] : ( 'bind$b'('fun_app$g'('some$',X2),'comp$f'(X0,X1)) = 'bind$b'('fun_app$g'('uve$'(X1),X2),X0) ),
inference(forward_demodulation,[],[f3261,f2245]) ).
tff(f3261,plain,
! [X2: 'B$',X0: 'B_c_option_fun$',X1: 'B_b_fun$'] : ( 'bind$b'('fun_app$g'('some$',X2),'comp$f'(X0,X1)) = 'bind$b'('fun_app$g'('some$','fun_app$h'(X1,X2)),X0) ),
inference(definition_unfolding,[],[f2582,f2234,f2234]) ).
tff(f2582,plain,
! [X2: 'B$',X0: 'B_c_option_fun$',X1: 'B_b_fun$'] : ( 'fun_app$n'('comp$f'(X0,X1),X2) = 'fun_app$n'(X0,'fun_app$h'(X1,X2)) ),
inference(cnf_transformation,[],[f562]) ).
tff(f562,axiom,
! [X0: 'B_c_option_fun$',X1: 'B_b_fun$',X2: 'B$'] : ( 'fun_app$n'('comp$f'(X0,X1),X2) = 'fun_app$n'(X0,'fun_app$h'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom560) ).
tff(f10002,plain,
spl249_801,
inference(avatar_split_clause,[],[f3529,f10000]) ).
tff(f10000,plain,
( spl249_801
<=> ! [X2: 'B_c_option_fun$',X1: 'B_option$',X3: 'B_c_option_fun$'] :
( ( 'bind$b'(X1,X2) = 'bind$b'(X1,X3) )
| 'member$c'(sK211(X1,X2,X3),'set_option$d'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_801])]) ).
tff(f3529,plain,
! [X2: 'B_c_option_fun$',X3: 'B_c_option_fun$',X1: 'B_option$'] :
( ( 'bind$b'(X1,X2) = 'bind$b'(X1,X3) )
| 'member$c'(sK211(X1,X2,X3),'set_option$d'(X1)) ),
inference(equality_resolution,[],[f3069]) ).
tff(f3069,plain,
! [X2: 'B_c_option_fun$',X3: 'B_c_option_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'bind$b'(X0,X2) = 'bind$b'(X1,X3) )
| 'member$c'(sK211(X1,X2,X3),'set_option$d'(X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1818]) ).
tff(f9998,plain,
spl249_800,
inference(avatar_split_clause,[],[f3521,f9996]) ).
tff(f9996,plain,
( spl249_800
<=> ! [X2: 'C_b_option_fun$',X1: 'C_option$',X3: 'C_b_option_fun$'] :
( ( 'bind$a'(X1,X2) = 'bind$a'(X1,X3) )
| 'member$b'(sK207(X1,X2,X3),'set_option$c'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_800])]) ).
tff(f3521,plain,
! [X2: 'C_b_option_fun$',X3: 'C_b_option_fun$',X1: 'C_option$'] :
( ( 'bind$a'(X1,X2) = 'bind$a'(X1,X3) )
| 'member$b'(sK207(X1,X2,X3),'set_option$c'(X1)) ),
inference(equality_resolution,[],[f3061]) ).
tff(f3061,plain,
! [X2: 'C_b_option_fun$',X3: 'C_b_option_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'bind$a'(X0,X2) = 'bind$a'(X1,X3) )
| 'member$b'(sK207(X1,X2,X3),'set_option$c'(X1))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1810]) ).
tff(f9994,plain,
spl249_799,
inference(avatar_split_clause,[],[f3252,f9992]) ).
tff(f9992,plain,
( spl249_799
<=> ! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$a'(X0,X1))
| ~ 'fun_app$a'('is_none$','bind$a'('fun_app$j'('some$a','fun_app$ak'('the$a',X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_799])]) ).
tff(f3252,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$a'(X0,X1))
| ~ 'fun_app$a'('is_none$','bind$a'('fun_app$j'('some$a','fun_app$ak'('the$a',X0)),X1)) ),
inference(definition_unfolding,[],[f2451,f2233]) ).
tff(f2451,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$a'(X0,X1))
| ~ 'fun_app$a'('is_none$','fun_app$l'(X1,'fun_app$ak'('the$a',X0))) ),
inference(cnf_transformation,[],[f1483]) ).
tff(f9990,plain,
spl249_798,
inference(avatar_split_clause,[],[f3250,f9988]) ).
tff(f9988,plain,
( spl249_798
<=> ! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$b'(X0,X1))
| ~ 'fun_app$'('is_none$a','bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_798])]) ).
tff(f3250,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$b'(X0,X1))
| ~ 'fun_app$'('is_none$a','bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1)) ),
inference(definition_unfolding,[],[f2439,f2234]) ).
tff(f2439,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$b'(X0,X1))
| ~ 'fun_app$'('is_none$a','fun_app$n'(X1,'fun_app$al'('the$',X0))) ),
inference(cnf_transformation,[],[f1476]) ).
tff(f9986,plain,
spl249_797,
inference(avatar_split_clause,[],[f3248,f9984]) ).
tff(f9984,plain,
( spl249_797
<=> ! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( 'none$a' = 'bind$a'(X0,X1) )
| ( 'none$a' != 'bind$a'('fun_app$j'('some$a','fun_app$ak'('the$a',X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_797])]) ).
tff(f3248,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( 'none$a' = 'bind$a'(X0,X1) )
| ( 'none$a' != 'bind$a'('fun_app$j'('some$a','fun_app$ak'('the$a',X0)),X1) ) ),
inference(definition_unfolding,[],[f2423,f2233]) ).
tff(f2423,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( ( 'none$a' = 'bind$a'(X0,X1) )
| ( 'none$a' != 'fun_app$l'(X1,'fun_app$ak'('the$a',X0)) ) ),
inference(cnf_transformation,[],[f1467]) ).
tff(f9982,plain,
spl249_796,
inference(avatar_split_clause,[],[f3246,f9980]) ).
tff(f9980,plain,
( spl249_796
<=> ! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( 'none$' = 'bind$b'(X0,X1) )
| ( 'none$' != 'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_796])]) ).
tff(f3246,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( 'none$' = 'bind$b'(X0,X1) )
| ( 'none$' != 'bind$b'('fun_app$g'('some$','fun_app$al'('the$',X0)),X1) ) ),
inference(definition_unfolding,[],[f2417,f2234]) ).
tff(f2417,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( ( 'none$' = 'bind$b'(X0,X1) )
| ( 'none$' != 'fun_app$n'(X1,'fun_app$al'('the$',X0)) ) ),
inference(cnf_transformation,[],[f1463]) ).
tff(f9978,plain,
spl249_795,
inference(avatar_split_clause,[],[f3034,f9976]) ).
tff(f9976,plain,
( spl249_795
<=> ! [X0: 'B$',X3: 'B_option$',X2: 'B_b_option_fun$',X1: 'B_option_b_fun$'] : ( 'case_option$l'(X0,X1,'map_option$k'(X2,X3)) = 'fun_app$al'('case_option$j'(X0,'comp$m'(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_795])]) ).
tff(f3034,plain,
! [X2: 'B_b_option_fun$',X3: 'B_option$',X0: 'B$',X1: 'B_option_b_fun$'] : ( 'case_option$l'(X0,X1,'map_option$k'(X2,X3)) = 'fun_app$al'('case_option$j'(X0,'comp$m'(X1,X2)),X3) ),
inference(cnf_transformation,[],[f498]) ).
tff(f498,axiom,
! [X0: 'B$',X1: 'B_option_b_fun$',X2: 'B_b_option_fun$',X3: 'B_option$'] : ( 'case_option$l'(X0,X1,'map_option$k'(X2,X3)) = 'fun_app$al'('case_option$j'(X0,'comp$m'(X1,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom496) ).
tff(f9974,plain,
spl249_794,
inference(avatar_split_clause,[],[f3033,f9972]) ).
tff(f9972,plain,
( spl249_794
<=> ! [X0: 'C$',X3: 'C_option$',X2: 'C_c_option_fun$',X1: 'C_option_c_fun$'] : ( 'case_option$m'(X0,X1,'map_option$l'(X2,X3)) = 'fun_app$ak'('case_option$k'(X0,'comp$n'(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_794])]) ).
tff(f3033,plain,
! [X2: 'C_c_option_fun$',X3: 'C_option$',X0: 'C$',X1: 'C_option_c_fun$'] : ( 'case_option$m'(X0,X1,'map_option$l'(X2,X3)) = 'fun_app$ak'('case_option$k'(X0,'comp$n'(X1,X2)),X3) ),
inference(cnf_transformation,[],[f499]) ).
tff(f499,axiom,
! [X0: 'C$',X1: 'C_option_c_fun$',X2: 'C_c_option_fun$',X3: 'C_option$'] : ( 'case_option$m'(X0,X1,'map_option$l'(X2,X3)) = 'fun_app$ak'('case_option$k'(X0,'comp$n'(X1,X2)),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom497) ).
tff(f9970,plain,
spl249_793,
inference(avatar_split_clause,[],[f2679,f9968]) ).
tff(f9968,plain,
( spl249_793
<=> ! [X2: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$s'('case_option$'(X0,X1),X2) = 'fun_app$g'(X1,'fun_app$al'('the$',X2)) )
| ( 'none$a' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_793])]) ).
tff(f2679,plain,
! [X2: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$s'('case_option$'(X0,X1),X2) = 'fun_app$g'(X1,'fun_app$al'('the$',X2)) )
| ( 'none$a' = X2 ) ),
inference(cnf_transformation,[],[f954]) ).
tff(f954,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$',X2: 'B_option$'] :
( ( ( 'fun_app$s'('case_option$'(X0,X1),X2) = 'fun_app$g'(X1,'fun_app$al'('the$',X2)) )
| ( 'none$a' = X2 ) )
& ( ( 'fun_app$s'('case_option$'(X0,X1),X2) = X0 )
| ( 'none$a' != X2 ) ) ),
inference(ennf_transformation,[],[f307]) ).
tff(f307,axiom,
! [X0: 'B_option$',X1: 'B_b_option_fun$',X2: 'B_option$'] :
( ( ( 'none$a' != X2 )
=> ( 'fun_app$s'('case_option$'(X0,X1),X2) = 'fun_app$g'(X1,'fun_app$al'('the$',X2)) ) )
& ( ( 'none$a' = X2 )
=> ( 'fun_app$s'('case_option$'(X0,X1),X2) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom305) ).
tff(f9966,plain,
spl249_792,
inference(avatar_split_clause,[],[f2675,f9964]) ).
tff(f9964,plain,
( spl249_792
<=> ! [X2: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$u'('case_option$a'(X0,X1),X2) = 'fun_app$j'(X1,'fun_app$ak'('the$a',X2)) )
| ( 'none$' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_792])]) ).
tff(f2675,plain,
! [X2: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$u'('case_option$a'(X0,X1),X2) = 'fun_app$j'(X1,'fun_app$ak'('the$a',X2)) )
| ( 'none$' = X2 ) ),
inference(cnf_transformation,[],[f952]) ).
tff(f952,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$',X2: 'C_option$'] :
( ( ( 'fun_app$u'('case_option$a'(X0,X1),X2) = 'fun_app$j'(X1,'fun_app$ak'('the$a',X2)) )
| ( 'none$' = X2 ) )
& ( ( 'fun_app$u'('case_option$a'(X0,X1),X2) = X0 )
| ( 'none$' != X2 ) ) ),
inference(ennf_transformation,[],[f308]) ).
tff(f308,axiom,
! [X0: 'C_option$',X1: 'C_c_option_fun$',X2: 'C_option$'] :
( ( ( 'none$' != X2 )
=> ( 'fun_app$u'('case_option$a'(X0,X1),X2) = 'fun_app$j'(X1,'fun_app$ak'('the$a',X2)) ) )
& ( ( 'none$' = X2 )
=> ( 'fun_app$u'('case_option$a'(X0,X1),X2) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom306) ).
tff(f9962,plain,
spl249_791,
inference(avatar_split_clause,[],[f2673,f9960]) ).
tff(f9960,plain,
( spl249_791
<=> ! [X2: 'A_option$',X0: 'B_option$',X1: 'A_b_option_fun$'] :
( ( 'fun_app$av'('case_option$d'(X0,X1),X2) = 'fun_app$f'(X1,'fun_app$bf'('the$b',X2)) )
| ( 'none$b' = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_791])]) ).
tff(f2673,plain,
! [X2: 'A_option$',X0: 'B_option$',X1: 'A_b_option_fun$'] :
( ( 'fun_app$av'('case_option$d'(X0,X1),X2) = 'fun_app$f'(X1,'fun_app$bf'('the$b',X2)) )
| ( 'none$b' = X2 ) ),
inference(cnf_transformation,[],[f951]) ).
tff(f951,plain,
! [X0: 'B_option$',X1: 'A_b_option_fun$',X2: 'A_option$'] :
( ( ( 'fun_app$av'('case_option$d'(X0,X1),X2) = 'fun_app$f'(X1,'fun_app$bf'('the$b',X2)) )
| ( 'none$b' = X2 ) )
& ( ( 'fun_app$av'('case_option$d'(X0,X1),X2) = X0 )
| ( 'none$b' != X2 ) ) ),
inference(ennf_transformation,[],[f310]) ).
tff(f310,axiom,
! [X0: 'B_option$',X1: 'A_b_option_fun$',X2: 'A_option$'] :
( ( ( 'none$b' != X2 )
=> ( 'fun_app$av'('case_option$d'(X0,X1),X2) = 'fun_app$f'(X1,'fun_app$bf'('the$b',X2)) ) )
& ( ( 'none$b' = X2 )
=> ( 'fun_app$av'('case_option$d'(X0,X1),X2) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom308) ).
tff(f9958,plain,
spl249_790,
inference(avatar_split_clause,[],[f2655,f9956]) ).
tff(f9956,plain,
( spl249_790
<=> ! [X2: 'B_option$',X0: 'B_b_fun$',X1: 'B_b_fun$'] : ( 'fun_app$s'('map_option$b'(X0),'fun_app$s'('map_option$b'(X1),X2)) = 'fun_app$s'('map_option$b'('comp$ai'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_790])]) ).
tff(f2655,plain,
! [X2: 'B_option$',X0: 'B_b_fun$',X1: 'B_b_fun$'] : ( 'fun_app$s'('map_option$b'(X0),'fun_app$s'('map_option$b'(X1),X2)) = 'fun_app$s'('map_option$b'('comp$ai'(X0,X1)),X2) ),
inference(cnf_transformation,[],[f520]) ).
tff(f520,axiom,
! [X0: 'B_b_fun$',X1: 'B_b_fun$',X2: 'B_option$'] : ( 'fun_app$s'('map_option$b'(X0),'fun_app$s'('map_option$b'(X1),X2)) = 'fun_app$s'('map_option$b'('comp$ai'(X0,X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom518) ).
tff(f9954,plain,
spl249_789,
inference(avatar_split_clause,[],[f2653,f9952]) ).
tff(f9952,plain,
( spl249_789
<=> ! [X2: 'C_option$',X0: 'B_b_fun$',X1: 'C_b_fun$'] : ( 'fun_app$s'('map_option$b'(X0),'fun_app$bg'('map_option$'(X1),X2)) = 'fun_app$bg'('map_option$'('comp$ag'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_789])]) ).
tff(f2653,plain,
! [X2: 'C_option$',X0: 'B_b_fun$',X1: 'C_b_fun$'] : ( 'fun_app$s'('map_option$b'(X0),'fun_app$bg'('map_option$'(X1),X2)) = 'fun_app$bg'('map_option$'('comp$ag'(X0,X1)),X2) ),
inference(cnf_transformation,[],[f529]) ).
tff(f529,axiom,
! [X0: 'B_b_fun$',X1: 'C_b_fun$',X2: 'C_option$'] : ( 'fun_app$s'('map_option$b'(X0),'fun_app$bg'('map_option$'(X1),X2)) = 'fun_app$bg'('map_option$'('comp$ag'(X0,X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom527) ).
tff(f9950,plain,
spl249_788,
inference(avatar_split_clause,[],[f2651,f9948]) ).
tff(f9948,plain,
( spl249_788
<=> ! [X2: 'B_option$',X0: 'B_c_fun$',X1: 'B_b_fun$'] : ( 'fun_app$an'('map_option$d'(X0),'fun_app$s'('map_option$b'(X1),X2)) = 'fun_app$an'('map_option$d'('comp$ac'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_788])]) ).
tff(f2651,plain,
! [X2: 'B_option$',X0: 'B_c_fun$',X1: 'B_b_fun$'] : ( 'fun_app$an'('map_option$d'(X0),'fun_app$s'('map_option$b'(X1),X2)) = 'fun_app$an'('map_option$d'('comp$ac'(X0,X1)),X2) ),
inference(cnf_transformation,[],[f517]) ).
tff(f517,axiom,
! [X0: 'B_c_fun$',X1: 'B_b_fun$',X2: 'B_option$'] : ( 'fun_app$an'('map_option$d'(X0),'fun_app$s'('map_option$b'(X1),X2)) = 'fun_app$an'('map_option$d'('comp$ac'(X0,X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom515) ).
tff(f9946,plain,
spl249_787,
inference(avatar_split_clause,[],[f2649,f9944]) ).
tff(f9944,plain,
( spl249_787
<=> ! [X2: 'A_option$',X0: 'B_c_fun$',X1: 'A_b_fun$'] : ( 'fun_app$an'('map_option$d'(X0),'fun_app$av'('map_option$e'(X1),X2)) = 'fun_app$bh'('map_option$f'('comp$ae'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_787])]) ).
tff(f2649,plain,
! [X2: 'A_option$',X0: 'B_c_fun$',X1: 'A_b_fun$'] : ( 'fun_app$an'('map_option$d'(X0),'fun_app$av'('map_option$e'(X1),X2)) = 'fun_app$bh'('map_option$f'('comp$ae'(X0,X1)),X2) ),
inference(cnf_transformation,[],[f528]) ).
tff(f528,axiom,
! [X0: 'B_c_fun$',X1: 'A_b_fun$',X2: 'A_option$'] : ( 'fun_app$an'('map_option$d'(X0),'fun_app$av'('map_option$e'(X1),X2)) = 'fun_app$bh'('map_option$f'('comp$ae'(X0,X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom526) ).
tff(f9942,plain,
spl249_786,
inference(avatar_split_clause,[],[f2647,f9940]) ).
tff(f9940,plain,
( spl249_786
<=> ! [X2: 'C_option$',X0: 'B_c_fun$',X1: 'C_b_fun$'] : ( 'fun_app$an'('map_option$d'(X0),'fun_app$bg'('map_option$'(X1),X2)) = 'fun_app$u'('map_option$c'('comp$aa'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_786])]) ).
tff(f2647,plain,
! [X2: 'C_option$',X0: 'B_c_fun$',X1: 'C_b_fun$'] : ( 'fun_app$an'('map_option$d'(X0),'fun_app$bg'('map_option$'(X1),X2)) = 'fun_app$u'('map_option$c'('comp$aa'(X0,X1)),X2) ),
inference(cnf_transformation,[],[f516]) ).
tff(f516,axiom,
! [X0: 'B_c_fun$',X1: 'C_b_fun$',X2: 'C_option$'] : ( 'fun_app$an'('map_option$d'(X0),'fun_app$bg'('map_option$'(X1),X2)) = 'fun_app$u'('map_option$c'('comp$aa'(X0,X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom514) ).
tff(f9938,plain,
spl249_785,
inference(avatar_split_clause,[],[f2646,f9936]) ).
tff(f9936,plain,
( spl249_785
<=> ! [X2: 'B_b_option_fun$',X0: 'B_c_fun$',X1: 'B_option$'] : ( 'fun_app$an'('map_option$d'(X0),'fun_app$ac'('bind$c'(X1),X2)) = 'bind$b'(X1,'comp$av'('map_option$d'(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_785])]) ).
tff(f2646,plain,
! [X2: 'B_b_option_fun$',X0: 'B_c_fun$',X1: 'B_option$'] : ( 'fun_app$an'('map_option$d'(X0),'fun_app$ac'('bind$c'(X1),X2)) = 'bind$b'(X1,'comp$av'('map_option$d'(X0),X2)) ),
inference(cnf_transformation,[],[f550]) ).
tff(f550,axiom,
! [X0: 'B_c_fun$',X1: 'B_option$',X2: 'B_b_option_fun$'] : ( 'fun_app$an'('map_option$d'(X0),'fun_app$ac'('bind$c'(X1),X2)) = 'bind$b'(X1,'comp$av'('map_option$d'(X0),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom548) ).
tff(f9934,plain,
spl249_784,
inference(avatar_split_clause,[],[f2644,f9932]) ).
tff(f9932,plain,
( spl249_784
<=> ! [X2: 'B_option$',X0: 'C_c_fun$',X1: 'B_c_fun$'] : ( 'fun_app$u'('map_option$c'(X0),'fun_app$an'('map_option$d'(X1),X2)) = 'fun_app$an'('map_option$d'('comp$q'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_784])]) ).
tff(f2644,plain,
! [X2: 'B_option$',X0: 'C_c_fun$',X1: 'B_c_fun$'] : ( 'fun_app$u'('map_option$c'(X0),'fun_app$an'('map_option$d'(X1),X2)) = 'fun_app$an'('map_option$d'('comp$q'(X0,X1)),X2) ),
inference(cnf_transformation,[],[f511]) ).
tff(f511,axiom,
! [X0: 'C_c_fun$',X1: 'B_c_fun$',X2: 'B_option$'] : ( 'fun_app$u'('map_option$c'(X0),'fun_app$an'('map_option$d'(X1),X2)) = 'fun_app$an'('map_option$d'('comp$q'(X0,X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom509) ).
tff(f9930,plain,
spl249_783,
inference(avatar_split_clause,[],[f2642,f9928]) ).
tff(f9928,plain,
( spl249_783
<=> ! [X2: 'B_option$',X0: 'C_b_fun$',X1: 'B_c_fun$'] : ( 'fun_app$bg'('map_option$'(X0),'fun_app$an'('map_option$d'(X1),X2)) = 'fun_app$s'('map_option$b'('comp$y'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_783])]) ).
tff(f2642,plain,
! [X2: 'B_option$',X0: 'C_b_fun$',X1: 'B_c_fun$'] : ( 'fun_app$bg'('map_option$'(X0),'fun_app$an'('map_option$d'(X1),X2)) = 'fun_app$s'('map_option$b'('comp$y'(X0,X1)),X2) ),
inference(cnf_transformation,[],[f525]) ).
tff(f525,axiom,
! [X0: 'C_b_fun$',X1: 'B_c_fun$',X2: 'B_option$'] : ( 'fun_app$bg'('map_option$'(X0),'fun_app$an'('map_option$d'(X1),X2)) = 'fun_app$s'('map_option$b'('comp$y'(X0,X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom523) ).
tff(f9926,plain,
spl249_782,
inference(avatar_split_clause,[],[f2640,f9924]) ).
tff(f9924,plain,
( spl249_782
<=> ! [X2: 'C_option$',X0: 'C_b_fun$',X1: 'C_c_fun$'] : ( 'fun_app$bg'('map_option$'(X0),'fun_app$u'('map_option$c'(X1),X2)) = 'fun_app$bg'('map_option$'('comp$u'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_782])]) ).
tff(f2640,plain,
! [X2: 'C_option$',X0: 'C_b_fun$',X1: 'C_c_fun$'] : ( 'fun_app$bg'('map_option$'(X0),'fun_app$u'('map_option$c'(X1),X2)) = 'fun_app$bg'('map_option$'('comp$u'(X0,X1)),X2) ),
inference(cnf_transformation,[],[f523]) ).
tff(f523,axiom,
! [X0: 'C_b_fun$',X1: 'C_c_fun$',X2: 'C_option$'] : ( 'fun_app$bg'('map_option$'(X0),'fun_app$u'('map_option$c'(X1),X2)) = 'fun_app$bg'('map_option$'('comp$u'(X0,X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom521) ).
tff(f9922,plain,
spl249_781,
inference(avatar_split_clause,[],[f2639,f9920]) ).
tff(f9920,plain,
( spl249_781
<=> ! [X2: 'C_c_option_fun$',X0: 'C_b_fun$',X1: 'C_option$'] : ( 'fun_app$bg'('map_option$'(X0),'fun_app$ab'('bind$'(X1),X2)) = 'bind$a'(X1,'comp$au'('map_option$'(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_781])]) ).
tff(f2639,plain,
! [X2: 'C_c_option_fun$',X0: 'C_b_fun$',X1: 'C_option$'] : ( 'fun_app$bg'('map_option$'(X0),'fun_app$ab'('bind$'(X1),X2)) = 'bind$a'(X1,'comp$au'('map_option$'(X0),X2)) ),
inference(cnf_transformation,[],[f549]) ).
tff(f549,axiom,
! [X0: 'C_b_fun$',X1: 'C_option$',X2: 'C_c_option_fun$'] : ( 'fun_app$bg'('map_option$'(X0),'fun_app$ab'('bind$'(X1),X2)) = 'bind$a'(X1,'comp$au'('map_option$'(X0),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom547) ).
tff(f9918,plain,
spl249_780,
inference(avatar_split_clause,[],[f2637,f9916]) ).
tff(f9916,plain,
( spl249_780
<=> ! [X2: 'A_option$',X0: 'C_b_fun$',X1: 'A_c_fun$'] : ( 'fun_app$bg'('map_option$'(X0),'fun_app$bh'('map_option$f'(X1),X2)) = 'fun_app$av'('map_option$e'('comp$w'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_780])]) ).
tff(f2637,plain,
! [X2: 'A_option$',X0: 'C_b_fun$',X1: 'A_c_fun$'] : ( 'fun_app$bg'('map_option$'(X0),'fun_app$bh'('map_option$f'(X1),X2)) = 'fun_app$av'('map_option$e'('comp$w'(X0,X1)),X2) ),
inference(cnf_transformation,[],[f514]) ).
tff(f514,axiom,
! [X0: 'C_b_fun$',X1: 'A_c_fun$',X2: 'A_option$'] : ( 'fun_app$bg'('map_option$'(X0),'fun_app$bh'('map_option$f'(X1),X2)) = 'fun_app$av'('map_option$e'('comp$w'(X0,X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom512) ).
tff(f9914,plain,
spl249_779,
inference(avatar_split_clause,[],[f2636,f9912]) ).
tff(f9912,plain,
( spl249_779
<=> ! [X2: 'B_b_option_fun$',X0: 'B_b_fun$',X1: 'B_option$'] : ( 'fun_app$ac'('bind$c'('fun_app$s'('map_option$b'(X0),X1)),X2) = 'fun_app$ac'('bind$c'(X1),'comp$c'(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_779])]) ).
tff(f2636,plain,
! [X2: 'B_b_option_fun$',X0: 'B_b_fun$',X1: 'B_option$'] : ( 'fun_app$ac'('bind$c'('fun_app$s'('map_option$b'(X0),X1)),X2) = 'fun_app$ac'('bind$c'(X1),'comp$c'(X2,X0)) ),
inference(cnf_transformation,[],[f542]) ).
tff(f542,axiom,
! [X0: 'B_b_fun$',X1: 'B_option$',X2: 'B_b_option_fun$'] : ( 'fun_app$ac'('bind$c'('fun_app$s'('map_option$b'(X0),X1)),X2) = 'fun_app$ac'('bind$c'(X1),'comp$c'(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom540) ).
tff(f9910,plain,
spl249_778,
inference(avatar_split_clause,[],[f2635,f9908]) ).
tff(f9908,plain,
( spl249_778
<=> ! [X2: 'C_c_option_fun$',X0: 'C_c_fun$',X1: 'C_option$'] : ( 'fun_app$ab'('bind$'('fun_app$u'('map_option$c'(X0),X1)),X2) = 'fun_app$ab'('bind$'(X1),'comp$'(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_778])]) ).
tff(f2635,plain,
! [X2: 'C_c_option_fun$',X0: 'C_c_fun$',X1: 'C_option$'] : ( 'fun_app$ab'('bind$'('fun_app$u'('map_option$c'(X0),X1)),X2) = 'fun_app$ab'('bind$'(X1),'comp$'(X2,X0)) ),
inference(cnf_transformation,[],[f537]) ).
tff(f537,axiom,
! [X0: 'C_c_fun$',X1: 'C_option$',X2: 'C_c_option_fun$'] : ( 'fun_app$ab'('bind$'('fun_app$u'('map_option$c'(X0),X1)),X2) = 'fun_app$ab'('bind$'(X1),'comp$'(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom535) ).
tff(f9906,plain,
spl249_777,
inference(avatar_split_clause,[],[f2633,f9904]) ).
tff(f9904,plain,
( spl249_777
<=> ! [X2: 'A_option$',X0: 'B_a_fun$',X1: 'A_b_fun$'] : ( 'fun_app$bj'('map_option$h'(X0),'fun_app$av'('map_option$e'(X1),X2)) = 'fun_app$be'('map_option$a'('comp$s'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_777])]) ).
tff(f2633,plain,
! [X2: 'A_option$',X0: 'B_a_fun$',X1: 'A_b_fun$'] : ( 'fun_app$bj'('map_option$h'(X0),'fun_app$av'('map_option$e'(X1),X2)) = 'fun_app$be'('map_option$a'('comp$s'(X0,X1)),X2) ),
inference(cnf_transformation,[],[f512]) ).
tff(f512,axiom,
! [X0: 'B_a_fun$',X1: 'A_b_fun$',X2: 'A_option$'] : ( 'fun_app$bj'('map_option$h'(X0),'fun_app$av'('map_option$e'(X1),X2)) = 'fun_app$be'('map_option$a'('comp$s'(X0,X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom510) ).
tff(f9902,plain,
spl249_776,
inference(avatar_split_clause,[],[f2630,f9900]) ).
tff(f9900,plain,
( spl249_776
<=> ! [X2: 'C_b_option_fun$',X0: 'B_c_fun$',X1: 'C_option$'] : ( 'fun_app$an'('map_option$d'(X0),'bind$a'(X1,X2)) = 'fun_app$ab'('bind$'(X1),'comp$aw'('map_option$d'(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_776])]) ).
tff(f2630,plain,
! [X2: 'C_b_option_fun$',X0: 'B_c_fun$',X1: 'C_option$'] : ( 'fun_app$an'('map_option$d'(X0),'bind$a'(X1,X2)) = 'fun_app$ab'('bind$'(X1),'comp$aw'('map_option$d'(X0),X2)) ),
inference(cnf_transformation,[],[f551]) ).
tff(f551,axiom,
! [X0: 'B_c_fun$',X1: 'C_option$',X2: 'C_b_option_fun$'] : ( 'fun_app$an'('map_option$d'(X0),'bind$a'(X1,X2)) = 'fun_app$ab'('bind$'(X1),'comp$aw'('map_option$d'(X0),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom549) ).
tff(f9898,plain,
spl249_775,
inference(avatar_split_clause,[],[f2629,f9896]) ).
tff(f9896,plain,
( spl249_775
<=> ! [X2: 'B$',X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'A$'] : ( 'fun_app$h'('fun_app$i'('setter$a'(X0),X1),X2) = 'fun_app$h'('register_apply$'(X0,'fun_app$aj'('uvo$',X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_775])]) ).
tff(f2629,plain,
! [X2: 'B$',X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'A$'] : ( 'fun_app$h'('fun_app$i'('setter$a'(X0),X1),X2) = 'fun_app$h'('register_apply$'(X0,'fun_app$aj'('uvo$',X1)),X2) ),
inference(cnf_transformation,[],[f316]) ).
tff(f316,axiom,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'A$',X2: 'B$'] : ( 'fun_app$h'('fun_app$i'('setter$a'(X0),X1),X2) = 'fun_app$h'('register_apply$'(X0,'fun_app$aj'('uvo$',X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom314) ).
tff(f9894,plain,
spl249_774,
inference(avatar_split_clause,[],[f2628,f9892]) ).
tff(f9892,plain,
( spl249_774
<=> ! [X2: 'B_a_option_fun$',X0: 'A_b_fun$',X1: 'B_option$'] : ( 'fun_app$av'('map_option$e'(X0),'bind$g'(X1,X2)) = 'fun_app$ac'('bind$c'(X1),'comp$az'('map_option$e'(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_774])]) ).
tff(f2628,plain,
! [X2: 'B_a_option_fun$',X0: 'A_b_fun$',X1: 'B_option$'] : ( 'fun_app$av'('map_option$e'(X0),'bind$g'(X1,X2)) = 'fun_app$ac'('bind$c'(X1),'comp$az'('map_option$e'(X0),X2)) ),
inference(cnf_transformation,[],[f554]) ).
tff(f554,axiom,
! [X0: 'A_b_fun$',X1: 'B_option$',X2: 'B_a_option_fun$'] : ( 'fun_app$av'('map_option$e'(X0),'bind$g'(X1,X2)) = 'fun_app$ac'('bind$c'(X1),'comp$az'('map_option$e'(X0),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom552) ).
tff(f9890,plain,
spl249_773,
inference(avatar_split_clause,[],[f2627,f9888]) ).
tff(f9888,plain,
( spl249_773
<=> ! [X2: 'B_c_option_fun$',X0: 'C_b_fun$',X1: 'B_option$'] : ( 'fun_app$bg'('map_option$'(X0),'bind$b'(X1,X2)) = 'fun_app$ac'('bind$c'(X1),'comp$at'('map_option$'(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_773])]) ).
tff(f2627,plain,
! [X2: 'B_c_option_fun$',X0: 'C_b_fun$',X1: 'B_option$'] : ( 'fun_app$bg'('map_option$'(X0),'bind$b'(X1,X2)) = 'fun_app$ac'('bind$c'(X1),'comp$at'('map_option$'(X0),X2)) ),
inference(cnf_transformation,[],[f548]) ).
tff(f548,axiom,
! [X0: 'C_b_fun$',X1: 'B_option$',X2: 'B_c_option_fun$'] : ( 'fun_app$bg'('map_option$'(X0),'bind$b'(X1,X2)) = 'fun_app$ac'('bind$c'(X1),'comp$at'('map_option$'(X0),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom546) ).
tff(f9886,plain,
spl249_772,
inference(avatar_split_clause,[],[f2626,f9884]) ).
tff(f9884,plain,
( spl249_772
<=> ! [X2: 'C$',X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'B$'] : ( 'fun_app$k'('fun_app$y'('setter$'(X0),X1),X2) = 'fun_app$k'('register_apply$a'(X0,'fun_app$ai'('uvp$',X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_772])]) ).
tff(f2626,plain,
! [X2: 'C$',X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'B$'] : ( 'fun_app$k'('fun_app$y'('setter$'(X0),X1),X2) = 'fun_app$k'('register_apply$a'(X0,'fun_app$ai'('uvp$',X1)),X2) ),
inference(cnf_transformation,[],[f317]) ).
tff(f317,axiom,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'B$',X2: 'C$'] : ( 'fun_app$k'('fun_app$y'('setter$'(X0),X1),X2) = 'fun_app$k'('register_apply$a'(X0,'fun_app$ai'('uvp$',X1)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom315) ).
tff(f9882,plain,
spl249_771,
inference(avatar_split_clause,[],[f2625,f9880]) ).
tff(f9880,plain,
( spl249_771
<=> ! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A_option$'] : ( 'fun_app$q'('uux$'(X0,X1),X2) = 'case_option$b'('fun_app$q'('some$b',X2),'uuw$'(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_771])]) ).
tff(f2625,plain,
! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A_option$'] : ( 'fun_app$q'('uux$'(X0,X1),X2) = 'case_option$b'('fun_app$q'('some$b',X2),'uuw$'(X0,X2),X1) ),
inference(cnf_transformation,[],[f22]) ).
tff(f22,axiom,
! [X0: 'A_a_a_fun_fun$',X1: 'A_option$',X2: 'A$'] : ( 'fun_app$q'('uux$'(X0,X1),X2) = 'case_option$b'('fun_app$q'('some$b',X2),'uuw$'(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom21) ).
tff(f9878,plain,
spl249_770,
inference(avatar_split_clause,[],[f2335,f9876]) ).
tff(f2335,plain,
! [X0: 'B_option_option$',X1: 'B_option_b_option_fun$'] :
( ( 'map_option$i'(X1,X0) = X0 )
| ( sK118(X0,X1) != 'fun_app$s'(X1,sK118(X0,X1)) ) ),
inference(cnf_transformation,[],[f1407]) ).
tff(f1407,plain,
! [X0: 'B_option_option$',X1: 'B_option_b_option_fun$'] :
( ( 'map_option$i'(X1,X0) = X0 )
| ( ( sK118(X0,X1) != 'fun_app$s'(X1,sK118(X0,X1)) )
& 'member$a'(sK118(X0,X1),'set_option$'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK118])],[f944,f1406]) ).
tff(f1406,plain,
! [X0: 'B_option_option$',X1: 'B_option_b_option_fun$'] :
( ? [X2: 'B_option$'] :
( ( 'fun_app$s'(X1,X2) != X2 )
& 'member$a'(X2,'set_option$'(X0)) )
=> ( ( sK118(X0,X1) != 'fun_app$s'(X1,sK118(X0,X1)) )
& 'member$a'(sK118(X0,X1),'set_option$'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f944,plain,
! [X0: 'B_option_option$',X1: 'B_option_b_option_fun$'] :
( ( 'map_option$i'(X1,X0) = X0 )
| ? [X2: 'B_option$'] :
( ( 'fun_app$s'(X1,X2) != X2 )
& 'member$a'(X2,'set_option$'(X0)) ) ),
inference(ennf_transformation,[],[f442]) ).
tff(f442,axiom,
! [X0: 'B_option_option$',X1: 'B_option_b_option_fun$'] :
( ! [X2: 'B_option$'] :
( 'member$a'(X2,'set_option$'(X0))
=> ( 'fun_app$s'(X1,X2) = X2 ) )
=> ( 'map_option$i'(X1,X0) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom440) ).
tff(f9874,plain,
spl249_769,
inference(avatar_split_clause,[],[f2333,f9872]) ).
tff(f2333,plain,
! [X0: 'C_option_option$',X1: 'C_option_c_option_fun$'] :
( ( 'map_option$j'(X1,X0) = X0 )
| ( sK117(X0,X1) != 'fun_app$u'(X1,sK117(X0,X1)) ) ),
inference(cnf_transformation,[],[f1405]) ).
tff(f1405,plain,
! [X0: 'C_option_option$',X1: 'C_option_c_option_fun$'] :
( ( 'map_option$j'(X1,X0) = X0 )
| ( ( sK117(X0,X1) != 'fun_app$u'(X1,sK117(X0,X1)) )
& 'member$'(sK117(X0,X1),'set_option$a'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK117])],[f943,f1404]) ).
tff(f1404,plain,
! [X0: 'C_option_option$',X1: 'C_option_c_option_fun$'] :
( ? [X2: 'C_option$'] :
( ( 'fun_app$u'(X1,X2) != X2 )
& 'member$'(X2,'set_option$a'(X0)) )
=> ( ( sK117(X0,X1) != 'fun_app$u'(X1,sK117(X0,X1)) )
& 'member$'(sK117(X0,X1),'set_option$a'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f943,plain,
! [X0: 'C_option_option$',X1: 'C_option_c_option_fun$'] :
( ( 'map_option$j'(X1,X0) = X0 )
| ? [X2: 'C_option$'] :
( ( 'fun_app$u'(X1,X2) != X2 )
& 'member$'(X2,'set_option$a'(X0)) ) ),
inference(ennf_transformation,[],[f443]) ).
tff(f443,axiom,
! [X0: 'C_option_option$',X1: 'C_option_c_option_fun$'] :
( ! [X2: 'C_option$'] :
( 'member$'(X2,'set_option$a'(X0))
=> ( 'fun_app$u'(X1,X2) = X2 ) )
=> ( 'map_option$j'(X1,X0) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom441) ).
tff(f9402,plain,
( spl249_768
| ~ spl249_252
| ~ spl249_513 ),
inference(avatar_split_clause,[],[f7011,f6597,f4736,f9400]) ).
tff(f9400,plain,
( spl249_768
<=> ! [X0: 'B_b_option_fun$',X1: 'B_option$'] : ~ sP31(X0,'bot$g',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_768])]) ).
tff(f7011,plain,
( ! [X0: 'B_b_option_fun$',X1: 'B_option$'] : ~ sP31(X0,'bot$g',X1)
| ~ spl249_252
| ~ spl249_513 ),
inference(resolution,[],[f6598,f4737]) ).
tff(f9274,plain,
( spl249_767
| ~ spl249_252
| ~ spl249_511 ),
inference(avatar_split_clause,[],[f6982,f6589,f4736,f9272]) ).
tff(f9272,plain,
( spl249_767
<=> ! [X0: 'B_b_option_fun$',X1: 'B_option$'] : ~ sP30(X0,'bot$g',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_767])]) ).
tff(f6982,plain,
( ! [X0: 'B_b_option_fun$',X1: 'B_option$'] : ~ sP30(X0,'bot$g',X1)
| ~ spl249_252
| ~ spl249_511 ),
inference(resolution,[],[f6590,f4737]) ).
tff(f9270,plain,
spl249_766,
inference(avatar_split_clause,[],[f3586,f9268]) ).
tff(f9268,plain,
( spl249_766
<=> ! [X2: 'B$',X0: 'B_b_b_fun_fun$',X1: 'B$'] : ( 'fun_app$g'('fun_app$t'('uva$'(X0),X1),X2) = 'fun_app$g'('uve$'('fun_app$ai'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_766])]) ).
tff(f3586,plain,
! [X2: 'B$',X0: 'B_b_b_fun_fun$',X1: 'B$'] : ( 'fun_app$g'('fun_app$t'('uva$'(X0),X1),X2) = 'fun_app$g'('uve$'('fun_app$ai'(X0,X1)),X2) ),
inference(forward_demodulation,[],[f2632,f2245]) ).
tff(f2632,plain,
! [X2: 'B$',X0: 'B_b_b_fun_fun$',X1: 'B$'] : ( 'fun_app$g'('fun_app$t'('uva$'(X0),X1),X2) = 'fun_app$g'('some$','fun_app$h'('fun_app$ai'(X0,X1),X2)) ),
inference(cnf_transformation,[],[f48]) ).
tff(f48,axiom,
! [X0: 'B_b_b_fun_fun$',X1: 'B$',X2: 'B$'] : ( 'fun_app$g'('fun_app$t'('uva$'(X0),X1),X2) = 'fun_app$g'('some$','fun_app$h'('fun_app$ai'(X0,X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom47) ).
tff(f9266,plain,
spl249_765,
inference(avatar_split_clause,[],[f3585,f9264]) ).
tff(f9264,plain,
( spl249_765
<=> ! [X2: 'C$',X0: 'C_c_c_fun_fun$',X1: 'C$'] : ( 'fun_app$j'('fun_app$v'('uuy$'(X0),X1),X2) = 'fun_app$j'('uvf$'('fun_app$ah'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_765])]) ).
tff(f3585,plain,
! [X2: 'C$',X0: 'C_c_c_fun_fun$',X1: 'C$'] : ( 'fun_app$j'('fun_app$v'('uuy$'(X0),X1),X2) = 'fun_app$j'('uvf$'('fun_app$ah'(X0,X1)),X2) ),
inference(forward_demodulation,[],[f2631,f2244]) ).
tff(f2631,plain,
! [X2: 'C$',X0: 'C_c_c_fun_fun$',X1: 'C$'] : ( 'fun_app$j'('fun_app$v'('uuy$'(X0),X1),X2) = 'fun_app$j'('some$a','fun_app$k'('fun_app$ah'(X0,X1),X2)) ),
inference(cnf_transformation,[],[f47]) ).
tff(f47,axiom,
! [X0: 'C_c_c_fun_fun$',X1: 'C$',X2: 'C$'] : ( 'fun_app$j'('fun_app$v'('uuy$'(X0),X1),X2) = 'fun_app$j'('some$a','fun_app$k'('fun_app$ah'(X0,X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom46) ).
tff(f9262,plain,
spl249_764,
inference(avatar_split_clause,[],[f3434,f9260]) ).
tff(f9260,plain,
( spl249_764
<=> ! [X2: 'A$',X1: 'A_bool_fun$'] :
( 'fun_app$z'(X1,X2)
| 'member$d'(sK157('fun_app$q'('some$b',X2),X1),'set_option$b'('fun_app$q'('some$b',X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_764])]) ).
tff(f3434,plain,
! [X2: 'A$',X1: 'A_bool_fun$'] :
( 'fun_app$z'(X1,X2)
| 'member$d'(sK157('fun_app$q'('some$b',X2),X1),'set_option$b'('fun_app$q'('some$b',X2))) ),
inference(equality_resolution,[],[f2765]) ).
tff(f2765,plain,
! [X2: 'A$',X0: 'A_option$',X1: 'A_bool_fun$'] :
( 'fun_app$z'(X1,X2)
| ( 'fun_app$q'('some$b',X2) != X0 )
| 'member$d'(sK157(X0,X1),'set_option$b'(X0)) ),
inference(cnf_transformation,[],[f1580]) ).
tff(f1580,plain,
! [X0: 'A_option$',X1: 'A_bool_fun$',X2: 'A$'] :
( 'fun_app$z'(X1,X2)
| ( 'fun_app$q'('some$b',X2) != X0 )
| ( ~ 'fun_app$z'(X1,sK157(X0,X1))
& 'member$d'(sK157(X0,X1),'set_option$b'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK157])],[f987,f1579]) ).
tff(f1579,plain,
! [X0: 'A_option$',X1: 'A_bool_fun$'] :
( ? [X3: 'A$'] :
( ~ 'fun_app$z'(X1,X3)
& 'member$d'(X3,'set_option$b'(X0)) )
=> ( ~ 'fun_app$z'(X1,sK157(X0,X1))
& 'member$d'(sK157(X0,X1),'set_option$b'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f987,plain,
! [X0: 'A_option$',X1: 'A_bool_fun$',X2: 'A$'] :
( 'fun_app$z'(X1,X2)
| ( 'fun_app$q'('some$b',X2) != X0 )
| ? [X3: 'A$'] :
( ~ 'fun_app$z'(X1,X3)
& 'member$d'(X3,'set_option$b'(X0)) ) ),
inference(flattening,[],[f986]) ).
tff(f986,plain,
! [X0: 'A_option$',X1: 'A_bool_fun$',X2: 'A$'] :
( 'fun_app$z'(X1,X2)
| ( 'fun_app$q'('some$b',X2) != X0 )
| ? [X3: 'A$'] :
( ~ 'fun_app$z'(X1,X3)
& 'member$d'(X3,'set_option$b'(X0)) ) ),
inference(ennf_transformation,[],[f429]) ).
tff(f429,axiom,
! [X0: 'A_option$',X1: 'A_bool_fun$',X2: 'A$'] :
( ( ( 'fun_app$q'('some$b',X2) = X0 )
& ! [X3: 'A$'] :
( 'member$d'(X3,'set_option$b'(X0))
=> 'fun_app$z'(X1,X3) ) )
=> 'fun_app$z'(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom427) ).
tff(f9258,plain,
spl249_763,
inference(avatar_split_clause,[],[f3264,f9256]) ).
tff(f3264,plain,
! [X2: 'B$',X0: 'B_c_option_fun$',X1: 'C_b_option_fun$'] : ( 'fun_app$g'('uvv$'(X0,X1),X2) = 'bind$a'('bind$b'('fun_app$g'('some$',X2),X0),X1) ),
inference(definition_unfolding,[],[f2589,f2234]) ).
tff(f2589,plain,
! [X2: 'B$',X0: 'B_c_option_fun$',X1: 'C_b_option_fun$'] : ( 'fun_app$g'('uvv$'(X0,X1),X2) = 'bind$a'('fun_app$n'(X0,X2),X1) ),
inference(cnf_transformation,[],[f34]) ).
tff(f34,axiom,
! [X0: 'B_c_option_fun$',X1: 'C_b_option_fun$',X2: 'B$'] : ( 'fun_app$g'('uvv$'(X0,X1),X2) = 'bind$a'('fun_app$n'(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom33) ).
tff(f9254,plain,
spl249_762,
inference(avatar_split_clause,[],[f3263,f9252]) ).
tff(f3263,plain,
! [X2: 'C$',X0: 'C_b_option_fun$',X1: 'B_c_option_fun$'] : ( 'fun_app$j'('uvy$'(X0,X1),X2) = 'bind$b'('bind$a'('fun_app$j'('some$a',X2),X0),X1) ),
inference(definition_unfolding,[],[f2587,f2233]) ).
tff(f2587,plain,
! [X2: 'C$',X0: 'C_b_option_fun$',X1: 'B_c_option_fun$'] : ( 'fun_app$j'('uvy$'(X0,X1),X2) = 'bind$b'('fun_app$l'(X0,X2),X1) ),
inference(cnf_transformation,[],[f31]) ).
tff(f31,axiom,
! [X0: 'C_b_option_fun$',X1: 'B_c_option_fun$',X2: 'C$'] : ( 'fun_app$j'('uvy$'(X0,X1),X2) = 'bind$b'('fun_app$l'(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom30) ).
tff(f9250,plain,
spl249_761,
inference(avatar_split_clause,[],[f3260,f9248]) ).
tff(f9248,plain,
( spl249_761
<=> ! [X2: 'B$',X0: 'B_c_c_option_fun_fun$',X1: 'C$'] : ( 'fun_app$j'('fun_app$w'(X0,X2),X1) = 'bind$b'('fun_app$g'('some$',X2),'uuu$'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_761])]) ).
tff(f3260,plain,
! [X2: 'B$',X0: 'B_c_c_option_fun_fun$',X1: 'C$'] : ( 'fun_app$j'('fun_app$w'(X0,X2),X1) = 'bind$b'('fun_app$g'('some$',X2),'uuu$'(X0,X1)) ),
inference(definition_unfolding,[],[f2581,f2234]) ).
tff(f2581,plain,
! [X2: 'B$',X0: 'B_c_c_option_fun_fun$',X1: 'C$'] : ( 'fun_app$n'('uuu$'(X0,X1),X2) = 'fun_app$j'('fun_app$w'(X0,X2),X1) ),
inference(cnf_transformation,[],[f24]) ).
tff(f24,axiom,
! [X0: 'B_c_c_option_fun_fun$',X1: 'C$',X2: 'B$'] : ( 'fun_app$n'('uuu$'(X0,X1),X2) = 'fun_app$j'('fun_app$w'(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom23) ).
tff(f9246,plain,
spl249_760,
inference(avatar_split_clause,[],[f3258,f9244]) ).
tff(f9244,plain,
( spl249_760
<=> ! [X2: 'B$',X0: 'B_b_option_fun$',X1: 'B_c_option_fun$'] : ( 'bind$b'('fun_app$g'(X0,X2),X1) = 'bind$b'('fun_app$g'('some$',X2),'uvx$'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_760])]) ).
tff(f3258,plain,
! [X2: 'B$',X0: 'B_b_option_fun$',X1: 'B_c_option_fun$'] : ( 'bind$b'('fun_app$g'(X0,X2),X1) = 'bind$b'('fun_app$g'('some$',X2),'uvx$'(X0,X1)) ),
inference(definition_unfolding,[],[f2579,f2234]) ).
tff(f2579,plain,
! [X2: 'B$',X0: 'B_b_option_fun$',X1: 'B_c_option_fun$'] : ( 'fun_app$n'('uvx$'(X0,X1),X2) = 'bind$b'('fun_app$g'(X0,X2),X1) ),
inference(cnf_transformation,[],[f35]) ).
tff(f35,axiom,
! [X0: 'B_b_option_fun$',X1: 'B_c_option_fun$',X2: 'B$'] : ( 'fun_app$n'('uvx$'(X0,X1),X2) = 'bind$b'('fun_app$g'(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom34) ).
tff(f9242,plain,
spl249_759,
inference(avatar_split_clause,[],[f3257,f9240]) ).
tff(f9240,plain,
( spl249_759
<=> ! [X2: 'B$',X0: 'Bool_c_option_fun$',X1: 'B_bool_fun$'] : ( 'fun_app$ae'(X0,def_2(X1,X2)) = 'bind$b'('fun_app$g'('some$',X2),'uum$'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_759])]) ).
tff(f3257,plain,
! [X2: 'B$',X0: 'Bool_c_option_fun$',X1: 'B_bool_fun$'] : ( 'fun_app$ae'(X0,def_2(X1,X2)) = 'bind$b'('fun_app$g'('some$',X2),'uum$'(X0,X1)) ),
inference(definition_unfolding,[],[f2578,f2234]) ).
tff(f2578,plain,
! [X2: 'B$',X0: 'Bool_c_option_fun$',X1: 'B_bool_fun$'] : ( 'fun_app$n'('uum$'(X0,X1),X2) = 'fun_app$ae'(X0,def_2(X1,X2)) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,axiom,
! [X0: 'Bool_c_option_fun$',X1: 'B_bool_fun$',X2: 'B$'] : ( 'fun_app$n'('uum$'(X0,X1),X2) = 'fun_app$ae'(X0,def_2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom42) ).
tff(f9238,plain,
spl249_758,
inference(avatar_split_clause,[],[f3256,f9236]) ).
tff(f9236,plain,
( spl249_758
<=> ! [X2: 'C$',X0: 'C_c_option_fun$',X1: 'C_b_option_fun$'] : ( 'bind$a'('fun_app$j'(X0,X2),X1) = 'bind$a'('fun_app$j'('some$a',X2),'uvw$'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_758])]) ).
tff(f3256,plain,
! [X2: 'C$',X0: 'C_c_option_fun$',X1: 'C_b_option_fun$'] : ( 'bind$a'('fun_app$j'(X0,X2),X1) = 'bind$a'('fun_app$j'('some$a',X2),'uvw$'(X0,X1)) ),
inference(definition_unfolding,[],[f2561,f2233]) ).
tff(f2561,plain,
! [X2: 'C$',X0: 'C_c_option_fun$',X1: 'C_b_option_fun$'] : ( 'fun_app$l'('uvw$'(X0,X1),X2) = 'bind$a'('fun_app$j'(X0,X2),X1) ),
inference(cnf_transformation,[],[f30]) ).
tff(f30,axiom,
! [X0: 'C_c_option_fun$',X1: 'C_b_option_fun$',X2: 'C$'] : ( 'fun_app$l'('uvw$'(X0,X1),X2) = 'bind$a'('fun_app$j'(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom29) ).
tff(f9234,plain,
spl249_757,
inference(avatar_split_clause,[],[f3255,f9232]) ).
tff(f9232,plain,
( spl249_757
<=> ! [X2: 'B$',X0: 'C_option$',X1: 'B_c_option_fun$'] : ( 'fun_app$an'('case_option$c'(X0,X1),'fun_app$g'('some$',X2)) = 'bind$b'('fun_app$g'('some$',X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_757])]) ).
tff(f3255,plain,
! [X2: 'B$',X0: 'C_option$',X1: 'B_c_option_fun$'] : ( 'fun_app$an'('case_option$c'(X0,X1),'fun_app$g'('some$',X2)) = 'bind$b'('fun_app$g'('some$',X2),X1) ),
inference(definition_unfolding,[],[f2550,f2234]) ).
tff(f2550,plain,
! [X2: 'B$',X0: 'C_option$',X1: 'B_c_option_fun$'] : ( 'fun_app$n'(X1,X2) = 'fun_app$an'('case_option$c'(X0,X1),'fun_app$g'('some$',X2)) ),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
! [X0: 'C_option$',X1: 'B_c_option_fun$',X2: 'B$'] : ( 'fun_app$n'(X1,X2) = 'fun_app$an'('case_option$c'(X0,X1),'fun_app$g'('some$',X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom102) ).
tff(f9230,plain,
( spl249_756
| ~ spl249_251
| ~ spl249_509 ),
inference(avatar_split_clause,[],[f6953,f6581,f4732,f9228]) ).
tff(f9228,plain,
( spl249_756
<=> ! [X0: 'C_c_option_fun$',X1: 'C_option$'] : ~ sP29(X0,'bot$h',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_756])]) ).
tff(f6953,plain,
( ! [X0: 'C_c_option_fun$',X1: 'C_option$'] : ~ sP29(X0,'bot$h',X1)
| ~ spl249_251
| ~ spl249_509 ),
inference(resolution,[],[f6582,f4733]) ).
tff(f9226,plain,
spl249_755,
inference(avatar_split_clause,[],[f3154,f9224]) ).
tff(f9224,plain,
( spl249_755
<=> ! [X0: 'B_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'B_bool_fun$'] :
( sP35(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_17(X1,X0))
| ~ 'fun_app$ag'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_755])]) ).
tff(f3154,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( sP35(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_17(X1,X0))
| ~ 'fun_app$ag'(X2,X3) ),
inference(cnf_transformation,[],[f1877]) ).
tff(f9222,plain,
spl249_754,
inference(avatar_split_clause,[],[f3153,f9220]) ).
tff(f9220,plain,
( spl249_754
<=> ! [X0: 'B_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'B_bool_fun$'] :
( sP35(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_17(X1,X0))
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_754])]) ).
tff(f3153,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( sP35(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_17(X1,X0))
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f1877]) ).
tff(f9218,plain,
spl249_753,
inference(avatar_split_clause,[],[f3146,f9216]) ).
tff(f9216,plain,
( spl249_753
<=> ! [X0: 'C_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'C_bool_fun$'] :
( sP34(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_19(X1,X0))
| ~ 'fun_app$ag'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_753])]) ).
tff(f3146,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( sP34(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_19(X1,X0))
| ~ 'fun_app$ag'(X2,X3) ),
inference(cnf_transformation,[],[f1873]) ).
tff(f9214,plain,
spl249_752,
inference(avatar_split_clause,[],[f3145,f9212]) ).
tff(f9212,plain,
( spl249_752
<=> ! [X0: 'C_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'C_bool_fun$'] :
( sP34(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_19(X1,X0))
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_752])]) ).
tff(f3145,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( sP34(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_19(X1,X0))
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f1873]) ).
tff(f9210,plain,
spl249_751,
inference(avatar_split_clause,[],[f3138,f9208]) ).
tff(f9208,plain,
( spl249_751
<=> ! [X0: 'B_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'B_bool_fun$'] :
( sP33(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_21(X1,X0))
| ~ 'fun_app$ag'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_751])]) ).
tff(f3138,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( sP33(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_21(X1,X0))
| ~ 'fun_app$ag'(X2,X3) ),
inference(cnf_transformation,[],[f1869]) ).
tff(f9206,plain,
spl249_750,
inference(avatar_split_clause,[],[f3137,f9204]) ).
tff(f9204,plain,
( spl249_750
<=> ! [X0: 'B_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'B_bool_fun$'] :
( sP33(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_21(X1,X0))
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_750])]) ).
tff(f3137,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( sP33(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_21(X1,X0))
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f1869]) ).
tff(f9202,plain,
spl249_749,
inference(avatar_split_clause,[],[f3130,f9200]) ).
tff(f9200,plain,
( spl249_749
<=> ! [X0: 'C_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'C_bool_fun$'] :
( sP32(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_23(X1,X0))
| ~ 'fun_app$ag'(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_749])]) ).
tff(f3130,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( sP32(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_23(X1,X0))
| ~ 'fun_app$ag'(X2,X3) ),
inference(cnf_transformation,[],[f1865]) ).
tff(f9198,plain,
spl249_748,
inference(avatar_split_clause,[],[f3129,f9196]) ).
tff(f9196,plain,
( spl249_748
<=> ! [X0: 'C_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'C_bool_fun$'] :
( sP32(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_23(X1,X0))
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_748])]) ).
tff(f3129,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( sP32(X0,X1,X2,X3)
| ~ 'fun_app$ag'(X2,def_23(X1,X0))
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f1865]) ).
tff(f9194,plain,
spl249_747,
inference(avatar_split_clause,[],[f2796,f9192]) ).
tff(f9192,plain,
( spl249_747
<=> ! [X2: 'B$',X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C$'] :
( 'fun_app$c'('uvr$'(X0,X1),X2)
| ( 'fun_app$k'('fun_app$y'('setter$'(X0),X2),X1) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_747])]) ).
tff(f2796,plain,
! [X2: 'B$',X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C$'] :
( 'fun_app$c'('uvr$'(X0,X1),X2)
| ( 'fun_app$k'('fun_app$y'('setter$'(X0),X2),X1) != X1 ) ),
inference(cnf_transformation,[],[f1605]) ).
tff(f1605,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C$',X2: 'B$'] :
( ( 'fun_app$c'('uvr$'(X0,X1),X2)
| ( 'fun_app$k'('fun_app$y'('setter$'(X0),X2),X1) != X1 ) )
& ( ( 'fun_app$k'('fun_app$y'('setter$'(X0),X2),X1) = X1 )
| ~ 'fun_app$c'('uvr$'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f27]) ).
tff(f27,axiom,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C$',X2: 'B$'] :
( 'fun_app$c'('uvr$'(X0,X1),X2)
<=> ( 'fun_app$k'('fun_app$y'('setter$'(X0),X2),X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom26) ).
tff(f9190,plain,
spl249_746,
inference(avatar_split_clause,[],[f2795,f9188]) ).
tff(f9188,plain,
( spl249_746
<=> ! [X2: 'B$',X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C$'] :
( ( 'fun_app$k'('fun_app$y'('setter$'(X0),X2),X1) = X1 )
| ~ 'fun_app$c'('uvr$'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_746])]) ).
tff(f2795,plain,
! [X2: 'B$',X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C$'] :
( ( 'fun_app$k'('fun_app$y'('setter$'(X0),X2),X1) = X1 )
| ~ 'fun_app$c'('uvr$'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1605]) ).
tff(f9186,plain,
( spl249_745
| ~ spl249_251
| ~ spl249_506 ),
inference(avatar_split_clause,[],[f6919,f6569,f4732,f9184]) ).
tff(f9184,plain,
( spl249_745
<=> ! [X0: 'C_c_option_fun$',X1: 'C_option$'] : ~ sP28(X0,'bot$h',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_745])]) ).
tff(f6919,plain,
( ! [X0: 'C_c_option_fun$',X1: 'C_option$'] : ~ sP28(X0,'bot$h',X1)
| ~ spl249_251
| ~ spl249_506 ),
inference(resolution,[],[f6570,f4733]) ).
tff(f9182,plain,
spl249_744,
inference(avatar_split_clause,[],[f2784,f9180]) ).
tff(f9180,plain,
( spl249_744
<=> ! [X2: 'A$',X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B$'] :
( 'fun_app$z'('uvq$'(X0,X1),X2)
| ( 'fun_app$h'('fun_app$i'('setter$a'(X0),X2),X1) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_744])]) ).
tff(f2784,plain,
! [X2: 'A$',X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B$'] :
( 'fun_app$z'('uvq$'(X0,X1),X2)
| ( 'fun_app$h'('fun_app$i'('setter$a'(X0),X2),X1) != X1 ) ),
inference(cnf_transformation,[],[f1599]) ).
tff(f1599,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B$',X2: 'A$'] :
( ( 'fun_app$z'('uvq$'(X0,X1),X2)
| ( 'fun_app$h'('fun_app$i'('setter$a'(X0),X2),X1) != X1 ) )
& ( ( 'fun_app$h'('fun_app$i'('setter$a'(X0),X2),X1) = X1 )
| ~ 'fun_app$z'('uvq$'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f28]) ).
tff(f28,axiom,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B$',X2: 'A$'] :
( 'fun_app$z'('uvq$'(X0,X1),X2)
<=> ( 'fun_app$h'('fun_app$i'('setter$a'(X0),X2),X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom27) ).
tff(f9178,plain,
spl249_743,
inference(avatar_split_clause,[],[f2783,f9176]) ).
tff(f9176,plain,
( spl249_743
<=> ! [X2: 'A$',X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B$'] :
( ( 'fun_app$h'('fun_app$i'('setter$a'(X0),X2),X1) = X1 )
| ~ 'fun_app$z'('uvq$'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_743])]) ).
tff(f2783,plain,
! [X2: 'A$',X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B$'] :
( ( 'fun_app$h'('fun_app$i'('setter$a'(X0),X2),X1) = X1 )
| ~ 'fun_app$z'('uvq$'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1599]) ).
tff(f9174,plain,
spl249_742,
inference(avatar_split_clause,[],[f2697,f9172]) ).
tff(f9172,plain,
( spl249_742
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,sK136(X1,X2))
| ( tltrue = X0 )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_742])]) ).
tff(f2697,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,sK136(X1,X2))
| ( tltrue = X0 )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1538]) ).
tff(f9170,plain,
spl249_741,
inference(avatar_split_clause,[],[f2696,f9168]) ).
tff(f9168,plain,
( spl249_741
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,sK136(X1,X2))
| ( 'none$a' = X2 )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_741])]) ).
tff(f2696,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,sK136(X1,X2))
| ( 'none$a' = X2 )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1538]) ).
tff(f9166,plain,
spl249_740,
inference(avatar_split_clause,[],[f2693,f9164]) ).
tff(f9164,plain,
( spl249_740
<=> ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,sK135(X1,X2))
| ( tltrue = X0 )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_740])]) ).
tff(f2693,plain,
! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,sK135(X1,X2))
| ( tltrue = X0 )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1536]) ).
tff(f9162,plain,
spl249_739,
inference(avatar_split_clause,[],[f2692,f9160]) ).
tff(f9160,plain,
( spl249_739
<=> ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,sK135(X1,X2))
| ( 'none$' = X2 )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_739])]) ).
tff(f2692,plain,
! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,sK135(X1,X2))
| ( 'none$' = X2 )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1536]) ).
tff(f9158,plain,
spl249_738,
inference(avatar_split_clause,[],[f2689,f9156]) ).
tff(f9156,plain,
( spl249_738
<=> ! [X2: 'A_option$',X0: tlbool,X1: 'A_bool_fun$'] :
( 'fun_app$z'(X1,sK134(X1,X2))
| ( tltrue = X0 )
| ~ 'fun_app$aw'('case_option$g'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_738])]) ).
tff(f2689,plain,
! [X2: 'A_option$',X0: tlbool,X1: 'A_bool_fun$'] :
( 'fun_app$z'(X1,sK134(X1,X2))
| ( tltrue = X0 )
| ~ 'fun_app$aw'('case_option$g'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1534]) ).
tff(f9154,plain,
spl249_737,
inference(avatar_split_clause,[],[f2688,f9152]) ).
tff(f9152,plain,
( spl249_737
<=> ! [X2: 'A_option$',X0: tlbool,X1: 'A_bool_fun$'] :
( 'fun_app$z'(X1,sK134(X1,X2))
| ( 'none$b' = X2 )
| ~ 'fun_app$aw'('case_option$g'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_737])]) ).
tff(f2688,plain,
! [X2: 'A_option$',X0: tlbool,X1: 'A_bool_fun$'] :
( 'fun_app$z'(X1,sK134(X1,X2))
| ( 'none$b' = X2 )
| ~ 'fun_app$aw'('case_option$g'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1534]) ).
tff(f9150,plain,
spl249_736,
inference(avatar_split_clause,[],[f2624,f9148]) ).
tff(f2624,plain,
! [X2: 'B_b_option_fun$',X0: 'A_b_fun$',X1: 'A_option$'] : ( 'fun_app$ac'('bind$c'('fun_app$av'('map_option$e'(X0),X1)),X2) = 'bind$e'(X1,'comp$d'(X2,X0)) ),
inference(cnf_transformation,[],[f544]) ).
tff(f544,axiom,
! [X0: 'A_b_fun$',X1: 'A_option$',X2: 'B_b_option_fun$'] : ( 'fun_app$ac'('bind$c'('fun_app$av'('map_option$e'(X0),X1)),X2) = 'bind$e'(X1,'comp$d'(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom542) ).
tff(f9146,plain,
spl249_735,
inference(avatar_split_clause,[],[f2623,f9144]) ).
tff(f2623,plain,
! [X2: 'B_b_option_fun$',X0: 'C_b_fun$',X1: 'C_option$'] : ( 'fun_app$ac'('bind$c'('fun_app$bg'('map_option$'(X0),X1)),X2) = 'bind$a'(X1,'comp$a'(X2,X0)) ),
inference(cnf_transformation,[],[f538]) ).
tff(f538,axiom,
! [X0: 'C_b_fun$',X1: 'C_option$',X2: 'B_b_option_fun$'] : ( 'fun_app$ac'('bind$c'('fun_app$bg'('map_option$'(X0),X1)),X2) = 'bind$a'(X1,'comp$a'(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom536) ).
tff(f9142,plain,
( spl249_734
| ~ spl249_252
| ~ spl249_435 ),
inference(avatar_split_clause,[],[f6300,f5764,f4736,f9140]) ).
tff(f9140,plain,
( spl249_734
<=> ! [X0: 'C_b_option_fun$',X1: 'C_option$'] : ~ sP24(X0,'bot$g',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_734])]) ).
tff(f6300,plain,
( ! [X0: 'C_b_option_fun$',X1: 'C_option$'] : ~ sP24(X0,'bot$g',X1)
| ~ spl249_252
| ~ spl249_435 ),
inference(resolution,[],[f5765,f4737]) ).
tff(f9138,plain,
spl249_733,
inference(avatar_split_clause,[],[f2622,f9136]) ).
tff(f2622,plain,
! [X2: 'C_c_option_fun$',X0: 'B_c_fun$',X1: 'B_option$'] : ( 'fun_app$ab'('bind$'('fun_app$an'('map_option$d'(X0),X1)),X2) = 'bind$b'(X1,'comp$b'(X2,X0)) ),
inference(cnf_transformation,[],[f541]) ).
tff(f541,axiom,
! [X0: 'B_c_fun$',X1: 'B_option$',X2: 'C_c_option_fun$'] : ( 'fun_app$ab'('bind$'('fun_app$an'('map_option$d'(X0),X1)),X2) = 'bind$b'(X1,'comp$b'(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom539) ).
tff(f9134,plain,
spl249_732,
inference(avatar_split_clause,[],[f2621,f9132]) ).
tff(f9132,plain,
( spl249_732
<=> ! [X2: 'B$',X0: 'B_b_option_fun$',X1: 'B_b_option_fun$'] : ( 'fun_app$g'('fun_app$ad'('uvt$'(X0),X1),X2) = 'fun_app$ac'('bind$c'('fun_app$g'(X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_732])]) ).
tff(f2621,plain,
! [X2: 'B$',X0: 'B_b_option_fun$',X1: 'B_b_option_fun$'] : ( 'fun_app$g'('fun_app$ad'('uvt$'(X0),X1),X2) = 'fun_app$ac'('bind$c'('fun_app$g'(X0,X2)),X1) ),
inference(cnf_transformation,[],[f36]) ).
tff(f36,axiom,
! [X0: 'B_b_option_fun$',X1: 'B_b_option_fun$',X2: 'B$'] : ( 'fun_app$g'('fun_app$ad'('uvt$'(X0),X1),X2) = 'fun_app$ac'('bind$c'('fun_app$g'(X0,X2)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom35) ).
tff(f9130,plain,
spl249_731,
inference(avatar_split_clause,[],[f2620,f9128]) ).
tff(f9128,plain,
( spl249_731
<=> ! [X2: 'C$',X0: 'C_c_option_fun$',X1: 'C_c_option_fun$'] : ( 'fun_app$j'('fun_app$aa'('uwa$'(X0),X1),X2) = 'fun_app$ab'('bind$'('fun_app$j'(X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_731])]) ).
tff(f2620,plain,
! [X2: 'C$',X0: 'C_c_option_fun$',X1: 'C_c_option_fun$'] : ( 'fun_app$j'('fun_app$aa'('uwa$'(X0),X1),X2) = 'fun_app$ab'('bind$'('fun_app$j'(X0,X2)),X1) ),
inference(cnf_transformation,[],[f29]) ).
tff(f29,axiom,
! [X0: 'C_c_option_fun$',X1: 'C_c_option_fun$',X2: 'C$'] : ( 'fun_app$j'('fun_app$aa'('uwa$'(X0),X1),X2) = 'fun_app$ab'('bind$'('fun_app$j'(X0,X2)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom28) ).
tff(f9126,plain,
spl249_730,
inference(avatar_split_clause,[],[f2619,f9124]) ).
tff(f9124,plain,
( spl249_730
<=> ! [X2: 'C_b_option_fun$',X0: 'B_b_fun$',X1: 'C_option$'] : ( 'fun_app$s'('map_option$b'(X0),'bind$a'(X1,X2)) = 'bind$a'(X1,'comp$ay'('map_option$b'(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_730])]) ).
tff(f2619,plain,
! [X2: 'C_b_option_fun$',X0: 'B_b_fun$',X1: 'C_option$'] : ( 'fun_app$s'('map_option$b'(X0),'bind$a'(X1,X2)) = 'bind$a'(X1,'comp$ay'('map_option$b'(X0),X2)) ),
inference(cnf_transformation,[],[f553]) ).
tff(f553,axiom,
! [X0: 'B_b_fun$',X1: 'C_option$',X2: 'C_b_option_fun$'] : ( 'fun_app$s'('map_option$b'(X0),'bind$a'(X1,X2)) = 'bind$a'(X1,'comp$ay'('map_option$b'(X0),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom551) ).
tff(f9122,plain,
spl249_729,
inference(avatar_split_clause,[],[f2618,f9120]) ).
tff(f9120,plain,
( spl249_729
<=> ! [X2: 'B_c_option_fun$',X0: 'C_c_fun$',X1: 'B_option$'] : ( 'fun_app$u'('map_option$c'(X0),'bind$b'(X1,X2)) = 'bind$b'(X1,'comp$ar'('map_option$c'(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_729])]) ).
tff(f2618,plain,
! [X2: 'B_c_option_fun$',X0: 'C_c_fun$',X1: 'B_option$'] : ( 'fun_app$u'('map_option$c'(X0),'bind$b'(X1,X2)) = 'bind$b'(X1,'comp$ar'('map_option$c'(X0),X2)) ),
inference(cnf_transformation,[],[f546]) ).
tff(f546,axiom,
! [X0: 'C_c_fun$',X1: 'B_option$',X2: 'B_c_option_fun$'] : ( 'fun_app$u'('map_option$c'(X0),'bind$b'(X1,X2)) = 'bind$b'(X1,'comp$ar'('map_option$c'(X0),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom544) ).
tff(f9118,plain,
spl249_728,
inference(avatar_split_clause,[],[f2617,f9116]) ).
tff(f9116,plain,
( spl249_728
<=> ! [X2: 'C_a_option_fun$',X0: 'A_b_fun$',X1: 'C_option$'] : ( 'fun_app$av'('map_option$e'(X0),'bind$f'(X1,X2)) = 'bind$a'(X1,'comp$ba'('map_option$e'(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_728])]) ).
tff(f2617,plain,
! [X2: 'C_a_option_fun$',X0: 'A_b_fun$',X1: 'C_option$'] : ( 'fun_app$av'('map_option$e'(X0),'bind$f'(X1,X2)) = 'bind$a'(X1,'comp$ba'('map_option$e'(X0),X2)) ),
inference(cnf_transformation,[],[f555]) ).
tff(f555,axiom,
! [X0: 'A_b_fun$',X1: 'C_option$',X2: 'C_a_option_fun$'] : ( 'fun_app$av'('map_option$e'(X0),'bind$f'(X1,X2)) = 'bind$a'(X1,'comp$ba'('map_option$e'(X0),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom553) ).
tff(f9114,plain,
spl249_727,
inference(avatar_split_clause,[],[f2616,f9112]) ).
tff(f9112,plain,
( spl249_727
<=> ! [X2: 'C_b_option_fun$',X0: 'B_c_fun$',X1: 'B_option$'] : ( 'bind$a'('fun_app$an'('map_option$d'(X0),X1),X2) = 'fun_app$ac'('bind$c'(X1),'comp$o'(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_727])]) ).
tff(f2616,plain,
! [X2: 'C_b_option_fun$',X0: 'B_c_fun$',X1: 'B_option$'] : ( 'bind$a'('fun_app$an'('map_option$d'(X0),X1),X2) = 'fun_app$ac'('bind$c'(X1),'comp$o'(X2,X0)) ),
inference(cnf_transformation,[],[f540]) ).
tff(f540,axiom,
! [X0: 'B_c_fun$',X1: 'B_option$',X2: 'C_b_option_fun$'] : ( 'bind$a'('fun_app$an'('map_option$d'(X0),X1),X2) = 'fun_app$ac'('bind$c'(X1),'comp$o'(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom538) ).
tff(f9110,plain,
spl249_726,
inference(avatar_split_clause,[],[f2615,f9108]) ).
tff(f9108,plain,
( spl249_726
<=> ! [X2: 'B_c_option_fun$',X0: 'C_b_fun$',X1: 'C_option$'] : ( 'bind$b'('fun_app$bg'('map_option$'(X0),X1),X2) = 'fun_app$ab'('bind$'(X1),'comp$ap'(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_726])]) ).
tff(f2615,plain,
! [X2: 'B_c_option_fun$',X0: 'C_b_fun$',X1: 'C_option$'] : ( 'bind$b'('fun_app$bg'('map_option$'(X0),X1),X2) = 'fun_app$ab'('bind$'(X1),'comp$ap'(X2,X0)) ),
inference(cnf_transformation,[],[f539]) ).
tff(f539,axiom,
! [X0: 'C_b_fun$',X1: 'C_option$',X2: 'B_c_option_fun$'] : ( 'bind$b'('fun_app$bg'('map_option$'(X0),X1),X2) = 'fun_app$ab'('bind$'(X1),'comp$ap'(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom537) ).
tff(f9106,plain,
spl249_725,
inference(avatar_split_clause,[],[f2614,f9104]) ).
tff(f2614,plain,
! [X2: 'A$',X0: 'A_a_a_fun_fun$',X1: 'A$'] : ( 'fun_app$q'('uuw$'(X0,X1),X2) = 'fun_app$q'('some$b','fun_app$r'('fun_app$aj'(X0,X1),X2)) ),
inference(cnf_transformation,[],[f49]) ).
tff(f49,axiom,
! [X0: 'A_a_a_fun_fun$',X1: 'A$',X2: 'A$'] : ( 'fun_app$q'('uuw$'(X0,X1),X2) = 'fun_app$q'('some$b','fun_app$r'('fun_app$aj'(X0,X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom48) ).
tff(f9102,plain,
spl249_724,
inference(avatar_split_clause,[],[f2613,f9100]) ).
tff(f9100,plain,
( spl249_724
<=> ! [X2: 'B_option$',X0: 'B_b_b_fun_fun$',X1: 'B_option$'] : ( 'fun_app$s'('combine_options$b'(X0,X1),X2) = 'fun_app$s'('case_option$'(X2,'uvb$'(X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_724])]) ).
tff(f2613,plain,
! [X2: 'B_option$',X0: 'B_b_b_fun_fun$',X1: 'B_option$'] : ( 'fun_app$s'('combine_options$b'(X0,X1),X2) = 'fun_app$s'('case_option$'(X2,'uvb$'(X0,X2)),X1) ),
inference(cnf_transformation,[],[f179]) ).
tff(f179,axiom,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$',X2: 'B_option$'] : ( 'fun_app$s'('combine_options$b'(X0,X1),X2) = 'fun_app$s'('case_option$'(X2,'uvb$'(X0,X2)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom177) ).
tff(f9098,plain,
( spl249_723
| ~ spl249_252
| ~ spl249_433 ),
inference(avatar_split_clause,[],[f6277,f5756,f4736,f9096]) ).
tff(f9096,plain,
( spl249_723
<=> ! [X0: 'C_b_option_fun$',X1: 'C_option$'] : ~ sP23(X0,'bot$g',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_723])]) ).
tff(f6277,plain,
( ! [X0: 'C_b_option_fun$',X1: 'C_option$'] : ~ sP23(X0,'bot$g',X1)
| ~ spl249_252
| ~ spl249_433 ),
inference(resolution,[],[f5757,f4737]) ).
tff(f9094,plain,
spl249_722,
inference(avatar_split_clause,[],[f2612,f9092]) ).
tff(f9092,plain,
( spl249_722
<=> ! [X2: 'C_option$',X0: 'C_c_c_fun_fun$',X1: 'C_option$'] : ( 'fun_app$u'('combine_options$a'(X0,X1),X2) = 'fun_app$u'('case_option$a'(X2,'uuz$'(X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_722])]) ).
tff(f2612,plain,
! [X2: 'C_option$',X0: 'C_c_c_fun_fun$',X1: 'C_option$'] : ( 'fun_app$u'('combine_options$a'(X0,X1),X2) = 'fun_app$u'('case_option$a'(X2,'uuz$'(X0,X2)),X1) ),
inference(cnf_transformation,[],[f178]) ).
tff(f178,axiom,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$',X2: 'C_option$'] : ( 'fun_app$u'('combine_options$a'(X0,X1),X2) = 'fun_app$u'('case_option$a'(X2,'uuz$'(X0,X2)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom176) ).
tff(f9090,plain,
spl249_721,
inference(avatar_split_clause,[],[f2610,f9088]) ).
tff(f2610,plain,
! [X2: 'A$',X0: 'A_b_b_fun_fun$',X1: 'B$'] : ( 'fun_app$f'('uua$'(X0,X1),X2) = 'fun_app$g'('some$','fun_app$h'('fun_app$i'(X0,X2),X1)) ),
inference(cnf_transformation,[],[f51]) ).
tff(f51,axiom,
! [X0: 'A_b_b_fun_fun$',X1: 'B$',X2: 'A$'] : ( 'fun_app$f'('uua$'(X0,X1),X2) = 'fun_app$g'('some$','fun_app$h'('fun_app$i'(X0,X2),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom50) ).
tff(f9086,plain,
spl249_720,
inference(avatar_split_clause,[],[f2609,f9084]) ).
tff(f9084,plain,
( spl249_720
<=> ! [X2: 'B_b_fun$',X0: 'B_c_option_fun$',X1: 'B_b_fun$'] : ( 'comp$bk'(X0,'case_sum$b'(X1,X2)) = 'case_sum$c'('comp$f'(X0,X1),'comp$f'(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_720])]) ).
tff(f2609,plain,
! [X2: 'B_b_fun$',X0: 'B_c_option_fun$',X1: 'B_b_fun$'] : ( 'comp$bk'(X0,'case_sum$b'(X1,X2)) = 'case_sum$c'('comp$f'(X0,X1),'comp$f'(X0,X2)) ),
inference(cnf_transformation,[],[f673]) ).
tff(f673,axiom,
! [X0: 'B_c_option_fun$',X1: 'B_b_fun$',X2: 'B_b_fun$'] : ( 'comp$bk'(X0,'case_sum$b'(X1,X2)) = 'case_sum$c'('comp$f'(X0,X1),'comp$f'(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom671) ).
tff(f9082,plain,
spl249_719,
inference(avatar_split_clause,[],[f2608,f9080]) ).
tff(f9080,plain,
( spl249_719
<=> ! [X2: 'B_b_option_fun$',X0: 'B_option_b_fun$',X1: 'B_b_option_fun$'] : ( 'comp$bl'(X0,'case_sum$d'(X1,X2)) = 'case_sum$b'('comp$m'(X0,X1),'comp$m'(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_719])]) ).
tff(f2608,plain,
! [X2: 'B_b_option_fun$',X0: 'B_option_b_fun$',X1: 'B_b_option_fun$'] : ( 'comp$bl'(X0,'case_sum$d'(X1,X2)) = 'case_sum$b'('comp$m'(X0,X1),'comp$m'(X0,X2)) ),
inference(cnf_transformation,[],[f674]) ).
tff(f674,axiom,
! [X0: 'B_option_b_fun$',X1: 'B_b_option_fun$',X2: 'B_b_option_fun$'] : ( 'comp$bl'(X0,'case_sum$d'(X1,X2)) = 'case_sum$b'('comp$m'(X0,X1),'comp$m'(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom672) ).
tff(f9078,plain,
spl249_718,
inference(avatar_split_clause,[],[f2607,f9076]) ).
tff(f9076,plain,
( spl249_718
<=> ! [X2: 'A_a_fun$',X0: 'A_b_option_fun$',X1: 'A_a_fun$'] : ( 'comp$bj'(X0,'case_sum$'(X1,X2)) = 'case_sum$a'('comp$g'(X0,X1),'comp$g'(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_718])]) ).
tff(f2607,plain,
! [X2: 'A_a_fun$',X0: 'A_b_option_fun$',X1: 'A_a_fun$'] : ( 'comp$bj'(X0,'case_sum$'(X1,X2)) = 'case_sum$a'('comp$g'(X0,X1),'comp$g'(X0,X2)) ),
inference(cnf_transformation,[],[f672]) ).
tff(f672,axiom,
! [X0: 'A_b_option_fun$',X1: 'A_a_fun$',X2: 'A_a_fun$'] : ( 'comp$bj'(X0,'case_sum$'(X1,X2)) = 'case_sum$a'('comp$g'(X0,X1),'comp$g'(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom670) ).
tff(f9074,plain,
spl249_717,
inference(avatar_split_clause,[],[f2606,f9072]) ).
tff(f9072,plain,
( spl249_717
<=> ! [X2: 'C_c_option_fun$',X0: 'C_option_c_fun$',X1: 'C_c_option_fun$'] : ( 'comp$bm'(X0,'case_sum$e'(X1,X2)) = 'case_sum$f'('comp$n'(X0,X1),'comp$n'(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_717])]) ).
tff(f2606,plain,
! [X2: 'C_c_option_fun$',X0: 'C_option_c_fun$',X1: 'C_c_option_fun$'] : ( 'comp$bm'(X0,'case_sum$e'(X1,X2)) = 'case_sum$f'('comp$n'(X0,X1),'comp$n'(X0,X2)) ),
inference(cnf_transformation,[],[f675]) ).
tff(f675,axiom,
! [X0: 'C_option_c_fun$',X1: 'C_c_option_fun$',X2: 'C_c_option_fun$'] : ( 'comp$bm'(X0,'case_sum$e'(X1,X2)) = 'case_sum$f'('comp$n'(X0,X1),'comp$n'(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom673) ).
tff(f9070,plain,
spl249_716,
inference(avatar_split_clause,[],[f2532,f9068]) ).
tff(f9068,plain,
( spl249_716
<=> ! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'('is_none$','fun_app$ac'('bind$c'(X0),X1))
| ~ 'fun_app$a'('is_none$','fun_app$g'(X1,'fun_app$al'('the$',X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_716])]) ).
tff(f2532,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'('is_none$','fun_app$ac'('bind$c'(X0),X1))
| ~ 'fun_app$a'('is_none$','fun_app$g'(X1,'fun_app$al'('the$',X0))) ),
inference(cnf_transformation,[],[f1526]) ).
tff(f9066,plain,
spl249_715,
inference(avatar_split_clause,[],[f2525,f9064]) ).
tff(f9064,plain,
( spl249_715
<=> ! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( 'fun_app$'('is_none$a','fun_app$ab'('bind$'(X0),X1))
| ~ 'fun_app$'('is_none$a','fun_app$j'(X1,'fun_app$ak'('the$a',X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_715])]) ).
tff(f2525,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( 'fun_app$'('is_none$a','fun_app$ab'('bind$'(X0),X1))
| ~ 'fun_app$'('is_none$a','fun_app$j'(X1,'fun_app$ak'('the$a',X0))) ),
inference(cnf_transformation,[],[f1522]) ).
tff(f9062,plain,
spl249_714,
inference(avatar_split_clause,[],[f2502,f9060]) ).
tff(f9060,plain,
( spl249_714
<=> ! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( 'none$a' = 'fun_app$ac'('bind$c'(X0),X1) )
| ( 'none$a' != 'fun_app$g'(X1,'fun_app$al'('the$',X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_714])]) ).
tff(f2502,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( ( 'none$a' = 'fun_app$ac'('bind$c'(X0),X1) )
| ( 'none$a' != 'fun_app$g'(X1,'fun_app$al'('the$',X0)) ) ),
inference(cnf_transformation,[],[f1510]) ).
tff(f9058,plain,
spl249_713,
inference(avatar_split_clause,[],[f2487,f9056]) ).
tff(f9056,plain,
( spl249_713
<=> ! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( 'none$' = 'fun_app$ab'('bind$'(X0),X1) )
| ( 'none$' != 'fun_app$j'(X1,'fun_app$ak'('the$a',X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_713])]) ).
tff(f2487,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( ( 'none$' = 'fun_app$ab'('bind$'(X0),X1) )
| ( 'none$' != 'fun_app$j'(X1,'fun_app$ak'('the$a',X0)) ) ),
inference(cnf_transformation,[],[f1502]) ).
tff(f9054,plain,
( spl249_712
| ~ spl249_252
| ~ spl249_431 ),
inference(avatar_split_clause,[],[f6257,f5748,f4736,f9052]) ).
tff(f9052,plain,
( spl249_712
<=> ! [X0: 'A_b_option_fun$',X1: 'A_option$'] : ~ sP22(X0,'bot$g',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_712])]) ).
tff(f5748,plain,
( spl249_431
<=> ! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$a'(X0,'bind$e'(X1,X2))
| ~ sP22(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_431])]) ).
tff(f6257,plain,
( ! [X0: 'A_b_option_fun$',X1: 'A_option$'] : ~ sP22(X0,'bot$g',X1)
| ~ spl249_252
| ~ spl249_431 ),
inference(resolution,[],[f5749,f4737]) ).
tff(f5749,plain,
( ! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$a'(X0,'bind$e'(X1,X2))
| ~ sP22(X2,X0,X1) )
| ~ spl249_431 ),
inference(avatar_component_clause,[],[f5748]) ).
tff(f9050,plain,
spl249_711,
inference(avatar_split_clause,[],[f2460,f9048]) ).
tff(f9048,plain,
( spl249_711
<=> ! [X0: 'A_option$',X1: 'A_a_option_fun$'] :
( ( 'none$b' = 'fun_app$bp'('bind$h'(X0),X1) )
| ( 'none$b' != 'fun_app$q'(X1,'fun_app$bf'('the$b',X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_711])]) ).
tff(f2460,plain,
! [X0: 'A_option$',X1: 'A_a_option_fun$'] :
( ( 'none$b' = 'fun_app$bp'('bind$h'(X0),X1) )
| ( 'none$b' != 'fun_app$q'(X1,'fun_app$bf'('the$b',X0)) ) ),
inference(cnf_transformation,[],[f1488]) ).
tff(f8891,plain,
( spl249_710
| ~ spl249_252
| ~ spl249_429 ),
inference(avatar_split_clause,[],[f6236,f5740,f4736,f8889]) ).
tff(f8889,plain,
( spl249_710
<=> ! [X0: 'A_b_option_fun$',X1: 'A_option$'] : ~ sP21(X0,'bot$g',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_710])]) ).
tff(f5740,plain,
( spl249_429
<=> ! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$a'(X0,'bind$e'(X1,X2))
| ~ sP21(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_429])]) ).
tff(f6236,plain,
( ! [X0: 'A_b_option_fun$',X1: 'A_option$'] : ~ sP21(X0,'bot$g',X1)
| ~ spl249_252
| ~ spl249_429 ),
inference(resolution,[],[f5741,f4737]) ).
tff(f5741,plain,
( ! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$a'(X0,'bind$e'(X1,X2))
| ~ sP21(X2,X0,X1) )
| ~ spl249_429 ),
inference(avatar_component_clause,[],[f5740]) ).
tff(f8735,plain,
( spl249_709
| ~ spl249_251
| ~ spl249_425 ),
inference(avatar_split_clause,[],[f6191,f5722,f4732,f8733]) ).
tff(f8733,plain,
( spl249_709
<=> ! [X0: 'B_c_option_fun$',X1: 'B_option$'] : ~ sP19(X0,'bot$h',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_709])]) ).
tff(f6191,plain,
( ! [X0: 'B_c_option_fun$',X1: 'B_option$'] : ~ sP19(X0,'bot$h',X1)
| ~ spl249_251
| ~ spl249_425 ),
inference(resolution,[],[f5723,f4733]) ).
tff(f8676,plain,
( spl249_708
| ~ spl249_251
| ~ spl249_423 ),
inference(avatar_split_clause,[],[f6165,f5714,f4732,f8674]) ).
tff(f8674,plain,
( spl249_708
<=> ! [X0: 'B_c_option_fun$',X1: 'B_option$'] : ~ sP18(X0,'bot$h',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_708])]) ).
tff(f6165,plain,
( ! [X0: 'B_c_option_fun$',X1: 'B_option$'] : ~ sP18(X0,'bot$h',X1)
| ~ spl249_251
| ~ spl249_423 ),
inference(resolution,[],[f5715,f4733]) ).
tff(f8672,plain,
( spl249_707
| ~ spl249_251
| ~ spl249_421 ),
inference(avatar_split_clause,[],[f6143,f5706,f4732,f8670]) ).
tff(f8670,plain,
( spl249_707
<=> ! [X0: 'A_c_option_fun$',X1: 'A_option$'] : ~ sP17(X0,'bot$h',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_707])]) ).
tff(f5706,plain,
( spl249_421
<=> ! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$'(X0,'bind$d'(X1,X2))
| ~ sP17(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_421])]) ).
tff(f6143,plain,
( ! [X0: 'A_c_option_fun$',X1: 'A_option$'] : ~ sP17(X0,'bot$h',X1)
| ~ spl249_251
| ~ spl249_421 ),
inference(resolution,[],[f5707,f4733]) ).
tff(f5707,plain,
( ! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$'(X0,'bind$d'(X1,X2))
| ~ sP17(X2,X0,X1) )
| ~ spl249_421 ),
inference(avatar_component_clause,[],[f5706]) ).
tff(f8626,plain,
( spl249_706
| ~ spl249_251
| ~ spl249_419 ),
inference(avatar_split_clause,[],[f6121,f5698,f4732,f8624]) ).
tff(f8624,plain,
( spl249_706
<=> ! [X0: 'A_c_option_fun$',X1: 'A_option$'] : ~ sP16(X0,'bot$h',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_706])]) ).
tff(f5698,plain,
( spl249_419
<=> ! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$'(X0,'bind$d'(X1,X2))
| ~ sP16(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_419])]) ).
tff(f6121,plain,
( ! [X0: 'A_c_option_fun$',X1: 'A_option$'] : ~ sP16(X0,'bot$h',X1)
| ~ spl249_251
| ~ spl249_419 ),
inference(resolution,[],[f5699,f4733]) ).
tff(f5699,plain,
( ! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$'(X0,'bind$d'(X1,X2))
| ~ sP16(X2,X0,X1) )
| ~ spl249_419 ),
inference(avatar_component_clause,[],[f5698]) ).
tff(f8280,plain,
spl249_705,
inference(avatar_split_clause,[],[f3591,f8278]) ).
tff(f8278,plain,
( spl249_705
<=> ! [X2: 'B$',X1: 'B_bool_fun$'] :
( 'member$c'(sK159('fun_app$g'('some$',X2),X1),'insert$'(X2,'bot$d'))
| 'fun_app$c'(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_705])]) ).
tff(f3591,plain,
! [X2: 'B$',X1: 'B_bool_fun$'] :
( 'member$c'(sK159('fun_app$g'('some$',X2),X1),'insert$'(X2,'bot$d'))
| 'fun_app$c'(X1,X2) ),
inference(forward_demodulation,[],[f3438,f2033]) ).
tff(f2033,plain,
! [X0: 'B$'] : ( 'set_option$d'('fun_app$g'('some$',X0)) = 'insert$'(X0,'bot$d') ),
inference(cnf_transformation,[],[f695]) ).
tff(f695,axiom,
! [X0: 'B$'] : ( 'set_option$d'('fun_app$g'('some$',X0)) = 'insert$'(X0,'bot$d') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom693) ).
tff(f3438,plain,
! [X2: 'B$',X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,X2)
| 'member$c'(sK159('fun_app$g'('some$',X2),X1),'set_option$d'('fun_app$g'('some$',X2))) ),
inference(equality_resolution,[],[f2769]) ).
tff(f2769,plain,
! [X2: 'B$',X0: 'B_option$',X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,X2)
| ( 'fun_app$g'('some$',X2) != X0 )
| 'member$c'(sK159(X0,X1),'set_option$d'(X0)) ),
inference(cnf_transformation,[],[f1584]) ).
tff(f1584,plain,
! [X0: 'B_option$',X1: 'B_bool_fun$',X2: 'B$'] :
( 'fun_app$c'(X1,X2)
| ( 'fun_app$g'('some$',X2) != X0 )
| ( ~ 'fun_app$c'(X1,sK159(X0,X1))
& 'member$c'(sK159(X0,X1),'set_option$d'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK159])],[f991,f1583]) ).
tff(f1583,plain,
! [X0: 'B_option$',X1: 'B_bool_fun$'] :
( ? [X3: 'B$'] :
( ~ 'fun_app$c'(X1,X3)
& 'member$c'(X3,'set_option$d'(X0)) )
=> ( ~ 'fun_app$c'(X1,sK159(X0,X1))
& 'member$c'(sK159(X0,X1),'set_option$d'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f991,plain,
! [X0: 'B_option$',X1: 'B_bool_fun$',X2: 'B$'] :
( 'fun_app$c'(X1,X2)
| ( 'fun_app$g'('some$',X2) != X0 )
| ? [X3: 'B$'] :
( ~ 'fun_app$c'(X1,X3)
& 'member$c'(X3,'set_option$d'(X0)) ) ),
inference(flattening,[],[f990]) ).
tff(f990,plain,
! [X0: 'B_option$',X1: 'B_bool_fun$',X2: 'B$'] :
( 'fun_app$c'(X1,X2)
| ( 'fun_app$g'('some$',X2) != X0 )
| ? [X3: 'B$'] :
( ~ 'fun_app$c'(X1,X3)
& 'member$c'(X3,'set_option$d'(X0)) ) ),
inference(ennf_transformation,[],[f431]) ).
tff(f431,axiom,
! [X0: 'B_option$',X1: 'B_bool_fun$',X2: 'B$'] :
( ( ( 'fun_app$g'('some$',X2) = X0 )
& ! [X3: 'B$'] :
( 'member$c'(X3,'set_option$d'(X0))
=> 'fun_app$c'(X1,X3) ) )
=> 'fun_app$c'(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom429) ).
tff(f8276,plain,
spl249_704,
inference(avatar_split_clause,[],[f3590,f8274]) ).
tff(f8274,plain,
( spl249_704
<=> ! [X2: 'C$',X1: 'C_bool_fun$'] :
( 'member$b'(sK158('fun_app$j'('some$a',X2),X1),'insert$a'(X2,'bot$c'))
| 'fun_app$b'(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_704])]) ).
tff(f3590,plain,
! [X2: 'C$',X1: 'C_bool_fun$'] :
( 'member$b'(sK158('fun_app$j'('some$a',X2),X1),'insert$a'(X2,'bot$c'))
| 'fun_app$b'(X1,X2) ),
inference(forward_demodulation,[],[f3436,f2032]) ).
tff(f2032,plain,
! [X0: 'C$'] : ( 'set_option$c'('fun_app$j'('some$a',X0)) = 'insert$a'(X0,'bot$c') ),
inference(cnf_transformation,[],[f694]) ).
tff(f694,axiom,
! [X0: 'C$'] : ( 'set_option$c'('fun_app$j'('some$a',X0)) = 'insert$a'(X0,'bot$c') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom692) ).
tff(f3436,plain,
! [X2: 'C$',X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,X2)
| 'member$b'(sK158('fun_app$j'('some$a',X2),X1),'set_option$c'('fun_app$j'('some$a',X2))) ),
inference(equality_resolution,[],[f2767]) ).
tff(f2767,plain,
! [X2: 'C$',X0: 'C_option$',X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,X2)
| ( 'fun_app$j'('some$a',X2) != X0 )
| 'member$b'(sK158(X0,X1),'set_option$c'(X0)) ),
inference(cnf_transformation,[],[f1582]) ).
tff(f1582,plain,
! [X0: 'C_option$',X1: 'C_bool_fun$',X2: 'C$'] :
( 'fun_app$b'(X1,X2)
| ( 'fun_app$j'('some$a',X2) != X0 )
| ( ~ 'fun_app$b'(X1,sK158(X0,X1))
& 'member$b'(sK158(X0,X1),'set_option$c'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK158])],[f989,f1581]) ).
tff(f1581,plain,
! [X0: 'C_option$',X1: 'C_bool_fun$'] :
( ? [X3: 'C$'] :
( ~ 'fun_app$b'(X1,X3)
& 'member$b'(X3,'set_option$c'(X0)) )
=> ( ~ 'fun_app$b'(X1,sK158(X0,X1))
& 'member$b'(sK158(X0,X1),'set_option$c'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f989,plain,
! [X0: 'C_option$',X1: 'C_bool_fun$',X2: 'C$'] :
( 'fun_app$b'(X1,X2)
| ( 'fun_app$j'('some$a',X2) != X0 )
| ? [X3: 'C$'] :
( ~ 'fun_app$b'(X1,X3)
& 'member$b'(X3,'set_option$c'(X0)) ) ),
inference(flattening,[],[f988]) ).
tff(f988,plain,
! [X0: 'C_option$',X1: 'C_bool_fun$',X2: 'C$'] :
( 'fun_app$b'(X1,X2)
| ( 'fun_app$j'('some$a',X2) != X0 )
| ? [X3: 'C$'] :
( ~ 'fun_app$b'(X1,X3)
& 'member$b'(X3,'set_option$c'(X0)) ) ),
inference(ennf_transformation,[],[f430]) ).
tff(f430,axiom,
! [X0: 'C_option$',X1: 'C_bool_fun$',X2: 'C$'] :
( ( ( 'fun_app$j'('some$a',X2) = X0 )
& ! [X3: 'C$'] :
( 'member$b'(X3,'set_option$c'(X0))
=> 'fun_app$b'(X1,X3) ) )
=> 'fun_app$b'(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom428) ).
tff(f8272,plain,
spl249_703,
inference(avatar_split_clause,[],[f3270,f8270]) ).
tff(f3270,plain,
! [X2: 'B$',X0: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X0,'bind$b'('fun_app$g'('some$',X2),X1))
| ~ 'fun_app$c'('uul$'(X0,X1),X2) ),
inference(definition_unfolding,[],[f2791,f2234]) ).
tff(f2791,plain,
! [X2: 'B$',X0: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X0,'fun_app$n'(X1,X2))
| ~ 'fun_app$c'('uul$'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1603]) ).
tff(f1603,plain,
! [X0: 'C_option_bool_fun$',X1: 'B_c_option_fun$',X2: 'B$'] :
( ( 'fun_app$c'('uul$'(X0,X1),X2)
| ~ 'fun_app$'(X0,'fun_app$n'(X1,X2)) )
& ( 'fun_app$'(X0,'fun_app$n'(X1,X2))
| ~ 'fun_app$c'('uul$'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f39]) ).
tff(f39,axiom,
! [X0: 'C_option_bool_fun$',X1: 'B_c_option_fun$',X2: 'B$'] :
( 'fun_app$c'('uul$'(X0,X1),X2)
<=> 'fun_app$'(X0,'fun_app$n'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom38) ).
tff(f8268,plain,
spl249_702,
inference(avatar_split_clause,[],[f3269,f8266]) ).
tff(f8266,plain,
( spl249_702
<=> ! [X2: 'B$',X0: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( 'fun_app$c'('uul$'(X0,X1),X2)
| ~ 'fun_app$'(X0,'bind$b'('fun_app$g'('some$',X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_702])]) ).
tff(f3269,plain,
! [X2: 'B$',X0: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( 'fun_app$c'('uul$'(X0,X1),X2)
| ~ 'fun_app$'(X0,'bind$b'('fun_app$g'('some$',X2),X1)) ),
inference(definition_unfolding,[],[f2792,f2234]) ).
tff(f2792,plain,
! [X2: 'B$',X0: 'C_option_bool_fun$',X1: 'B_c_option_fun$'] :
( 'fun_app$c'('uul$'(X0,X1),X2)
| ~ 'fun_app$'(X0,'fun_app$n'(X1,X2)) ),
inference(cnf_transformation,[],[f1603]) ).
tff(f8264,plain,
spl249_701,
inference(avatar_split_clause,[],[f3245,f8262]) ).
tff(f8262,plain,
( spl249_701
<=> ! [X0: 'B_c_fun$',X1: 'B$'] : ( 'fun_app$j'('some$a','fun_app$o'(X0,X1)) = 'bind$b'('fun_app$g'('some$',X1),'uvg$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_701])]) ).
tff(f3245,plain,
! [X0: 'B_c_fun$',X1: 'B$'] : ( 'fun_app$j'('some$a','fun_app$o'(X0,X1)) = 'bind$b'('fun_app$g'('some$',X1),'uvg$'(X0)) ),
inference(definition_unfolding,[],[f2240,f2234]) ).
tff(f2240,plain,
! [X0: 'B_c_fun$',X1: 'B$'] : ( 'fun_app$n'('uvg$'(X0),X1) = 'fun_app$j'('some$a','fun_app$o'(X0,X1)) ),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
! [X0: 'B_c_fun$',X1: 'B$'] : ( 'fun_app$n'('uvg$'(X0),X1) = 'fun_app$j'('some$a','fun_app$o'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom15) ).
tff(f8260,plain,
spl249_700,
inference(avatar_split_clause,[],[f3244,f8258]) ).
tff(f8258,plain,
( spl249_700
<=> ! [X0: 'C_b_fun$',X1: 'C$'] : ( 'fun_app$g'('some$','fun_app$m'(X0,X1)) = 'bind$a'('fun_app$j'('some$a',X1),'uvc$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_700])]) ).
tff(f3244,plain,
! [X0: 'C_b_fun$',X1: 'C$'] : ( 'fun_app$g'('some$','fun_app$m'(X0,X1)) = 'bind$a'('fun_app$j'('some$a',X1),'uvc$'(X0)) ),
inference(definition_unfolding,[],[f2235,f2233]) ).
tff(f2235,plain,
! [X0: 'C_b_fun$',X1: 'C$'] : ( 'fun_app$l'('uvc$'(X0),X1) = 'fun_app$g'('some$','fun_app$m'(X0,X1)) ),
inference(cnf_transformation,[],[f15]) ).
tff(f15,axiom,
! [X0: 'C_b_fun$',X1: 'C$'] : ( 'fun_app$l'('uvc$'(X0),X1) = 'fun_app$g'('some$','fun_app$m'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom14) ).
tff(f8256,plain,
spl249_699,
inference(avatar_split_clause,[],[f3226,f8254]) ).
tff(f3226,plain,
! [X2: 'B_b_option_fun$',X3: 'B_option$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
| ~ sP43(X3,X2,X0,X1) ),
inference(cnf_transformation,[],[f1913]) ).
tff(f1913,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_option$'] :
( ( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
| ~ sP43(X3,X2,X0,X1) )
& ( sP43(X3,X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3)) ) ),
inference(nnf_transformation,[],[f1186]) ).
tff(f1186,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
<=> sP43(X3,X2,X0,X1) ),
inference(definition_folding,[],[f1094,f1185]) ).
tff(f1094,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
<=> ( ( 'fun_app$a'(X0,'fun_app$g'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$a' != X3 ) ) ) ),
inference(ennf_transformation,[],[f182]) ).
tff(f182,axiom,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
<=> ~ ( ( ~ 'fun_app$a'(X0,'fun_app$g'(X2,'fun_app$al'('the$',X3)))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$a'(X0,X1)
& ( 'none$a' = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom180) ).
tff(f8252,plain,
spl249_698,
inference(avatar_split_clause,[],[f3225,f8250]) ).
tff(f8250,plain,
( spl249_698
<=> ! [X0: 'B_option_bool_fun$',X3: 'B_option$',X2: 'B_b_option_fun$',X1: 'B_option$'] :
( sP43(X3,X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_698])]) ).
tff(f3225,plain,
! [X2: 'B_b_option_fun$',X3: 'B_option$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( sP43(X3,X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3)) ),
inference(cnf_transformation,[],[f1913]) ).
tff(f8248,plain,
spl249_697,
inference(avatar_split_clause,[],[f3218,f8246]) ).
tff(f3218,plain,
! [X2: 'B_b_option_fun$',X3: 'B_option$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
| ~ sP42(X3,X2,X0,X1) ),
inference(cnf_transformation,[],[f1909]) ).
tff(f1909,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_option$'] :
( ( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
| ~ sP42(X3,X2,X0,X1) )
& ( sP42(X3,X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3)) ) ),
inference(nnf_transformation,[],[f1184]) ).
tff(f1184,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
<=> sP42(X3,X2,X0,X1) ),
inference(definition_folding,[],[f1093,f1183]) ).
tff(f1093,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
<=> ( ( 'fun_app$a'(X0,'fun_app$g'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$a' != X3 ) ) ) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,axiom,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$',X3: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3))
<=> ( ( ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 )
=> 'fun_app$a'(X0,'fun_app$g'(X2,'fun_app$al'('the$',X3))) )
& ( ( 'none$a' = X3 )
=> 'fun_app$a'(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom186) ).
tff(f8244,plain,
spl249_696,
inference(avatar_split_clause,[],[f3217,f8242]) ).
tff(f8242,plain,
( spl249_696
<=> ! [X0: 'B_option_bool_fun$',X3: 'B_option$',X2: 'B_b_option_fun$',X1: 'B_option$'] :
( sP42(X3,X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_696])]) ).
tff(f3217,plain,
! [X2: 'B_b_option_fun$',X3: 'B_option$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( sP42(X3,X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$s'('case_option$'(X1,X2),X3)) ),
inference(cnf_transformation,[],[f1909]) ).
tff(f8238,plain,
spl249_695,
inference(avatar_split_clause,[],[f3208,f8236]) ).
tff(f3208,plain,
! [X2: 'A_b_option_fun$',X3: 'A_option$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3))
| ~ sP41(X3,X2,X0,X1) ),
inference(cnf_transformation,[],[f1904]) ).
tff(f1904,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'A_b_option_fun$',X3: 'A_option$'] :
( ( 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3))
| ~ sP41(X3,X2,X0,X1) )
& ( sP41(X3,X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3)) ) ),
inference(nnf_transformation,[],[f1182]) ).
tff(f1182,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'A_b_option_fun$',X3: 'A_option$'] :
( 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3))
<=> sP41(X3,X2,X0,X1) ),
inference(definition_folding,[],[f1092,f1181]) ).
tff(f1092,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'A_b_option_fun$',X3: 'A_option$'] :
( 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3))
<=> ( ( 'fun_app$a'(X0,'fun_app$f'(X2,'fun_app$bf'('the$b',X3)))
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$b' != X3 ) ) ) ),
inference(ennf_transformation,[],[f185]) ).
tff(f185,axiom,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'A_b_option_fun$',X3: 'A_option$'] :
( 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3))
<=> ~ ( ( ~ 'fun_app$a'(X0,'fun_app$f'(X2,'fun_app$bf'('the$b',X3)))
& ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X3)) = X3 ) )
| ( ~ 'fun_app$a'(X0,X1)
& ( 'none$b' = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom183) ).
tff(f8234,plain,
spl249_694,
inference(avatar_split_clause,[],[f3207,f8232]) ).
tff(f8232,plain,
( spl249_694
<=> ! [X0: 'B_option_bool_fun$',X3: 'A_option$',X2: 'A_b_option_fun$',X1: 'B_option$'] :
( sP41(X3,X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_694])]) ).
tff(f3207,plain,
! [X2: 'A_b_option_fun$',X3: 'A_option$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( sP41(X3,X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3)) ),
inference(cnf_transformation,[],[f1904]) ).
tff(f8230,plain,
spl249_693,
inference(avatar_split_clause,[],[f3200,f8228]) ).
tff(f3200,plain,
! [X2: 'A_b_option_fun$',X3: 'A_option$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3))
| ~ sP40(X3,X2,X0,X1) ),
inference(cnf_transformation,[],[f1900]) ).
tff(f1900,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'A_b_option_fun$',X3: 'A_option$'] :
( ( 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3))
| ~ sP40(X3,X2,X0,X1) )
& ( sP40(X3,X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3)) ) ),
inference(nnf_transformation,[],[f1180]) ).
tff(f1180,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'A_b_option_fun$',X3: 'A_option$'] :
( 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3))
<=> sP40(X3,X2,X0,X1) ),
inference(definition_folding,[],[f1091,f1179]) ).
tff(f1091,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'A_b_option_fun$',X3: 'A_option$'] :
( 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3))
<=> ( ( 'fun_app$a'(X0,'fun_app$f'(X2,'fun_app$bf'('the$b',X3)))
| ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X3)) != X3 ) )
& ( 'fun_app$a'(X0,X1)
| ( 'none$b' != X3 ) ) ) ),
inference(ennf_transformation,[],[f191]) ).
tff(f191,axiom,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'A_b_option_fun$',X3: 'A_option$'] :
( 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3))
<=> ( ( ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X3)) = X3 )
=> 'fun_app$a'(X0,'fun_app$f'(X2,'fun_app$bf'('the$b',X3))) )
& ( ( 'none$b' = X3 )
=> 'fun_app$a'(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom189) ).
tff(f8226,plain,
spl249_692,
inference(avatar_split_clause,[],[f3199,f8224]) ).
tff(f8224,plain,
( spl249_692
<=> ! [X0: 'B_option_bool_fun$',X3: 'A_option$',X2: 'A_b_option_fun$',X1: 'B_option$'] :
( sP40(X3,X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_692])]) ).
tff(f3199,plain,
! [X2: 'A_b_option_fun$',X3: 'A_option$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( sP40(X3,X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$av'('case_option$d'(X1,X2),X3)) ),
inference(cnf_transformation,[],[f1900]) ).
tff(f8222,plain,
spl249_691,
inference(avatar_split_clause,[],[f3192,f8220]) ).
tff(f3192,plain,
! [X2: 'B_c_option_fun$',X3: 'B_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
| ~ sP39(X3,X2,X0,X1) ),
inference(cnf_transformation,[],[f1896]) ).
tff(f1896,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'B_c_option_fun$',X3: 'B_option$'] :
( ( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
| ~ sP39(X3,X2,X0,X1) )
& ( sP39(X3,X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3)) ) ),
inference(nnf_transformation,[],[f1178]) ).
tff(f1178,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'B_c_option_fun$',X3: 'B_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
<=> sP39(X3,X2,X0,X1) ),
inference(definition_folding,[],[f1090,f1177]) ).
tff(f1090,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'B_c_option_fun$',X3: 'B_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
<=> ( ( 'fun_app$'(X0,'fun_app$n'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$a' != X3 ) ) ) ),
inference(ennf_transformation,[],[f184]) ).
tff(f184,axiom,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'B_c_option_fun$',X3: 'B_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
<=> ~ ( ( ~ 'fun_app$'(X0,'fun_app$n'(X2,'fun_app$al'('the$',X3)))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$'(X0,X1)
& ( 'none$a' = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom182) ).
tff(f8218,plain,
spl249_690,
inference(avatar_split_clause,[],[f3191,f8216]) ).
tff(f8216,plain,
( spl249_690
<=> ! [X0: 'C_option_bool_fun$',X3: 'B_option$',X2: 'B_c_option_fun$',X1: 'C_option$'] :
( sP39(X3,X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_690])]) ).
tff(f3191,plain,
! [X2: 'B_c_option_fun$',X3: 'B_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( sP39(X3,X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3)) ),
inference(cnf_transformation,[],[f1896]) ).
tff(f8214,plain,
spl249_689,
inference(avatar_split_clause,[],[f3184,f8212]) ).
tff(f3184,plain,
! [X2: 'B_c_option_fun$',X3: 'B_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
| ~ sP38(X3,X2,X0,X1) ),
inference(cnf_transformation,[],[f1892]) ).
tff(f1892,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'B_c_option_fun$',X3: 'B_option$'] :
( ( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
| ~ sP38(X3,X2,X0,X1) )
& ( sP38(X3,X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3)) ) ),
inference(nnf_transformation,[],[f1176]) ).
tff(f1176,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'B_c_option_fun$',X3: 'B_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
<=> sP38(X3,X2,X0,X1) ),
inference(definition_folding,[],[f1089,f1175]) ).
tff(f1089,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'B_c_option_fun$',X3: 'B_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
<=> ( ( 'fun_app$'(X0,'fun_app$n'(X2,'fun_app$al'('the$',X3)))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$a' != X3 ) ) ) ),
inference(ennf_transformation,[],[f190]) ).
tff(f190,axiom,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'B_c_option_fun$',X3: 'B_option$'] :
( 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3))
<=> ( ( ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 )
=> 'fun_app$'(X0,'fun_app$n'(X2,'fun_app$al'('the$',X3))) )
& ( ( 'none$a' = X3 )
=> 'fun_app$'(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom188) ).
tff(f8210,plain,
spl249_688,
inference(avatar_split_clause,[],[f3183,f8208]) ).
tff(f8208,plain,
( spl249_688
<=> ! [X0: 'C_option_bool_fun$',X3: 'B_option$',X2: 'B_c_option_fun$',X1: 'C_option$'] :
( sP38(X3,X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_688])]) ).
tff(f3183,plain,
! [X2: 'B_c_option_fun$',X3: 'B_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( sP38(X3,X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$an'('case_option$c'(X1,X2),X3)) ),
inference(cnf_transformation,[],[f1892]) ).
tff(f8206,plain,
spl249_687,
inference(avatar_split_clause,[],[f3174,f8204]) ).
tff(f3174,plain,
! [X2: 'C_c_option_fun$',X3: 'C_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
| ~ sP37(X3,X2,X0,X1) ),
inference(cnf_transformation,[],[f1887]) ).
tff(f1887,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_option$'] :
( ( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
| ~ sP37(X3,X2,X0,X1) )
& ( sP37(X3,X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3)) ) ),
inference(nnf_transformation,[],[f1174]) ).
tff(f1174,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
<=> sP37(X3,X2,X0,X1) ),
inference(definition_folding,[],[f1088,f1173]) ).
tff(f1088,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
<=> ( ( 'fun_app$'(X0,'fun_app$j'(X2,'fun_app$ak'('the$a',X3)))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$' != X3 ) ) ) ),
inference(ennf_transformation,[],[f183]) ).
tff(f183,axiom,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
<=> ~ ( ( ~ 'fun_app$'(X0,'fun_app$j'(X2,'fun_app$ak'('the$a',X3)))
& ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) = X3 ) )
| ( ~ 'fun_app$'(X0,X1)
& ( 'none$' = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom181) ).
tff(f8202,plain,
spl249_686,
inference(avatar_split_clause,[],[f3173,f8200]) ).
tff(f8200,plain,
( spl249_686
<=> ! [X0: 'C_option_bool_fun$',X3: 'C_option$',X2: 'C_c_option_fun$',X1: 'C_option$'] :
( sP37(X3,X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_686])]) ).
tff(f3173,plain,
! [X2: 'C_c_option_fun$',X3: 'C_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( sP37(X3,X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3)) ),
inference(cnf_transformation,[],[f1887]) ).
tff(f8196,plain,
spl249_685,
inference(avatar_split_clause,[],[f3166,f8194]) ).
tff(f3166,plain,
! [X2: 'C_c_option_fun$',X3: 'C_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
| ~ sP36(X3,X2,X0,X1) ),
inference(cnf_transformation,[],[f1883]) ).
tff(f1883,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_option$'] :
( ( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
| ~ sP36(X3,X2,X0,X1) )
& ( sP36(X3,X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3)) ) ),
inference(nnf_transformation,[],[f1172]) ).
tff(f1172,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
<=> sP36(X3,X2,X0,X1) ),
inference(definition_folding,[],[f1087,f1171]) ).
tff(f1087,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
<=> ( ( 'fun_app$'(X0,'fun_app$j'(X2,'fun_app$ak'('the$a',X3)))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$'(X0,X1)
| ( 'none$' != X3 ) ) ) ),
inference(ennf_transformation,[],[f189]) ).
tff(f189,axiom,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$',X3: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3))
<=> ( ( ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) = X3 )
=> 'fun_app$'(X0,'fun_app$j'(X2,'fun_app$ak'('the$a',X3))) )
& ( ( 'none$' = X3 )
=> 'fun_app$'(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom187) ).
tff(f8192,plain,
spl249_684,
inference(avatar_split_clause,[],[f3165,f8190]) ).
tff(f8190,plain,
( spl249_684
<=> ! [X0: 'C_option_bool_fun$',X3: 'C_option$',X2: 'C_c_option_fun$',X1: 'C_option$'] :
( sP36(X3,X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_684])]) ).
tff(f3165,plain,
! [X2: 'C_c_option_fun$',X3: 'C_option$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( sP36(X3,X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$u'('case_option$a'(X1,X2),X3)) ),
inference(cnf_transformation,[],[f1883]) ).
tff(f8188,plain,
spl249_683,
inference(avatar_split_clause,[],[f2905,f8186]) ).
tff(f2905,plain,
! [X2: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( sP25(X0,X1,X2)
| ~ 'fun_app$c'(X1,'fun_app$al'('the$',X0))
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f1684]) ).
tff(f1684,plain,
! [X0: 'B_option$',X1: 'B_bool_fun$',X2: tlbool] :
( ( sP25(X0,X1,X2)
| ( ~ 'fun_app$c'(X1,'fun_app$al'('the$',X0))
& ( 'none$a' != X0 ) )
| ( ( tltrue != X2 )
& ( 'none$a' = X0 ) ) )
& ( ( ( 'fun_app$c'(X1,'fun_app$al'('the$',X0))
| ( 'none$a' = X0 ) )
& ( ( tltrue = X2 )
| ( 'none$a' != X0 ) ) )
| ~ sP25(X0,X1,X2) ) ),
inference(rectify,[],[f1683]) ).
tff(f1683,plain,
! [X2: 'B_option$',X1: 'B_bool_fun$',X0: tlbool] :
( ( sP25(X2,X1,X0)
| ( ~ 'fun_app$c'(X1,'fun_app$al'('the$',X2))
& ( 'none$a' != X2 ) )
| ( ( tltrue != X0 )
& ( 'none$a' = X2 ) ) )
& ( ( ( 'fun_app$c'(X1,'fun_app$al'('the$',X2))
| ( 'none$a' = X2 ) )
& ( ( tltrue = X0 )
| ( 'none$a' != X2 ) ) )
| ~ sP25(X2,X1,X0) ) ),
inference(flattening,[],[f1682]) ).
tff(f1682,plain,
! [X2: 'B_option$',X1: 'B_bool_fun$',X0: tlbool] :
( ( sP25(X2,X1,X0)
| ( ~ 'fun_app$c'(X1,'fun_app$al'('the$',X2))
& ( 'none$a' != X2 ) )
| ( ( tltrue != X0 )
& ( 'none$a' = X2 ) ) )
& ( ( ( 'fun_app$c'(X1,'fun_app$al'('the$',X2))
| ( 'none$a' = X2 ) )
& ( ( tltrue = X0 )
| ( 'none$a' != X2 ) ) )
| ~ sP25(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f1149]) ).
tff(f1149,plain,
! [X2: 'B_option$',X1: 'B_bool_fun$',X0: tlbool] :
( sP25(X2,X1,X0)
<=> ( ( 'fun_app$c'(X1,'fun_app$al'('the$',X2))
| ( 'none$a' = X2 ) )
& ( ( tltrue = X0 )
| ( 'none$a' != X2 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP25])]) ).
tff(f8184,plain,
spl249_682,
inference(avatar_split_clause,[],[f2902,f8182]) ).
tff(f8182,plain,
( spl249_682
<=> ! [X2: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,'fun_app$al'('the$',X0))
| ( 'none$a' = X0 )
| ~ sP25(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_682])]) ).
tff(f2902,plain,
! [X2: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,'fun_app$al'('the$',X0))
| ( 'none$a' = X0 )
| ~ sP25(X0,X1,X2) ),
inference(cnf_transformation,[],[f1684]) ).
tff(f8180,plain,
spl249_681,
inference(avatar_split_clause,[],[f2865,f8178]) ).
tff(f2865,plain,
! [X2: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( sP20(X0,X1,X2)
| ~ 'fun_app$b'(X1,'fun_app$ak'('the$a',X0))
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f1656]) ).
tff(f1656,plain,
! [X0: 'C_option$',X1: 'C_bool_fun$',X2: tlbool] :
( ( sP20(X0,X1,X2)
| ( ~ 'fun_app$b'(X1,'fun_app$ak'('the$a',X0))
& ( 'none$' != X0 ) )
| ( ( tltrue != X2 )
& ( 'none$' = X0 ) ) )
& ( ( ( 'fun_app$b'(X1,'fun_app$ak'('the$a',X0))
| ( 'none$' = X0 ) )
& ( ( tltrue = X2 )
| ( 'none$' != X0 ) ) )
| ~ sP20(X0,X1,X2) ) ),
inference(rectify,[],[f1655]) ).
tff(f1655,plain,
! [X2: 'C_option$',X1: 'C_bool_fun$',X0: tlbool] :
( ( sP20(X2,X1,X0)
| ( ~ 'fun_app$b'(X1,'fun_app$ak'('the$a',X2))
& ( 'none$' != X2 ) )
| ( ( tltrue != X0 )
& ( 'none$' = X2 ) ) )
& ( ( ( 'fun_app$b'(X1,'fun_app$ak'('the$a',X2))
| ( 'none$' = X2 ) )
& ( ( tltrue = X0 )
| ( 'none$' != X2 ) ) )
| ~ sP20(X2,X1,X0) ) ),
inference(flattening,[],[f1654]) ).
tff(f1654,plain,
! [X2: 'C_option$',X1: 'C_bool_fun$',X0: tlbool] :
( ( sP20(X2,X1,X0)
| ( ~ 'fun_app$b'(X1,'fun_app$ak'('the$a',X2))
& ( 'none$' != X2 ) )
| ( ( tltrue != X0 )
& ( 'none$' = X2 ) ) )
& ( ( ( 'fun_app$b'(X1,'fun_app$ak'('the$a',X2))
| ( 'none$' = X2 ) )
& ( ( tltrue = X0 )
| ( 'none$' != X2 ) ) )
| ~ sP20(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f1139]) ).
tff(f1139,plain,
! [X2: 'C_option$',X1: 'C_bool_fun$',X0: tlbool] :
( sP20(X2,X1,X0)
<=> ( ( 'fun_app$b'(X1,'fun_app$ak'('the$a',X2))
| ( 'none$' = X2 ) )
& ( ( tltrue = X0 )
| ( 'none$' != X2 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).
tff(f8176,plain,
spl249_680,
inference(avatar_split_clause,[],[f2862,f8174]) ).
tff(f8174,plain,
( spl249_680
<=> ! [X2: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,'fun_app$ak'('the$a',X0))
| ( 'none$' = X0 )
| ~ sP20(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_680])]) ).
tff(f2862,plain,
! [X2: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,'fun_app$ak'('the$a',X0))
| ( 'none$' = X0 )
| ~ sP20(X0,X1,X2) ),
inference(cnf_transformation,[],[f1656]) ).
tff(f8172,plain,
spl249_679,
inference(avatar_split_clause,[],[f2755,f8170]) ).
tff(f8170,plain,
( spl249_679
<=> ! [X2: 'B_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',sK154(X0,X1,X2)) = X0 )
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_679])]) ).
tff(f2755,plain,
! [X2: 'B_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',sK154(X0,X1,X2)) = X0 )
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f1574]) ).
tff(f1574,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_option_b_option_bool_fun_fun$'] :
( ( ~ 'fun_app$a'('fun_app$e'(X2,X1),X0)
& ( 'fun_app$g'('some$',sK154(X0,X1,X2)) = X0 )
& ( 'fun_app$g'('some$',sK153(X0,X1,X2)) = X1 ) )
| ~ sP11(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK153,sK154])],[f1572,f1573]) ).
tff(f1573,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_option_b_option_bool_fun_fun$'] :
( ? [X3: 'B$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$e'(X2,X1),X0)
& ( 'fun_app$g'('some$',X4) = X0 )
& ( 'fun_app$g'('some$',X3) = X1 ) )
=> ( ~ 'fun_app$a'('fun_app$e'(X2,X1),X0)
& ( 'fun_app$g'('some$',sK154(X0,X1,X2)) = X0 )
& ( 'fun_app$g'('some$',sK153(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1572,plain,
! [X0: 'B_option$',X1: 'B_option$',X2: 'B_option_b_option_bool_fun_fun$'] :
( ? [X3: 'B$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$e'(X2,X1),X0)
& ( 'fun_app$g'('some$',X4) = X0 )
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ~ sP11(X0,X1,X2) ),
inference(rectify,[],[f1571]) ).
tff(f1571,plain,
! [X2: 'B_option$',X0: 'B_option$',X1: 'B_option_b_option_bool_fun_fun$'] :
( ? [X3: 'B$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$e'(X1,X0),X2)
& ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ~ sP11(X2,X0,X1) ),
inference(nnf_transformation,[],[f1121]) ).
tff(f8168,plain,
spl249_678,
inference(avatar_split_clause,[],[f2754,f8166]) ).
tff(f8166,plain,
( spl249_678
<=> ! [X2: 'B_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',sK153(X0,X1,X2)) = X1 )
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_678])]) ).
tff(f2754,plain,
! [X2: 'B_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',sK153(X0,X1,X2)) = X1 )
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f1574]) ).
tff(f8164,plain,
spl249_677,
inference(avatar_split_clause,[],[f2748,f8162]) ).
tff(f8162,plain,
( spl249_677
<=> ! [X2: 'B_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'B_option$'] :
( ( 'fun_app$j'('some$a',sK152(X0,X1,X2)) = X0 )
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_677])]) ).
tff(f2748,plain,
! [X2: 'B_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'B_option$'] :
( ( 'fun_app$j'('some$a',sK152(X0,X1,X2)) = X0 )
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f1570]) ).
tff(f1570,plain,
! [X0: 'C_option$',X1: 'B_option$',X2: 'B_option_c_option_bool_fun_fun$'] :
( ( ~ 'fun_app$'('fun_app$bd'(X2,X1),X0)
& ( 'fun_app$j'('some$a',sK152(X0,X1,X2)) = X0 )
& ( 'fun_app$g'('some$',sK151(X0,X1,X2)) = X1 ) )
| ~ sP10(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK151,sK152])],[f1568,f1569]) ).
tff(f1569,plain,
! [X0: 'C_option$',X1: 'B_option$',X2: 'B_option_c_option_bool_fun_fun$'] :
( ? [X3: 'B$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$bd'(X2,X1),X0)
& ( 'fun_app$j'('some$a',X4) = X0 )
& ( 'fun_app$g'('some$',X3) = X1 ) )
=> ( ~ 'fun_app$'('fun_app$bd'(X2,X1),X0)
& ( 'fun_app$j'('some$a',sK152(X0,X1,X2)) = X0 )
& ( 'fun_app$g'('some$',sK151(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1568,plain,
! [X0: 'C_option$',X1: 'B_option$',X2: 'B_option_c_option_bool_fun_fun$'] :
( ? [X3: 'B$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$bd'(X2,X1),X0)
& ( 'fun_app$j'('some$a',X4) = X0 )
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ~ sP10(X0,X1,X2) ),
inference(rectify,[],[f1567]) ).
tff(f1567,plain,
! [X2: 'C_option$',X0: 'B_option$',X1: 'B_option_c_option_bool_fun_fun$'] :
( ? [X3: 'B$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$bd'(X1,X0),X2)
& ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ~ sP10(X2,X0,X1) ),
inference(nnf_transformation,[],[f1119]) ).
tff(f8160,plain,
spl249_676,
inference(avatar_split_clause,[],[f2747,f8158]) ).
tff(f8158,plain,
( spl249_676
<=> ! [X2: 'B_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',sK151(X0,X1,X2)) = X1 )
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_676])]) ).
tff(f2747,plain,
! [X2: 'B_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',sK151(X0,X1,X2)) = X1 )
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f1570]) ).
tff(f8156,plain,
spl249_675,
inference(avatar_split_clause,[],[f2741,f8154]) ).
tff(f8154,plain,
( spl249_675
<=> ! [X2: 'B_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'B_option$'] :
( ( 'fun_app$q'('some$b',sK150(X0,X1,X2)) = X0 )
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_675])]) ).
tff(f2741,plain,
! [X2: 'B_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'B_option$'] :
( ( 'fun_app$q'('some$b',sK150(X0,X1,X2)) = X0 )
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f1566]) ).
tff(f1566,plain,
! [X0: 'A_option$',X1: 'B_option$',X2: 'B_option_a_option_bool_fun_fun$'] :
( ( ~ 'fun_app$aw'('fun_app$ay'(X2,X1),X0)
& ( 'fun_app$q'('some$b',sK150(X0,X1,X2)) = X0 )
& ( 'fun_app$g'('some$',sK149(X0,X1,X2)) = X1 ) )
| ~ sP9(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK149,sK150])],[f1564,f1565]) ).
tff(f1565,plain,
! [X0: 'A_option$',X1: 'B_option$',X2: 'B_option_a_option_bool_fun_fun$'] :
( ? [X3: 'B$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$ay'(X2,X1),X0)
& ( 'fun_app$q'('some$b',X4) = X0 )
& ( 'fun_app$g'('some$',X3) = X1 ) )
=> ( ~ 'fun_app$aw'('fun_app$ay'(X2,X1),X0)
& ( 'fun_app$q'('some$b',sK150(X0,X1,X2)) = X0 )
& ( 'fun_app$g'('some$',sK149(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1564,plain,
! [X0: 'A_option$',X1: 'B_option$',X2: 'B_option_a_option_bool_fun_fun$'] :
( ? [X3: 'B$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$ay'(X2,X1),X0)
& ( 'fun_app$q'('some$b',X4) = X0 )
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ~ sP9(X0,X1,X2) ),
inference(rectify,[],[f1563]) ).
tff(f1563,plain,
! [X2: 'A_option$',X0: 'B_option$',X1: 'B_option_a_option_bool_fun_fun$'] :
( ? [X3: 'B$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$ay'(X1,X0),X2)
& ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$g'('some$',X3) = X0 ) )
| ~ sP9(X2,X0,X1) ),
inference(nnf_transformation,[],[f1117]) ).
tff(f8152,plain,
spl249_674,
inference(avatar_split_clause,[],[f2740,f8150]) ).
tff(f8150,plain,
( spl249_674
<=> ! [X2: 'B_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',sK149(X0,X1,X2)) = X1 )
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_674])]) ).
tff(f2740,plain,
! [X2: 'B_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',sK149(X0,X1,X2)) = X1 )
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f1566]) ).
tff(f8148,plain,
spl249_673,
inference(avatar_split_clause,[],[f2734,f8146]) ).
tff(f8146,plain,
( spl249_673
<=> ! [X2: 'C_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'C_option$'] :
( ( 'fun_app$g'('some$',sK148(X0,X1,X2)) = X0 )
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_673])]) ).
tff(f2734,plain,
! [X2: 'C_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'C_option$'] :
( ( 'fun_app$g'('some$',sK148(X0,X1,X2)) = X0 )
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f1562]) ).
tff(f1562,plain,
! [X0: 'B_option$',X1: 'C_option$',X2: 'C_option_b_option_bool_fun_fun$'] :
( ( ~ 'fun_app$a'('fun_app$bc'(X2,X1),X0)
& ( 'fun_app$g'('some$',sK148(X0,X1,X2)) = X0 )
& ( 'fun_app$j'('some$a',sK147(X0,X1,X2)) = X1 ) )
| ~ sP8(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK147,sK148])],[f1560,f1561]) ).
tff(f1561,plain,
! [X0: 'B_option$',X1: 'C_option$',X2: 'C_option_b_option_bool_fun_fun$'] :
( ? [X3: 'C$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$bc'(X2,X1),X0)
& ( 'fun_app$g'('some$',X4) = X0 )
& ( 'fun_app$j'('some$a',X3) = X1 ) )
=> ( ~ 'fun_app$a'('fun_app$bc'(X2,X1),X0)
& ( 'fun_app$g'('some$',sK148(X0,X1,X2)) = X0 )
& ( 'fun_app$j'('some$a',sK147(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1560,plain,
! [X0: 'B_option$',X1: 'C_option$',X2: 'C_option_b_option_bool_fun_fun$'] :
( ? [X3: 'C$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$bc'(X2,X1),X0)
& ( 'fun_app$g'('some$',X4) = X0 )
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ~ sP8(X0,X1,X2) ),
inference(rectify,[],[f1559]) ).
tff(f1559,plain,
! [X2: 'B_option$',X0: 'C_option$',X1: 'C_option_b_option_bool_fun_fun$'] :
( ? [X3: 'C$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$bc'(X1,X0),X2)
& ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ~ sP8(X2,X0,X1) ),
inference(nnf_transformation,[],[f1115]) ).
tff(f8144,plain,
spl249_672,
inference(avatar_split_clause,[],[f2733,f8142]) ).
tff(f8142,plain,
( spl249_672
<=> ! [X2: 'C_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK147(X0,X1,X2)) = X1 )
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_672])]) ).
tff(f2733,plain,
! [X2: 'C_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK147(X0,X1,X2)) = X1 )
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f1562]) ).
tff(f8140,plain,
spl249_671,
inference(avatar_split_clause,[],[f2727,f8138]) ).
tff(f8138,plain,
( spl249_671
<=> ! [X2: 'C_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK146(X0,X1,X2)) = X0 )
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_671])]) ).
tff(f2727,plain,
! [X2: 'C_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK146(X0,X1,X2)) = X0 )
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f1558]) ).
tff(f1558,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_option_c_option_bool_fun_fun$'] :
( ( ~ 'fun_app$'('fun_app$d'(X2,X1),X0)
& ( 'fun_app$j'('some$a',sK146(X0,X1,X2)) = X0 )
& ( 'fun_app$j'('some$a',sK145(X0,X1,X2)) = X1 ) )
| ~ sP7(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK145,sK146])],[f1556,f1557]) ).
tff(f1557,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_option_c_option_bool_fun_fun$'] :
( ? [X3: 'C$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$d'(X2,X1),X0)
& ( 'fun_app$j'('some$a',X4) = X0 )
& ( 'fun_app$j'('some$a',X3) = X1 ) )
=> ( ~ 'fun_app$'('fun_app$d'(X2,X1),X0)
& ( 'fun_app$j'('some$a',sK146(X0,X1,X2)) = X0 )
& ( 'fun_app$j'('some$a',sK145(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1556,plain,
! [X0: 'C_option$',X1: 'C_option$',X2: 'C_option_c_option_bool_fun_fun$'] :
( ? [X3: 'C$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$d'(X2,X1),X0)
& ( 'fun_app$j'('some$a',X4) = X0 )
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ~ sP7(X0,X1,X2) ),
inference(rectify,[],[f1555]) ).
tff(f1555,plain,
! [X2: 'C_option$',X0: 'C_option$',X1: 'C_option_c_option_bool_fun_fun$'] :
( ? [X3: 'C$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$d'(X1,X0),X2)
& ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ~ sP7(X2,X0,X1) ),
inference(nnf_transformation,[],[f1113]) ).
tff(f8136,plain,
spl249_670,
inference(avatar_split_clause,[],[f2726,f8134]) ).
tff(f8134,plain,
( spl249_670
<=> ! [X2: 'C_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK145(X0,X1,X2)) = X1 )
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_670])]) ).
tff(f2726,plain,
! [X2: 'C_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK145(X0,X1,X2)) = X1 )
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f1558]) ).
tff(f8132,plain,
spl249_669,
inference(avatar_split_clause,[],[f2720,f8130]) ).
tff(f8130,plain,
( spl249_669
<=> ! [X2: 'C_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'C_option$'] :
( ( 'fun_app$q'('some$b',sK144(X0,X1,X2)) = X0 )
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_669])]) ).
tff(f2720,plain,
! [X2: 'C_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'C_option$'] :
( ( 'fun_app$q'('some$b',sK144(X0,X1,X2)) = X0 )
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f1554]) ).
tff(f1554,plain,
! [X0: 'A_option$',X1: 'C_option$',X2: 'C_option_a_option_bool_fun_fun$'] :
( ( ~ 'fun_app$aw'('fun_app$ax'(X2,X1),X0)
& ( 'fun_app$q'('some$b',sK144(X0,X1,X2)) = X0 )
& ( 'fun_app$j'('some$a',sK143(X0,X1,X2)) = X1 ) )
| ~ sP6(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK143,sK144])],[f1552,f1553]) ).
tff(f1553,plain,
! [X0: 'A_option$',X1: 'C_option$',X2: 'C_option_a_option_bool_fun_fun$'] :
( ? [X3: 'C$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$ax'(X2,X1),X0)
& ( 'fun_app$q'('some$b',X4) = X0 )
& ( 'fun_app$j'('some$a',X3) = X1 ) )
=> ( ~ 'fun_app$aw'('fun_app$ax'(X2,X1),X0)
& ( 'fun_app$q'('some$b',sK144(X0,X1,X2)) = X0 )
& ( 'fun_app$j'('some$a',sK143(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1552,plain,
! [X0: 'A_option$',X1: 'C_option$',X2: 'C_option_a_option_bool_fun_fun$'] :
( ? [X3: 'C$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$ax'(X2,X1),X0)
& ( 'fun_app$q'('some$b',X4) = X0 )
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ~ sP6(X0,X1,X2) ),
inference(rectify,[],[f1551]) ).
tff(f1551,plain,
! [X2: 'A_option$',X0: 'C_option$',X1: 'C_option_a_option_bool_fun_fun$'] :
( ? [X3: 'C$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$ax'(X1,X0),X2)
& ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$j'('some$a',X3) = X0 ) )
| ~ sP6(X2,X0,X1) ),
inference(nnf_transformation,[],[f1111]) ).
tff(f8128,plain,
spl249_668,
inference(avatar_split_clause,[],[f2719,f8126]) ).
tff(f8126,plain,
( spl249_668
<=> ! [X2: 'C_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK143(X0,X1,X2)) = X1 )
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_668])]) ).
tff(f2719,plain,
! [X2: 'C_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK143(X0,X1,X2)) = X1 )
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f1554]) ).
tff(f8124,plain,
spl249_667,
inference(avatar_split_clause,[],[f2713,f8122]) ).
tff(f8122,plain,
( spl249_667
<=> ! [X2: 'A_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'A_option$'] :
( ( 'fun_app$g'('some$',sK142(X0,X1,X2)) = X0 )
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_667])]) ).
tff(f2713,plain,
! [X2: 'A_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'A_option$'] :
( ( 'fun_app$g'('some$',sK142(X0,X1,X2)) = X0 )
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f1550]) ).
tff(f1550,plain,
! [X0: 'B_option$',X1: 'A_option$',X2: 'A_option_b_option_bool_fun_fun$'] :
( ( ~ 'fun_app$a'('fun_app$ba'(X2,X1),X0)
& ( 'fun_app$g'('some$',sK142(X0,X1,X2)) = X0 )
& ( 'fun_app$q'('some$b',sK141(X0,X1,X2)) = X1 ) )
| ~ sP5(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK141,sK142])],[f1548,f1549]) ).
tff(f1549,plain,
! [X0: 'B_option$',X1: 'A_option$',X2: 'A_option_b_option_bool_fun_fun$'] :
( ? [X3: 'A$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$ba'(X2,X1),X0)
& ( 'fun_app$g'('some$',X4) = X0 )
& ( 'fun_app$q'('some$b',X3) = X1 ) )
=> ( ~ 'fun_app$a'('fun_app$ba'(X2,X1),X0)
& ( 'fun_app$g'('some$',sK142(X0,X1,X2)) = X0 )
& ( 'fun_app$q'('some$b',sK141(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1548,plain,
! [X0: 'B_option$',X1: 'A_option$',X2: 'A_option_b_option_bool_fun_fun$'] :
( ? [X3: 'A$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$ba'(X2,X1),X0)
& ( 'fun_app$g'('some$',X4) = X0 )
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ~ sP5(X0,X1,X2) ),
inference(rectify,[],[f1547]) ).
tff(f1547,plain,
! [X2: 'B_option$',X0: 'A_option$',X1: 'A_option_b_option_bool_fun_fun$'] :
( ? [X3: 'A$',X4: 'B$'] :
( ~ 'fun_app$a'('fun_app$ba'(X1,X0),X2)
& ( 'fun_app$g'('some$',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ~ sP5(X2,X0,X1) ),
inference(nnf_transformation,[],[f1109]) ).
tff(f8120,plain,
spl249_666,
inference(avatar_split_clause,[],[f2712,f8118]) ).
tff(f8118,plain,
( spl249_666
<=> ! [X2: 'A_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK141(X0,X1,X2)) = X1 )
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_666])]) ).
tff(f2712,plain,
! [X2: 'A_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK141(X0,X1,X2)) = X1 )
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f1550]) ).
tff(f8116,plain,
spl249_665,
inference(avatar_split_clause,[],[f2706,f8114]) ).
tff(f8114,plain,
( spl249_665
<=> ! [X2: 'A_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'A_option$'] :
( ( 'fun_app$j'('some$a',sK140(X0,X1,X2)) = X0 )
| ~ sP4(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_665])]) ).
tff(f2706,plain,
! [X2: 'A_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'A_option$'] :
( ( 'fun_app$j'('some$a',sK140(X0,X1,X2)) = X0 )
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f1546]) ).
tff(f1546,plain,
! [X0: 'C_option$',X1: 'A_option$',X2: 'A_option_c_option_bool_fun_fun$'] :
( ( ~ 'fun_app$'('fun_app$az'(X2,X1),X0)
& ( 'fun_app$j'('some$a',sK140(X0,X1,X2)) = X0 )
& ( 'fun_app$q'('some$b',sK139(X0,X1,X2)) = X1 ) )
| ~ sP4(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK139,sK140])],[f1544,f1545]) ).
tff(f1545,plain,
! [X0: 'C_option$',X1: 'A_option$',X2: 'A_option_c_option_bool_fun_fun$'] :
( ? [X3: 'A$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$az'(X2,X1),X0)
& ( 'fun_app$j'('some$a',X4) = X0 )
& ( 'fun_app$q'('some$b',X3) = X1 ) )
=> ( ~ 'fun_app$'('fun_app$az'(X2,X1),X0)
& ( 'fun_app$j'('some$a',sK140(X0,X1,X2)) = X0 )
& ( 'fun_app$q'('some$b',sK139(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1544,plain,
! [X0: 'C_option$',X1: 'A_option$',X2: 'A_option_c_option_bool_fun_fun$'] :
( ? [X3: 'A$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$az'(X2,X1),X0)
& ( 'fun_app$j'('some$a',X4) = X0 )
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ~ sP4(X0,X1,X2) ),
inference(rectify,[],[f1543]) ).
tff(f1543,plain,
! [X2: 'C_option$',X0: 'A_option$',X1: 'A_option_c_option_bool_fun_fun$'] :
( ? [X3: 'A$',X4: 'C$'] :
( ~ 'fun_app$'('fun_app$az'(X1,X0),X2)
& ( 'fun_app$j'('some$a',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ~ sP4(X2,X0,X1) ),
inference(nnf_transformation,[],[f1107]) ).
tff(f8112,plain,
spl249_664,
inference(avatar_split_clause,[],[f2705,f8110]) ).
tff(f8110,plain,
( spl249_664
<=> ! [X2: 'A_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK139(X0,X1,X2)) = X1 )
| ~ sP4(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_664])]) ).
tff(f2705,plain,
! [X2: 'A_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK139(X0,X1,X2)) = X1 )
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f1546]) ).
tff(f8108,plain,
spl249_663,
inference(avatar_split_clause,[],[f2699,f8106]) ).
tff(f8106,plain,
( spl249_663
<=> ! [X2: 'A_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK138(X0,X1,X2)) = X0 )
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_663])]) ).
tff(f2699,plain,
! [X2: 'A_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK138(X0,X1,X2)) = X0 )
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f1542]) ).
tff(f1542,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_option_a_option_bool_fun_fun$'] :
( ( ~ 'fun_app$aw'('fun_app$bb'(X2,X1),X0)
& ( 'fun_app$q'('some$b',sK138(X0,X1,X2)) = X0 )
& ( 'fun_app$q'('some$b',sK137(X0,X1,X2)) = X1 ) )
| ~ sP3(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK137,sK138])],[f1540,f1541]) ).
tff(f1541,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_option_a_option_bool_fun_fun$'] :
( ? [X3: 'A$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$bb'(X2,X1),X0)
& ( 'fun_app$q'('some$b',X4) = X0 )
& ( 'fun_app$q'('some$b',X3) = X1 ) )
=> ( ~ 'fun_app$aw'('fun_app$bb'(X2,X1),X0)
& ( 'fun_app$q'('some$b',sK138(X0,X1,X2)) = X0 )
& ( 'fun_app$q'('some$b',sK137(X0,X1,X2)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1540,plain,
! [X0: 'A_option$',X1: 'A_option$',X2: 'A_option_a_option_bool_fun_fun$'] :
( ? [X3: 'A$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$bb'(X2,X1),X0)
& ( 'fun_app$q'('some$b',X4) = X0 )
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ~ sP3(X0,X1,X2) ),
inference(rectify,[],[f1539]) ).
tff(f1539,plain,
! [X2: 'A_option$',X0: 'A_option$',X1: 'A_option_a_option_bool_fun_fun$'] :
( ? [X3: 'A$',X4: 'A$'] :
( ~ 'fun_app$aw'('fun_app$bb'(X1,X0),X2)
& ( 'fun_app$q'('some$b',X4) = X2 )
& ( 'fun_app$q'('some$b',X3) = X0 ) )
| ~ sP3(X2,X0,X1) ),
inference(nnf_transformation,[],[f1105]) ).
tff(f8104,plain,
spl249_662,
inference(avatar_split_clause,[],[f2698,f8102]) ).
tff(f8102,plain,
( spl249_662
<=> ! [X2: 'A_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK137(X0,X1,X2)) = X1 )
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_662])]) ).
tff(f2698,plain,
! [X2: 'A_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK137(X0,X1,X2)) = X1 )
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f1542]) ).
tff(f8100,plain,
spl249_661,
inference(avatar_split_clause,[],[f2685,f8098]) ).
tff(f8098,plain,
( spl249_661
<=> ! [X2: 'B$',X0: 'B_option_b_fun$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$al'(X0,'fun_app$g'(X1,X2)) = X2 )
| ( 'comp$m'(X0,X1) != 'id$b' ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_661])]) ).
tff(f2685,plain,
! [X2: 'B$',X0: 'B_option_b_fun$',X1: 'B_b_option_fun$'] :
( ( 'fun_app$al'(X0,'fun_app$g'(X1,X2)) = X2 )
| ( 'comp$m'(X0,X1) != 'id$b' ) ),
inference(cnf_transformation,[],[f960]) ).
tff(f960,plain,
! [X0: 'B_option_b_fun$',X1: 'B_b_option_fun$',X2: 'B$'] :
( ( 'fun_app$al'(X0,'fun_app$g'(X1,X2)) = X2 )
| ( 'comp$m'(X0,X1) != 'id$b' ) ),
inference(ennf_transformation,[],[f680]) ).
tff(f680,axiom,
! [X0: 'B_option_b_fun$',X1: 'B_b_option_fun$',X2: 'B$'] :
( ( 'comp$m'(X0,X1) = 'id$b' )
=> ( 'fun_app$al'(X0,'fun_app$g'(X1,X2)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom678) ).
tff(f8096,plain,
spl249_660,
inference(avatar_split_clause,[],[f2684,f8094]) ).
tff(f8094,plain,
( spl249_660
<=> ! [X2: 'C$',X0: 'C_option_c_fun$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$ak'(X0,'fun_app$j'(X1,X2)) = X2 )
| ( 'comp$n'(X0,X1) != 'id$a' ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_660])]) ).
tff(f2684,plain,
! [X2: 'C$',X0: 'C_option_c_fun$',X1: 'C_c_option_fun$'] :
( ( 'fun_app$ak'(X0,'fun_app$j'(X1,X2)) = X2 )
| ( 'comp$n'(X0,X1) != 'id$a' ) ),
inference(cnf_transformation,[],[f959]) ).
tff(f959,plain,
! [X0: 'C_option_c_fun$',X1: 'C_c_option_fun$',X2: 'C$'] :
( ( 'fun_app$ak'(X0,'fun_app$j'(X1,X2)) = X2 )
| ( 'comp$n'(X0,X1) != 'id$a' ) ),
inference(ennf_transformation,[],[f681]) ).
tff(f681,axiom,
! [X0: 'C_option_c_fun$',X1: 'C_c_option_fun$',X2: 'C$'] :
( ( 'comp$n'(X0,X1) = 'id$a' )
=> ( 'fun_app$ak'(X0,'fun_app$j'(X1,X2)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom679) ).
tff(f8092,plain,
spl249_659,
inference(avatar_split_clause,[],[f2605,f8090]) ).
tff(f8090,plain,
( spl249_659
<=> ! [X2: 'B$',X0: 'B_b_b_option_fun_fun$',X1: 'B$'] : ( 'fun_app$g'('fun_app$t'('uus$'(X0),X1),X2) = 'fun_app$g'('fun_app$t'(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_659])]) ).
tff(f2605,plain,
! [X2: 'B$',X0: 'B_b_b_option_fun_fun$',X1: 'B$'] : ( 'fun_app$g'('fun_app$t'('uus$'(X0),X1),X2) = 'fun_app$g'('fun_app$t'(X0,X2),X1) ),
inference(cnf_transformation,[],[f25]) ).
tff(f25,axiom,
! [X0: 'B_b_b_option_fun_fun$',X1: 'B$',X2: 'B$'] : ( 'fun_app$g'('fun_app$t'('uus$'(X0),X1),X2) = 'fun_app$g'('fun_app$t'(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom24) ).
tff(f8088,plain,
spl249_658,
inference(avatar_split_clause,[],[f2604,f8086]) ).
tff(f8086,plain,
( spl249_658
<=> ! [X2: 'C$',X0: 'C_c_c_option_fun_fun$',X1: 'C$'] : ( 'fun_app$j'('fun_app$v'('uut$'(X0),X1),X2) = 'fun_app$j'('fun_app$v'(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_658])]) ).
tff(f2604,plain,
! [X2: 'C$',X0: 'C_c_c_option_fun_fun$',X1: 'C$'] : ( 'fun_app$j'('fun_app$v'('uut$'(X0),X1),X2) = 'fun_app$j'('fun_app$v'(X0,X2),X1) ),
inference(cnf_transformation,[],[f23]) ).
tff(f23,axiom,
! [X0: 'C_c_c_option_fun_fun$',X1: 'C$',X2: 'C$'] : ( 'fun_app$j'('fun_app$v'('uut$'(X0),X1),X2) = 'fun_app$j'('fun_app$v'(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom22) ).
tff(f8084,plain,
spl249_657,
inference(avatar_split_clause,[],[f2603,f8082]) ).
tff(f2603,plain,
! [X2: 'B_b_option_fun$',X0: 'C_option$',X1: 'C_b_option_fun$'] : ( 'fun_app$ac'('bind$c'('bind$a'(X0,X1)),X2) = 'bind$a'(X0,'uvu$'(X1,X2)) ),
inference(cnf_transformation,[],[f356]) ).
tff(f356,axiom,
! [X0: 'C_option$',X1: 'C_b_option_fun$',X2: 'B_b_option_fun$'] : ( 'fun_app$ac'('bind$c'('bind$a'(X0,X1)),X2) = 'bind$a'(X0,'uvu$'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom354) ).
tff(f8080,plain,
spl249_656,
inference(avatar_split_clause,[],[f2602,f8078]) ).
tff(f2602,plain,
! [X2: 'B_c_option_fun$',X0: 'B_b_fun$',X1: 'B_option$'] : ( 'bind$b'('fun_app$s'('map_option$b'(X0),X1),X2) = 'bind$b'(X1,'comp$f'(X2,X0)) ),
inference(cnf_transformation,[],[f543]) ).
tff(f543,axiom,
! [X0: 'B_b_fun$',X1: 'B_option$',X2: 'B_c_option_fun$'] : ( 'bind$b'('fun_app$s'('map_option$b'(X0),X1),X2) = 'bind$b'(X1,'comp$f'(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom541) ).
tff(f8076,plain,
( spl249_655
| ~ spl249_23
| ~ spl249_513 ),
inference(avatar_split_clause,[],[f7009,f6597,f3704,f8074]) ).
tff(f8074,plain,
( spl249_655
<=> ! [X0: 'B_b_option_fun$',X1: 'B_option$'] : ~ sP31(X0,'uwf$',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_655])]) ).
tff(f7009,plain,
( ! [X0: 'B_b_option_fun$',X1: 'B_option$'] : ~ sP31(X0,'uwf$',X1)
| ~ spl249_23
| ~ spl249_513 ),
inference(resolution,[],[f6598,f3705]) ).
tff(f8072,plain,
spl249_654,
inference(avatar_split_clause,[],[f2601,f8070]) ).
tff(f2601,plain,
! [X2: 'C_b_option_fun$',X0: 'C_c_fun$',X1: 'C_option$'] : ( 'bind$a'('fun_app$u'('map_option$c'(X0),X1),X2) = 'bind$a'(X1,'comp$ao'(X2,X0)) ),
inference(cnf_transformation,[],[f536]) ).
tff(f536,axiom,
! [X0: 'C_c_fun$',X1: 'C_option$',X2: 'C_b_option_fun$'] : ( 'bind$a'('fun_app$u'('map_option$c'(X0),X1),X2) = 'bind$a'(X1,'comp$ao'(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom534) ).
tff(f8068,plain,
spl249_653,
inference(avatar_split_clause,[],[f2600,f8066]) ).
tff(f2600,plain,
! [X2: 'B_c_option_fun$',X0: 'A_b_fun$',X1: 'A_option$'] : ( 'bind$b'('fun_app$av'('map_option$e'(X0),X1),X2) = 'bind$d'(X1,'comp$aq'(X2,X0)) ),
inference(cnf_transformation,[],[f545]) ).
tff(f545,axiom,
! [X0: 'A_b_fun$',X1: 'A_option$',X2: 'B_c_option_fun$'] : ( 'bind$b'('fun_app$av'('map_option$e'(X0),X1),X2) = 'bind$d'(X1,'comp$aq'(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom543) ).
tff(f8064,plain,
spl249_652,
inference(avatar_split_clause,[],[f2599,f8062]) ).
tff(f2599,plain,
! [X2: 'B_c_option_fun$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ( 'bind$b'('fun_app$ac'('bind$c'(X0),X1),X2) = 'bind$b'(X0,'uvx$'(X1,X2)) ),
inference(cnf_transformation,[],[f359]) ).
tff(f359,axiom,
! [X0: 'B_option$',X1: 'B_b_option_fun$',X2: 'B_c_option_fun$'] : ( 'bind$b'('fun_app$ac'('bind$c'(X0),X1),X2) = 'bind$b'(X0,'uvx$'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom357) ).
tff(f8060,plain,
spl249_651,
inference(avatar_split_clause,[],[f2598,f8058]) ).
tff(f2598,plain,
! [X2: 'C_b_option_fun$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ( 'bind$a'('fun_app$ab'('bind$'(X0),X1),X2) = 'bind$a'(X0,'uvw$'(X1,X2)) ),
inference(cnf_transformation,[],[f358]) ).
tff(f358,axiom,
! [X0: 'C_option$',X1: 'C_c_option_fun$',X2: 'C_b_option_fun$'] : ( 'bind$a'('fun_app$ab'('bind$'(X0),X1),X2) = 'bind$a'(X0,'uvw$'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom356) ).
tff(f8056,plain,
spl249_650,
inference(avatar_split_clause,[],[f2597,f8054]) ).
tff(f2597,plain,
! [X2: 'C_c_option_fun$',X0: 'B_option$',X1: 'B_c_option_fun$'] : ( 'fun_app$ab'('bind$'('bind$b'(X0,X1)),X2) = 'bind$b'(X0,'uvz$'(X1,X2)) ),
inference(cnf_transformation,[],[f361]) ).
tff(f361,axiom,
! [X0: 'B_option$',X1: 'B_c_option_fun$',X2: 'C_c_option_fun$'] : ( 'fun_app$ab'('bind$'('bind$b'(X0,X1)),X2) = 'bind$b'(X0,'uvz$'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom359) ).
tff(f8052,plain,
spl249_649,
inference(avatar_split_clause,[],[f2595,f8050]) ).
tff(f8050,plain,
( spl249_649
<=> ! [X2: 'B_b_option_fun$',X0: 'B_option_b_fun$',X1: 'B_option_b_option_fun$'] : ( 'comp$m'(X0,'fun_app$ad'('comp$ax'(X1),X2)) = 'comp$m'('comp$bh'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_649])]) ).
tff(f2595,plain,
! [X2: 'B_b_option_fun$',X0: 'B_option_b_fun$',X1: 'B_option_b_option_fun$'] : ( 'comp$m'(X0,'fun_app$ad'('comp$ax'(X1),X2)) = 'comp$m'('comp$bh'(X0,X1),X2) ),
inference(cnf_transformation,[],[f624]) ).
tff(f624,axiom,
! [X0: 'B_option_b_fun$',X1: 'B_option_b_option_fun$',X2: 'B_b_option_fun$'] : ( 'comp$m'(X0,'fun_app$ad'('comp$ax'(X1),X2)) = 'comp$m'('comp$bh'(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom622) ).
tff(f8048,plain,
spl249_648,
inference(avatar_split_clause,[],[f2593,f8046]) ).
tff(f8046,plain,
( spl249_648
<=> ! [X2: 'C_b_option_fun$',X0: 'B_option$',X1: 'B_c_option_fun$'] : ( 'bind$a'('bind$b'(X0,X1),X2) = 'fun_app$ac'('bind$c'(X0),'uvv$'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_648])]) ).
tff(f2593,plain,
! [X2: 'C_b_option_fun$',X0: 'B_option$',X1: 'B_c_option_fun$'] : ( 'bind$a'('bind$b'(X0,X1),X2) = 'fun_app$ac'('bind$c'(X0),'uvv$'(X1,X2)) ),
inference(cnf_transformation,[],[f357]) ).
tff(f357,axiom,
! [X0: 'B_option$',X1: 'B_c_option_fun$',X2: 'C_b_option_fun$'] : ( 'bind$a'('bind$b'(X0,X1),X2) = 'fun_app$ac'('bind$c'(X0),'uvv$'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom355) ).
tff(f8044,plain,
spl249_647,
inference(avatar_split_clause,[],[f2592,f8042]) ).
tff(f8042,plain,
( spl249_647
<=> ! [X2: 'B_c_option_fun$',X0: 'C_option$',X1: 'C_b_option_fun$'] : ( 'bind$b'('bind$a'(X0,X1),X2) = 'fun_app$ab'('bind$'(X0),'uvy$'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_647])]) ).
tff(f2592,plain,
! [X2: 'B_c_option_fun$',X0: 'C_option$',X1: 'C_b_option_fun$'] : ( 'bind$b'('bind$a'(X0,X1),X2) = 'fun_app$ab'('bind$'(X0),'uvy$'(X1,X2)) ),
inference(cnf_transformation,[],[f360]) ).
tff(f360,axiom,
! [X0: 'C_option$',X1: 'C_b_option_fun$',X2: 'B_c_option_fun$'] : ( 'bind$b'('bind$a'(X0,X1),X2) = 'fun_app$ab'('bind$'(X0),'uvy$'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom358) ).
tff(f8040,plain,
spl249_646,
inference(avatar_split_clause,[],[f2591,f8038]) ).
tff(f8038,plain,
( spl249_646
<=> ! [X2: 'A_option$',X0: 'A_a_a_fun_fun$',X1: 'A_option$'] : ( 'fun_app$be'('combine_options$'(X0,X1),X2) = 'case_option$b'(X2,'uux$'(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_646])]) ).
tff(f2591,plain,
! [X2: 'A_option$',X0: 'A_a_a_fun_fun$',X1: 'A_option$'] : ( 'fun_app$be'('combine_options$'(X0,X1),X2) = 'case_option$b'(X2,'uux$'(X0,X2),X1) ),
inference(cnf_transformation,[],[f177]) ).
tff(f177,axiom,
! [X0: 'A_a_a_fun_fun$',X1: 'A_option$',X2: 'A_option$'] : ( 'fun_app$be'('combine_options$'(X0,X1),X2) = 'case_option$b'(X2,'uux$'(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom175) ).
tff(f8036,plain,
spl249_645,
inference(avatar_split_clause,[],[f2448,f8034]) ).
tff(f8034,plain,
( spl249_645
<=> ! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$e'(X0,X1))
| ~ 'fun_app$a'('is_none$','fun_app$f'(X1,'fun_app$bf'('the$b',X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_645])]) ).
tff(f2448,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$e'(X0,X1))
| ~ 'fun_app$a'('is_none$','fun_app$f'(X1,'fun_app$bf'('the$b',X0))) ),
inference(cnf_transformation,[],[f1481]) ).
tff(f8032,plain,
( spl249_644
| ~ spl249_23
| ~ spl249_511 ),
inference(avatar_split_clause,[],[f6980,f6589,f3704,f8030]) ).
tff(f8030,plain,
( spl249_644
<=> ! [X0: 'B_b_option_fun$',X1: 'B_option$'] : ~ sP30(X0,'uwf$',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_644])]) ).
tff(f6980,plain,
( ! [X0: 'B_b_option_fun$',X1: 'B_option$'] : ~ sP30(X0,'uwf$',X1)
| ~ spl249_23
| ~ spl249_511 ),
inference(resolution,[],[f6590,f3705]) ).
tff(f8028,plain,
spl249_643,
inference(avatar_split_clause,[],[f2436,f8026]) ).
tff(f8026,plain,
( spl249_643
<=> ! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$d'(X0,X1))
| ~ 'fun_app$'('is_none$a','fun_app$bm'(X1,'fun_app$bf'('the$b',X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_643])]) ).
tff(f2436,plain,
! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$d'(X0,X1))
| ~ 'fun_app$'('is_none$a','fun_app$bm'(X1,'fun_app$bf'('the$b',X0))) ),
inference(cnf_transformation,[],[f1474]) ).
tff(f8024,plain,
spl249_642,
inference(avatar_split_clause,[],[f2420,f8022]) ).
tff(f8022,plain,
( spl249_642
<=> ! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( ( 'none$a' = 'bind$e'(X0,X1) )
| ( 'none$a' != 'fun_app$f'(X1,'fun_app$bf'('the$b',X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_642])]) ).
tff(f2420,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( ( 'none$a' = 'bind$e'(X0,X1) )
| ( 'none$a' != 'fun_app$f'(X1,'fun_app$bf'('the$b',X0)) ) ),
inference(cnf_transformation,[],[f1465]) ).
tff(f8020,plain,
spl249_641,
inference(avatar_split_clause,[],[f2414,f8018]) ).
tff(f8018,plain,
( spl249_641
<=> ! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( ( 'none$' = 'bind$d'(X0,X1) )
| ( 'none$' != 'fun_app$bm'(X1,'fun_app$bf'('the$b',X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_641])]) ).
tff(f2414,plain,
! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( ( 'none$' = 'bind$d'(X0,X1) )
| ( 'none$' != 'fun_app$bm'(X1,'fun_app$bf'('the$b',X0)) ) ),
inference(cnf_transformation,[],[f1461]) ).
tff(f8016,plain,
spl249_640,
inference(avatar_split_clause,[],[f2411,f8014]) ).
tff(f8014,plain,
( spl249_640
<=> ! [X0: 'B_option$',X1: 'B_a_option_fun$'] :
( ( 'none$b' = 'bind$g'(X0,X1) )
| ( 'none$b' != 'fun_app$bo'(X1,'fun_app$al'('the$',X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_640])]) ).
tff(f2411,plain,
! [X0: 'B_option$',X1: 'B_a_option_fun$'] :
( ( 'none$b' = 'bind$g'(X0,X1) )
| ( 'none$b' != 'fun_app$bo'(X1,'fun_app$al'('the$',X0)) ) ),
inference(cnf_transformation,[],[f1459]) ).
tff(f8012,plain,
spl249_639,
inference(avatar_split_clause,[],[f2408,f8010]) ).
tff(f8010,plain,
( spl249_639
<=> ! [X0: 'C_option$',X1: 'C_a_option_fun$'] :
( ( 'none$b' = 'bind$f'(X0,X1) )
| ( 'none$b' != 'fun_app$bn'(X1,'fun_app$ak'('the$a',X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_639])]) ).
tff(f2408,plain,
! [X0: 'C_option$',X1: 'C_a_option_fun$'] :
( ( 'none$b' = 'bind$f'(X0,X1) )
| ( 'none$b' != 'fun_app$bn'(X1,'fun_app$ak'('the$a',X0)) ) ),
inference(cnf_transformation,[],[f1457]) ).
tff(f8008,plain,
spl249_638,
inference(avatar_split_clause,[],[f2347,f8006]) ).
tff(f8006,plain,
( spl249_638
<=> ! [X11: 'A$',X0: 'B_a_fun$',X12: 'B$',X1: 'A_b_b_fun_fun$'] :
( ( 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,X11),X12)) = X11 )
| ~ 'valid_getter_setter$a'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_638])]) ).
tff(f2347,plain,
! [X0: 'B_a_fun$',X11: 'A$',X1: 'A_b_b_fun_fun$',X12: 'B$'] :
( ( 'fun_app$ao'(X0,'fun_app$h'('fun_app$i'(X1,X11),X12)) = X11 )
| ~ 'valid_getter_setter$a'(X0,X1) ),
inference(cnf_transformation,[],[f1427]) ).
tff(f8004,plain,
spl249_637,
inference(avatar_split_clause,[],[f2346,f8002]) ).
tff(f8002,plain,
( spl249_637
<=> ! [X13: 'B$',X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ( 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,X13)),X13) = X13 )
| ~ 'valid_getter_setter$a'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_637])]) ).
tff(f2346,plain,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$',X13: 'B$'] :
( ( 'fun_app$h'('fun_app$i'(X1,'fun_app$ao'(X0,X13)),X13) = X13 )
| ~ 'valid_getter_setter$a'(X0,X1) ),
inference(cnf_transformation,[],[f1427]) ).
tff(f8000,plain,
spl249_636,
inference(avatar_split_clause,[],[f2343,f7998]) ).
tff(f7998,plain,
( spl249_636
<=> ! [X11: 'B$',X0: 'C_b_fun$',X12: 'C$',X1: 'B_c_c_fun_fun$'] :
( ( 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,X11),X12)) = X11 )
| ~ 'valid_getter_setter$'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_636])]) ).
tff(f2343,plain,
! [X0: 'C_b_fun$',X11: 'B$',X1: 'B_c_c_fun_fun$',X12: 'C$'] :
( ( 'fun_app$m'(X0,'fun_app$k'('fun_app$y'(X1,X11),X12)) = X11 )
| ~ 'valid_getter_setter$'(X0,X1) ),
inference(cnf_transformation,[],[f1420]) ).
tff(f7996,plain,
spl249_635,
inference(avatar_split_clause,[],[f2342,f7994]) ).
tff(f7994,plain,
( spl249_635
<=> ! [X13: 'C$',X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ( 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,X13)),X13) = X13 )
| ~ 'valid_getter_setter$'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_635])]) ).
tff(f2342,plain,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$',X13: 'C$'] :
( ( 'fun_app$k'('fun_app$y'(X1,'fun_app$m'(X0,X13)),X13) = X13 )
| ~ 'valid_getter_setter$'(X0,X1) ),
inference(cnf_transformation,[],[f1420]) ).
tff(f7992,plain,
spl249_634,
inference(avatar_split_clause,[],[f2340,f7990]) ).
tff(f7990,plain,
( spl249_634
<=> ! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X1),X0) = X0 )
| 'member$c'(sK121(X0,X1),'set_option$d'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_634])]) ).
tff(f2340,plain,
! [X0: 'B_option$',X1: 'B_b_fun$'] :
( ( 'fun_app$s'('map_option$b'(X1),X0) = X0 )
| 'member$c'(sK121(X0,X1),'set_option$d'(X0)) ),
inference(cnf_transformation,[],[f1413]) ).
tff(f7988,plain,
( spl249_633
| ~ spl249_22
| ~ spl249_509 ),
inference(avatar_split_clause,[],[f6948,f6581,f3700,f7986]) ).
tff(f7986,plain,
( spl249_633
<=> ! [X0: 'C_c_option_fun$',X1: 'C_option$'] : ~ sP29(X0,'uwg$',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_633])]) ).
tff(f6948,plain,
( ! [X0: 'C_c_option_fun$',X1: 'C_option$'] : ~ sP29(X0,'uwg$',X1)
| ~ spl249_22
| ~ spl249_509 ),
inference(resolution,[],[f6582,f3701]) ).
tff(f7984,plain,
spl249_632,
inference(avatar_split_clause,[],[f2338,f7982]) ).
tff(f7982,plain,
( spl249_632
<=> ! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ( 'fun_app$u'('map_option$c'(X1),X0) = X0 )
| 'member$b'(sK120(X0,X1),'set_option$c'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_632])]) ).
tff(f2338,plain,
! [X0: 'C_option$',X1: 'C_c_fun$'] :
( ( 'fun_app$u'('map_option$c'(X1),X0) = X0 )
| 'member$b'(sK120(X0,X1),'set_option$c'(X0)) ),
inference(cnf_transformation,[],[f1411]) ).
tff(f7980,plain,
spl249_631,
inference(avatar_split_clause,[],[f2336,f7978]) ).
tff(f7978,plain,
( spl249_631
<=> ! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X1),X0) = X0 )
| 'member$d'(sK119(X0,X1),'set_option$b'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_631])]) ).
tff(f2336,plain,
! [X0: 'A_option$',X1: 'A_a_fun$'] :
( ( 'fun_app$be'('map_option$a'(X1),X0) = X0 )
| 'member$d'(sK119(X0,X1),'set_option$b'(X0)) ),
inference(cnf_transformation,[],[f1409]) ).
tff(f7976,plain,
spl249_630,
inference(avatar_split_clause,[],[f2330,f7974]) ).
tff(f7974,plain,
( spl249_630
<=> ! [X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| sP2(X1,X0)
| ( 'none$a' = X1 )
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_630])]) ).
tff(f2330,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| sP2(X1,X0)
| ( 'none$a' = X1 )
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f1403]) ).
tff(f1403,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| sP2(X1,X0)
| ( ( ( 'none$a' != X1 )
| ( 'none$a' != X0 ) )
& ( ( 'none$a' = X1 )
| ( 'none$a' = X0 ) ) ) ),
inference(nnf_transformation,[],[f1104]) ).
tff(f1104,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| sP2(X1,X0)
| ( ( 'none$a' = X0 )
<~> ( 'none$a' = X1 ) ) ),
inference(definition_folding,[],[f942,f1103]) ).
tff(f1103,plain,
! [X1: 'B_option$',X0: 'B_option$'] :
( ( ( 'fun_app$al'('the$',X0) != 'fun_app$al'('the$',X1) )
& ( 'none$a' != X1 )
& ( 'none$a' != X0 ) )
| ~ sP2(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f942,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( ( 'fun_app$al'('the$',X0) != 'fun_app$al'('the$',X1) )
& ( 'none$a' != X1 )
& ( 'none$a' != X0 ) )
| ( ( 'none$a' = X0 )
<~> ( 'none$a' = X1 ) ) ),
inference(flattening,[],[f941]) ).
tff(f941,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| ( ( 'fun_app$al'('the$',X0) != 'fun_app$al'('the$',X1) )
& ( 'none$a' != X1 )
& ( 'none$a' != X0 ) )
| ( ( 'none$a' = X0 )
<~> ( 'none$a' = X1 ) ) ),
inference(ennf_transformation,[],[f298]) ).
tff(f298,axiom,
! [X0: 'B_option$',X1: 'B_option$'] :
( ( ( ( ( 'none$a' != X1 )
& ( 'none$a' != X0 ) )
=> ( 'fun_app$al'('the$',X0) = 'fun_app$al'('the$',X1) ) )
& ( ( 'none$a' = X0 )
<=> ( 'none$a' = X1 ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom296) ).
tff(f7972,plain,
spl249_629,
inference(avatar_split_clause,[],[f2325,f7970]) ).
tff(f7970,plain,
( spl249_629
<=> ! [X0: 'C_option$',X1: 'C_option$'] :
( ( X0 = X1 )
| sP1(X1,X0)
| ( 'none$' = X1 )
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_629])]) ).
tff(f2325,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( ( X0 = X1 )
| sP1(X1,X0)
| ( 'none$' = X1 )
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f1400]) ).
tff(f1400,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( ( X0 = X1 )
| sP1(X1,X0)
| ( ( ( 'none$' != X1 )
| ( 'none$' != X0 ) )
& ( ( 'none$' = X1 )
| ( 'none$' = X0 ) ) ) ),
inference(nnf_transformation,[],[f1102]) ).
tff(f1102,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( ( X0 = X1 )
| sP1(X1,X0)
| ( ( 'none$' = X0 )
<~> ( 'none$' = X1 ) ) ),
inference(definition_folding,[],[f940,f1101]) ).
tff(f1101,plain,
! [X1: 'C_option$',X0: 'C_option$'] :
( ( ( 'fun_app$ak'('the$a',X0) != 'fun_app$ak'('the$a',X1) )
& ( 'none$' != X1 )
& ( 'none$' != X0 ) )
| ~ sP1(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f940,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( ( X0 = X1 )
| ( ( 'fun_app$ak'('the$a',X0) != 'fun_app$ak'('the$a',X1) )
& ( 'none$' != X1 )
& ( 'none$' != X0 ) )
| ( ( 'none$' = X0 )
<~> ( 'none$' = X1 ) ) ),
inference(flattening,[],[f939]) ).
tff(f939,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( ( X0 = X1 )
| ( ( 'fun_app$ak'('the$a',X0) != 'fun_app$ak'('the$a',X1) )
& ( 'none$' != X1 )
& ( 'none$' != X0 ) )
| ( ( 'none$' = X0 )
<~> ( 'none$' = X1 ) ) ),
inference(ennf_transformation,[],[f297]) ).
tff(f297,axiom,
! [X0: 'C_option$',X1: 'C_option$'] :
( ( ( ( ( 'none$' != X1 )
& ( 'none$' != X0 ) )
=> ( 'fun_app$ak'('the$a',X0) = 'fun_app$ak'('the$a',X1) ) )
& ( ( 'none$' = X0 )
<=> ( 'none$' = X1 ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom295) ).
tff(f7968,plain,
spl249_628,
inference(avatar_split_clause,[],[f2320,f7966]) ).
tff(f7966,plain,
( spl249_628
<=> ! [X0: 'A_option$',X1: 'A_option$'] :
( ( X0 = X1 )
| sP0(X1,X0)
| ( 'none$b' = X1 )
| ( 'none$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_628])]) ).
tff(f2320,plain,
! [X0: 'A_option$',X1: 'A_option$'] :
( ( X0 = X1 )
| sP0(X1,X0)
| ( 'none$b' = X1 )
| ( 'none$b' = X0 ) ),
inference(cnf_transformation,[],[f1397]) ).
tff(f1397,plain,
! [X0: 'A_option$',X1: 'A_option$'] :
( ( X0 = X1 )
| sP0(X1,X0)
| ( ( ( 'none$b' != X1 )
| ( 'none$b' != X0 ) )
& ( ( 'none$b' = X1 )
| ( 'none$b' = X0 ) ) ) ),
inference(nnf_transformation,[],[f1100]) ).
tff(f1100,plain,
! [X0: 'A_option$',X1: 'A_option$'] :
( ( X0 = X1 )
| sP0(X1,X0)
| ( ( 'none$b' = X0 )
<~> ( 'none$b' = X1 ) ) ),
inference(definition_folding,[],[f938,f1099]) ).
tff(f1099,plain,
! [X1: 'A_option$',X0: 'A_option$'] :
( ( ( 'fun_app$bf'('the$b',X0) != 'fun_app$bf'('the$b',X1) )
& ( 'none$b' != X1 )
& ( 'none$b' != X0 ) )
| ~ sP0(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f938,plain,
! [X0: 'A_option$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( ( 'fun_app$bf'('the$b',X0) != 'fun_app$bf'('the$b',X1) )
& ( 'none$b' != X1 )
& ( 'none$b' != X0 ) )
| ( ( 'none$b' = X0 )
<~> ( 'none$b' = X1 ) ) ),
inference(flattening,[],[f937]) ).
tff(f937,plain,
! [X0: 'A_option$',X1: 'A_option$'] :
( ( X0 = X1 )
| ( ( 'fun_app$bf'('the$b',X0) != 'fun_app$bf'('the$b',X1) )
& ( 'none$b' != X1 )
& ( 'none$b' != X0 ) )
| ( ( 'none$b' = X0 )
<~> ( 'none$b' = X1 ) ) ),
inference(ennf_transformation,[],[f296]) ).
tff(f296,axiom,
! [X0: 'A_option$',X1: 'A_option$'] :
( ( ( ( ( 'none$b' != X1 )
& ( 'none$b' != X0 ) )
=> ( 'fun_app$bf'('the$b',X0) = 'fun_app$bf'('the$b',X1) ) )
& ( ( 'none$b' = X0 )
<=> ( 'none$b' = X1 ) ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom294) ).
tff(f7964,plain,
spl249_627,
inference(avatar_split_clause,[],[f2276,f7962]) ).
tff(f7962,plain,
( spl249_627
<=> ! [X0: 'A_c_fun$',X1: 'A$'] : ( 'fun_app$bh'('map_option$f'(X0),'fun_app$q'('some$b',X1)) = 'fun_app$j'('some$a','fun_app$bk'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_627])]) ).
tff(f2276,plain,
! [X0: 'A_c_fun$',X1: 'A$'] : ( 'fun_app$bh'('map_option$f'(X0),'fun_app$q'('some$b',X1)) = 'fun_app$j'('some$a','fun_app$bk'(X0,X1)) ),
inference(cnf_transformation,[],[f284]) ).
tff(f284,axiom,
! [X0: 'A_c_fun$',X1: 'A$'] : ( 'fun_app$bh'('map_option$f'(X0),'fun_app$q'('some$b',X1)) = 'fun_app$j'('some$a','fun_app$bk'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom282) ).
tff(f7960,plain,
spl249_626,
inference(avatar_split_clause,[],[f2275,f7958]) ).
tff(f7958,plain,
( spl249_626
<=> ! [X0: 'B_a_fun$',X1: 'B$'] : ( 'fun_app$bj'('map_option$h'(X0),'fun_app$g'('some$',X1)) = 'fun_app$q'('some$b','fun_app$ao'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_626])]) ).
tff(f2275,plain,
! [X0: 'B_a_fun$',X1: 'B$'] : ( 'fun_app$bj'('map_option$h'(X0),'fun_app$g'('some$',X1)) = 'fun_app$q'('some$b','fun_app$ao'(X0,X1)) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,axiom,
! [X0: 'B_a_fun$',X1: 'B$'] : ( 'fun_app$bj'('map_option$h'(X0),'fun_app$g'('some$',X1)) = 'fun_app$q'('some$b','fun_app$ao'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom281) ).
tff(f7956,plain,
spl249_625,
inference(avatar_split_clause,[],[f2274,f7954]) ).
tff(f7954,plain,
( spl249_625
<=> ! [X0: 'C_a_fun$',X1: 'C$'] : ( 'fun_app$bi'('map_option$g'(X0),'fun_app$j'('some$a',X1)) = 'fun_app$q'('some$b','fun_app$bl'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_625])]) ).
tff(f2274,plain,
! [X0: 'C_a_fun$',X1: 'C$'] : ( 'fun_app$bi'('map_option$g'(X0),'fun_app$j'('some$a',X1)) = 'fun_app$q'('some$b','fun_app$bl'(X0,X1)) ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,axiom,
! [X0: 'C_a_fun$',X1: 'C$'] : ( 'fun_app$bi'('map_option$g'(X0),'fun_app$j'('some$a',X1)) = 'fun_app$q'('some$b','fun_app$bl'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom280) ).
tff(f7952,plain,
spl249_624,
inference(avatar_split_clause,[],[f2272,f7950]) ).
tff(f7950,plain,
( spl249_624
<=> ! [X0: 'C_b_fun$',X1: 'C$'] : ( 'fun_app$g'('some$','fun_app$m'(X0,X1)) = 'fun_app$bg'('map_option$'(X0),'fun_app$j'('some$a',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_624])]) ).
tff(f2272,plain,
! [X0: 'C_b_fun$',X1: 'C$'] : ( 'fun_app$g'('some$','fun_app$m'(X0,X1)) = 'fun_app$bg'('map_option$'(X0),'fun_app$j'('some$a',X1)) ),
inference(cnf_transformation,[],[f288]) ).
tff(f288,axiom,
! [X0: 'C_b_fun$',X1: 'C$'] : ( 'fun_app$g'('some$','fun_app$m'(X0,X1)) = 'fun_app$bg'('map_option$'(X0),'fun_app$j'('some$a',X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom286) ).
tff(f7948,plain,
spl249_623,
inference(avatar_split_clause,[],[f2269,f7946]) ).
tff(f7946,plain,
( spl249_623
<=> ! [X0: 'B_c_fun$',X1: 'B$'] : ( 'fun_app$j'('some$a','fun_app$o'(X0,X1)) = 'fun_app$an'('map_option$d'(X0),'fun_app$g'('some$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_623])]) ).
tff(f2269,plain,
! [X0: 'B_c_fun$',X1: 'B$'] : ( 'fun_app$j'('some$a','fun_app$o'(X0,X1)) = 'fun_app$an'('map_option$d'(X0),'fun_app$g'('some$',X1)) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,axiom,
! [X0: 'B_c_fun$',X1: 'B$'] : ( 'fun_app$j'('some$a','fun_app$o'(X0,X1)) = 'fun_app$an'('map_option$d'(X0),'fun_app$g'('some$',X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom287) ).
tff(f7944,plain,
( spl249_622
| ~ spl249_22
| ~ spl249_506 ),
inference(avatar_split_clause,[],[f6914,f6569,f3700,f7942]) ).
tff(f7942,plain,
( spl249_622
<=> ! [X0: 'C_c_option_fun$',X1: 'C_option$'] : ~ sP28(X0,'uwg$',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_622])]) ).
tff(f6914,plain,
( ! [X0: 'C_c_option_fun$',X1: 'C_option$'] : ~ sP28(X0,'uwg$',X1)
| ~ spl249_22
| ~ spl249_506 ),
inference(resolution,[],[f6570,f3701]) ).
tff(f7940,plain,
spl249_621,
inference(avatar_split_clause,[],[f2267,f7938]) ).
tff(f2267,plain,
! [X0: 'B$',X1: 'A$'] : ( 'fun_app$f'('uur$'(X0),X1) = 'fun_app$g'('some$','fun_app$h'('fun_app$i'('sF$',X1),X0)) ),
inference(cnf_transformation,[],[f13]) ).
tff(f13,axiom,
! [X0: 'B$',X1: 'A$'] : ( 'fun_app$f'('uur$'(X0),X1) = 'fun_app$g'('some$','fun_app$h'('fun_app$i'('sF$',X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom12) ).
tff(f7936,plain,
spl249_620,
inference(avatar_split_clause,[],[f2208,f7934]) ).
tff(f7934,plain,
( spl249_620
<=> ! [X4: 'B_option$',X0: 'B_option_bool_fun$'] :
( 'fun_app$a'(X0,'fun_app$g'('some$',sK110(X0)))
| 'fun_app$a'(X0,'none$a')
| ~ 'fun_app$a'(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_620])]) ).
tff(f2208,plain,
! [X0: 'B_option_bool_fun$',X4: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$g'('some$',sK110(X0)))
| 'fun_app$a'(X0,'none$a')
| ~ 'fun_app$a'(X0,X4) ),
inference(cnf_transformation,[],[f1382]) ).
tff(f1382,plain,
! [X0: 'B_option_bool_fun$'] :
( ( 'fun_app$a'(X0,sK109(X0))
| ( ! [X2: 'B$'] : ~ 'fun_app$a'(X0,'fun_app$g'('some$',X2))
& ~ 'fun_app$a'(X0,'none$a') ) )
& ( 'fun_app$a'(X0,'fun_app$g'('some$',sK110(X0)))
| 'fun_app$a'(X0,'none$a')
| ! [X4: 'B_option$'] : ~ 'fun_app$a'(X0,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK109,sK110])],[f1379,f1381,f1380]) ).
tff(f1380,plain,
! [X0: 'B_option_bool_fun$'] :
( ? [X1: 'B_option$'] : 'fun_app$a'(X0,X1)
=> 'fun_app$a'(X0,sK109(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1381,plain,
! [X0: 'B_option_bool_fun$'] :
( ? [X3: 'B$'] : 'fun_app$a'(X0,'fun_app$g'('some$',X3))
=> 'fun_app$a'(X0,'fun_app$g'('some$',sK110(X0))) ),
introduced(choice_axiom,[]) ).
tff(f1379,plain,
! [X0: 'B_option_bool_fun$'] :
( ( ? [X1: 'B_option$'] : 'fun_app$a'(X0,X1)
| ( ! [X2: 'B$'] : ~ 'fun_app$a'(X0,'fun_app$g'('some$',X2))
& ~ 'fun_app$a'(X0,'none$a') ) )
& ( ? [X3: 'B$'] : 'fun_app$a'(X0,'fun_app$g'('some$',X3))
| 'fun_app$a'(X0,'none$a')
| ! [X4: 'B_option$'] : ~ 'fun_app$a'(X0,X4) ) ),
inference(rectify,[],[f1378]) ).
tff(f1378,plain,
! [X0: 'B_option_bool_fun$'] :
( ( ? [X1: 'B_option$'] : 'fun_app$a'(X0,X1)
| ( ! [X2: 'B$'] : ~ 'fun_app$a'(X0,'fun_app$g'('some$',X2))
& ~ 'fun_app$a'(X0,'none$a') ) )
& ( ? [X2: 'B$'] : 'fun_app$a'(X0,'fun_app$g'('some$',X2))
| 'fun_app$a'(X0,'none$a')
| ! [X1: 'B_option$'] : ~ 'fun_app$a'(X0,X1) ) ),
inference(flattening,[],[f1377]) ).
tff(f1377,plain,
! [X0: 'B_option_bool_fun$'] :
( ( ? [X1: 'B_option$'] : 'fun_app$a'(X0,X1)
| ( ! [X2: 'B$'] : ~ 'fun_app$a'(X0,'fun_app$g'('some$',X2))
& ~ 'fun_app$a'(X0,'none$a') ) )
& ( ? [X2: 'B$'] : 'fun_app$a'(X0,'fun_app$g'('some$',X2))
| 'fun_app$a'(X0,'none$a')
| ! [X1: 'B_option$'] : ~ 'fun_app$a'(X0,X1) ) ),
inference(nnf_transformation,[],[f809]) ).
tff(f809,plain,
! [X0: 'B_option_bool_fun$'] :
( ? [X1: 'B_option$'] : 'fun_app$a'(X0,X1)
<=> ( ? [X2: 'B$'] : 'fun_app$a'(X0,'fun_app$g'('some$',X2))
| 'fun_app$a'(X0,'none$a') ) ),
inference(rectify,[],[f123]) ).
tff(f123,axiom,
! [X0: 'B_option_bool_fun$'] :
( ? [X1: 'B_option$'] : 'fun_app$a'(X0,X1)
<=> ( ? [X1: 'B$'] : 'fun_app$a'(X0,'fun_app$g'('some$',X1))
| 'fun_app$a'(X0,'none$a') ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom121) ).
tff(f7932,plain,
spl249_619,
inference(avatar_split_clause,[],[f2205,f7930]) ).
tff(f7930,plain,
( spl249_619
<=> ! [X4: 'C_option$',X0: 'C_option_bool_fun$'] :
( 'fun_app$'(X0,'fun_app$j'('some$a',sK108(X0)))
| 'fun_app$'(X0,'none$')
| ~ 'fun_app$'(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_619])]) ).
tff(f2205,plain,
! [X0: 'C_option_bool_fun$',X4: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$j'('some$a',sK108(X0)))
| 'fun_app$'(X0,'none$')
| ~ 'fun_app$'(X0,X4) ),
inference(cnf_transformation,[],[f1376]) ).
tff(f1376,plain,
! [X0: 'C_option_bool_fun$'] :
( ( 'fun_app$'(X0,sK107(X0))
| ( ! [X2: 'C$'] : ~ 'fun_app$'(X0,'fun_app$j'('some$a',X2))
& ~ 'fun_app$'(X0,'none$') ) )
& ( 'fun_app$'(X0,'fun_app$j'('some$a',sK108(X0)))
| 'fun_app$'(X0,'none$')
| ! [X4: 'C_option$'] : ~ 'fun_app$'(X0,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK107,sK108])],[f1373,f1375,f1374]) ).
tff(f1374,plain,
! [X0: 'C_option_bool_fun$'] :
( ? [X1: 'C_option$'] : 'fun_app$'(X0,X1)
=> 'fun_app$'(X0,sK107(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1375,plain,
! [X0: 'C_option_bool_fun$'] :
( ? [X3: 'C$'] : 'fun_app$'(X0,'fun_app$j'('some$a',X3))
=> 'fun_app$'(X0,'fun_app$j'('some$a',sK108(X0))) ),
introduced(choice_axiom,[]) ).
tff(f1373,plain,
! [X0: 'C_option_bool_fun$'] :
( ( ? [X1: 'C_option$'] : 'fun_app$'(X0,X1)
| ( ! [X2: 'C$'] : ~ 'fun_app$'(X0,'fun_app$j'('some$a',X2))
& ~ 'fun_app$'(X0,'none$') ) )
& ( ? [X3: 'C$'] : 'fun_app$'(X0,'fun_app$j'('some$a',X3))
| 'fun_app$'(X0,'none$')
| ! [X4: 'C_option$'] : ~ 'fun_app$'(X0,X4) ) ),
inference(rectify,[],[f1372]) ).
tff(f1372,plain,
! [X0: 'C_option_bool_fun$'] :
( ( ? [X1: 'C_option$'] : 'fun_app$'(X0,X1)
| ( ! [X2: 'C$'] : ~ 'fun_app$'(X0,'fun_app$j'('some$a',X2))
& ~ 'fun_app$'(X0,'none$') ) )
& ( ? [X2: 'C$'] : 'fun_app$'(X0,'fun_app$j'('some$a',X2))
| 'fun_app$'(X0,'none$')
| ! [X1: 'C_option$'] : ~ 'fun_app$'(X0,X1) ) ),
inference(flattening,[],[f1371]) ).
tff(f1371,plain,
! [X0: 'C_option_bool_fun$'] :
( ( ? [X1: 'C_option$'] : 'fun_app$'(X0,X1)
| ( ! [X2: 'C$'] : ~ 'fun_app$'(X0,'fun_app$j'('some$a',X2))
& ~ 'fun_app$'(X0,'none$') ) )
& ( ? [X2: 'C$'] : 'fun_app$'(X0,'fun_app$j'('some$a',X2))
| 'fun_app$'(X0,'none$')
| ! [X1: 'C_option$'] : ~ 'fun_app$'(X0,X1) ) ),
inference(nnf_transformation,[],[f808]) ).
tff(f808,plain,
! [X0: 'C_option_bool_fun$'] :
( ? [X1: 'C_option$'] : 'fun_app$'(X0,X1)
<=> ( ? [X2: 'C$'] : 'fun_app$'(X0,'fun_app$j'('some$a',X2))
| 'fun_app$'(X0,'none$') ) ),
inference(rectify,[],[f122]) ).
tff(f122,axiom,
! [X0: 'C_option_bool_fun$'] :
( ? [X1: 'C_option$'] : 'fun_app$'(X0,X1)
<=> ( ? [X1: 'C$'] : 'fun_app$'(X0,'fun_app$j'('some$a',X1))
| 'fun_app$'(X0,'none$') ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom120) ).
tff(f7928,plain,
spl249_618,
inference(avatar_split_clause,[],[f2202,f7926]) ).
tff(f7926,plain,
( spl249_618
<=> ! [X4: 'A_option$',X0: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X0,'fun_app$q'('some$b',sK106(X0)))
| 'fun_app$aw'(X0,'none$b')
| ~ 'fun_app$aw'(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_618])]) ).
tff(f2202,plain,
! [X0: 'A_option_bool_fun$',X4: 'A_option$'] :
( 'fun_app$aw'(X0,'fun_app$q'('some$b',sK106(X0)))
| 'fun_app$aw'(X0,'none$b')
| ~ 'fun_app$aw'(X0,X4) ),
inference(cnf_transformation,[],[f1370]) ).
tff(f1370,plain,
! [X0: 'A_option_bool_fun$'] :
( ( 'fun_app$aw'(X0,sK105(X0))
| ( ! [X2: 'A$'] : ~ 'fun_app$aw'(X0,'fun_app$q'('some$b',X2))
& ~ 'fun_app$aw'(X0,'none$b') ) )
& ( 'fun_app$aw'(X0,'fun_app$q'('some$b',sK106(X0)))
| 'fun_app$aw'(X0,'none$b')
| ! [X4: 'A_option$'] : ~ 'fun_app$aw'(X0,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK105,sK106])],[f1367,f1369,f1368]) ).
tff(f1368,plain,
! [X0: 'A_option_bool_fun$'] :
( ? [X1: 'A_option$'] : 'fun_app$aw'(X0,X1)
=> 'fun_app$aw'(X0,sK105(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1369,plain,
! [X0: 'A_option_bool_fun$'] :
( ? [X3: 'A$'] : 'fun_app$aw'(X0,'fun_app$q'('some$b',X3))
=> 'fun_app$aw'(X0,'fun_app$q'('some$b',sK106(X0))) ),
introduced(choice_axiom,[]) ).
tff(f1367,plain,
! [X0: 'A_option_bool_fun$'] :
( ( ? [X1: 'A_option$'] : 'fun_app$aw'(X0,X1)
| ( ! [X2: 'A$'] : ~ 'fun_app$aw'(X0,'fun_app$q'('some$b',X2))
& ~ 'fun_app$aw'(X0,'none$b') ) )
& ( ? [X3: 'A$'] : 'fun_app$aw'(X0,'fun_app$q'('some$b',X3))
| 'fun_app$aw'(X0,'none$b')
| ! [X4: 'A_option$'] : ~ 'fun_app$aw'(X0,X4) ) ),
inference(rectify,[],[f1366]) ).
tff(f1366,plain,
! [X0: 'A_option_bool_fun$'] :
( ( ? [X1: 'A_option$'] : 'fun_app$aw'(X0,X1)
| ( ! [X2: 'A$'] : ~ 'fun_app$aw'(X0,'fun_app$q'('some$b',X2))
& ~ 'fun_app$aw'(X0,'none$b') ) )
& ( ? [X2: 'A$'] : 'fun_app$aw'(X0,'fun_app$q'('some$b',X2))
| 'fun_app$aw'(X0,'none$b')
| ! [X1: 'A_option$'] : ~ 'fun_app$aw'(X0,X1) ) ),
inference(flattening,[],[f1365]) ).
tff(f1365,plain,
! [X0: 'A_option_bool_fun$'] :
( ( ? [X1: 'A_option$'] : 'fun_app$aw'(X0,X1)
| ( ! [X2: 'A$'] : ~ 'fun_app$aw'(X0,'fun_app$q'('some$b',X2))
& ~ 'fun_app$aw'(X0,'none$b') ) )
& ( ? [X2: 'A$'] : 'fun_app$aw'(X0,'fun_app$q'('some$b',X2))
| 'fun_app$aw'(X0,'none$b')
| ! [X1: 'A_option$'] : ~ 'fun_app$aw'(X0,X1) ) ),
inference(nnf_transformation,[],[f807]) ).
tff(f807,plain,
! [X0: 'A_option_bool_fun$'] :
( ? [X1: 'A_option$'] : 'fun_app$aw'(X0,X1)
<=> ( ? [X2: 'A$'] : 'fun_app$aw'(X0,'fun_app$q'('some$b',X2))
| 'fun_app$aw'(X0,'none$b') ) ),
inference(rectify,[],[f121]) ).
tff(f121,axiom,
! [X0: 'A_option_bool_fun$'] :
( ? [X1: 'A_option$'] : 'fun_app$aw'(X0,X1)
<=> ( ? [X1: 'A$'] : 'fun_app$aw'(X0,'fun_app$q'('some$b',X1))
| 'fun_app$aw'(X0,'none$b') ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom119) ).
tff(f7924,plain,
spl249_617,
inference(avatar_split_clause,[],[f2191,f7922]) ).
tff(f7922,plain,
( spl249_617
<=> ! [X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$g'('some$',sK98(X0)))
| ~ 'fun_app$a'(X0,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_617])]) ).
tff(f2191,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$g'('some$',sK98(X0)))
| ~ 'fun_app$a'(X0,'none$a') ),
inference(cnf_transformation,[],[f1344]) ).
tff(f1344,plain,
! [X0: 'B_option_bool_fun$'] :
( ( ! [X1: 'B_option$'] : 'fun_app$a'(X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$g'('some$',sK98(X0)))
| ~ 'fun_app$a'(X0,'none$a') )
& ( ( ! [X3: 'B$'] : 'fun_app$a'(X0,'fun_app$g'('some$',X3))
& 'fun_app$a'(X0,'none$a') )
| ~ 'fun_app$a'(X0,sK99(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK98,sK99])],[f1341,f1343,f1342]) ).
tff(f1342,plain,
! [X0: 'B_option_bool_fun$'] :
( ? [X2: 'B$'] : ~ 'fun_app$a'(X0,'fun_app$g'('some$',X2))
=> ~ 'fun_app$a'(X0,'fun_app$g'('some$',sK98(X0))) ),
introduced(choice_axiom,[]) ).
tff(f1343,plain,
! [X0: 'B_option_bool_fun$'] :
( ? [X4: 'B_option$'] : ~ 'fun_app$a'(X0,X4)
=> ~ 'fun_app$a'(X0,sK99(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1341,plain,
! [X0: 'B_option_bool_fun$'] :
( ( ! [X1: 'B_option$'] : 'fun_app$a'(X0,X1)
| ? [X2: 'B$'] : ~ 'fun_app$a'(X0,'fun_app$g'('some$',X2))
| ~ 'fun_app$a'(X0,'none$a') )
& ( ( ! [X3: 'B$'] : 'fun_app$a'(X0,'fun_app$g'('some$',X3))
& 'fun_app$a'(X0,'none$a') )
| ? [X4: 'B_option$'] : ~ 'fun_app$a'(X0,X4) ) ),
inference(rectify,[],[f1340]) ).
tff(f1340,plain,
! [X0: 'B_option_bool_fun$'] :
( ( ! [X1: 'B_option$'] : 'fun_app$a'(X0,X1)
| ? [X2: 'B$'] : ~ 'fun_app$a'(X0,'fun_app$g'('some$',X2))
| ~ 'fun_app$a'(X0,'none$a') )
& ( ( ! [X2: 'B$'] : 'fun_app$a'(X0,'fun_app$g'('some$',X2))
& 'fun_app$a'(X0,'none$a') )
| ? [X1: 'B_option$'] : ~ 'fun_app$a'(X0,X1) ) ),
inference(flattening,[],[f1339]) ).
tff(f1339,plain,
! [X0: 'B_option_bool_fun$'] :
( ( ! [X1: 'B_option$'] : 'fun_app$a'(X0,X1)
| ? [X2: 'B$'] : ~ 'fun_app$a'(X0,'fun_app$g'('some$',X2))
| ~ 'fun_app$a'(X0,'none$a') )
& ( ( ! [X2: 'B$'] : 'fun_app$a'(X0,'fun_app$g'('some$',X2))
& 'fun_app$a'(X0,'none$a') )
| ? [X1: 'B_option$'] : ~ 'fun_app$a'(X0,X1) ) ),
inference(nnf_transformation,[],[f806]) ).
tff(f806,plain,
! [X0: 'B_option_bool_fun$'] :
( ! [X1: 'B_option$'] : 'fun_app$a'(X0,X1)
<=> ( ! [X2: 'B$'] : 'fun_app$a'(X0,'fun_app$g'('some$',X2))
& 'fun_app$a'(X0,'none$a') ) ),
inference(rectify,[],[f164]) ).
tff(f164,axiom,
! [X0: 'B_option_bool_fun$'] :
( ! [X1: 'B_option$'] : 'fun_app$a'(X0,X1)
<=> ( ! [X1: 'B$'] : 'fun_app$a'(X0,'fun_app$g'('some$',X1))
& 'fun_app$a'(X0,'none$a') ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom162) ).
tff(f7920,plain,
spl249_616,
inference(avatar_split_clause,[],[f2188,f7918]) ).
tff(f7918,plain,
( spl249_616
<=> ! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,X1)
| ~ 'fun_app$'(X0,'fun_app$j'('some$a',sK96(X0)))
| ~ 'fun_app$'(X0,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_616])]) ).
tff(f2188,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,X1)
| ~ 'fun_app$'(X0,'fun_app$j'('some$a',sK96(X0)))
| ~ 'fun_app$'(X0,'none$') ),
inference(cnf_transformation,[],[f1338]) ).
tff(f1338,plain,
! [X0: 'C_option_bool_fun$'] :
( ( ! [X1: 'C_option$'] : 'fun_app$'(X0,X1)
| ~ 'fun_app$'(X0,'fun_app$j'('some$a',sK96(X0)))
| ~ 'fun_app$'(X0,'none$') )
& ( ( ! [X3: 'C$'] : 'fun_app$'(X0,'fun_app$j'('some$a',X3))
& 'fun_app$'(X0,'none$') )
| ~ 'fun_app$'(X0,sK97(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK96,sK97])],[f1335,f1337,f1336]) ).
tff(f1336,plain,
! [X0: 'C_option_bool_fun$'] :
( ? [X2: 'C$'] : ~ 'fun_app$'(X0,'fun_app$j'('some$a',X2))
=> ~ 'fun_app$'(X0,'fun_app$j'('some$a',sK96(X0))) ),
introduced(choice_axiom,[]) ).
tff(f1337,plain,
! [X0: 'C_option_bool_fun$'] :
( ? [X4: 'C_option$'] : ~ 'fun_app$'(X0,X4)
=> ~ 'fun_app$'(X0,sK97(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1335,plain,
! [X0: 'C_option_bool_fun$'] :
( ( ! [X1: 'C_option$'] : 'fun_app$'(X0,X1)
| ? [X2: 'C$'] : ~ 'fun_app$'(X0,'fun_app$j'('some$a',X2))
| ~ 'fun_app$'(X0,'none$') )
& ( ( ! [X3: 'C$'] : 'fun_app$'(X0,'fun_app$j'('some$a',X3))
& 'fun_app$'(X0,'none$') )
| ? [X4: 'C_option$'] : ~ 'fun_app$'(X0,X4) ) ),
inference(rectify,[],[f1334]) ).
tff(f1334,plain,
! [X0: 'C_option_bool_fun$'] :
( ( ! [X1: 'C_option$'] : 'fun_app$'(X0,X1)
| ? [X2: 'C$'] : ~ 'fun_app$'(X0,'fun_app$j'('some$a',X2))
| ~ 'fun_app$'(X0,'none$') )
& ( ( ! [X2: 'C$'] : 'fun_app$'(X0,'fun_app$j'('some$a',X2))
& 'fun_app$'(X0,'none$') )
| ? [X1: 'C_option$'] : ~ 'fun_app$'(X0,X1) ) ),
inference(flattening,[],[f1333]) ).
tff(f1333,plain,
! [X0: 'C_option_bool_fun$'] :
( ( ! [X1: 'C_option$'] : 'fun_app$'(X0,X1)
| ? [X2: 'C$'] : ~ 'fun_app$'(X0,'fun_app$j'('some$a',X2))
| ~ 'fun_app$'(X0,'none$') )
& ( ( ! [X2: 'C$'] : 'fun_app$'(X0,'fun_app$j'('some$a',X2))
& 'fun_app$'(X0,'none$') )
| ? [X1: 'C_option$'] : ~ 'fun_app$'(X0,X1) ) ),
inference(nnf_transformation,[],[f805]) ).
tff(f805,plain,
! [X0: 'C_option_bool_fun$'] :
( ! [X1: 'C_option$'] : 'fun_app$'(X0,X1)
<=> ( ! [X2: 'C$'] : 'fun_app$'(X0,'fun_app$j'('some$a',X2))
& 'fun_app$'(X0,'none$') ) ),
inference(rectify,[],[f163]) ).
tff(f163,axiom,
! [X0: 'C_option_bool_fun$'] :
( ! [X1: 'C_option$'] : 'fun_app$'(X0,X1)
<=> ( ! [X1: 'C$'] : 'fun_app$'(X0,'fun_app$j'('some$a',X1))
& 'fun_app$'(X0,'none$') ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom161) ).
tff(f7916,plain,
spl249_615,
inference(avatar_split_clause,[],[f2185,f7914]) ).
tff(f7914,plain,
( spl249_615
<=> ! [X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$aw'(X0,X1)
| ~ 'fun_app$aw'(X0,'fun_app$q'('some$b',sK94(X0)))
| ~ 'fun_app$aw'(X0,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_615])]) ).
tff(f2185,plain,
! [X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$aw'(X0,X1)
| ~ 'fun_app$aw'(X0,'fun_app$q'('some$b',sK94(X0)))
| ~ 'fun_app$aw'(X0,'none$b') ),
inference(cnf_transformation,[],[f1332]) ).
tff(f1332,plain,
! [X0: 'A_option_bool_fun$'] :
( ( ! [X1: 'A_option$'] : 'fun_app$aw'(X0,X1)
| ~ 'fun_app$aw'(X0,'fun_app$q'('some$b',sK94(X0)))
| ~ 'fun_app$aw'(X0,'none$b') )
& ( ( ! [X3: 'A$'] : 'fun_app$aw'(X0,'fun_app$q'('some$b',X3))
& 'fun_app$aw'(X0,'none$b') )
| ~ 'fun_app$aw'(X0,sK95(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK94,sK95])],[f1329,f1331,f1330]) ).
tff(f1330,plain,
! [X0: 'A_option_bool_fun$'] :
( ? [X2: 'A$'] : ~ 'fun_app$aw'(X0,'fun_app$q'('some$b',X2))
=> ~ 'fun_app$aw'(X0,'fun_app$q'('some$b',sK94(X0))) ),
introduced(choice_axiom,[]) ).
tff(f1331,plain,
! [X0: 'A_option_bool_fun$'] :
( ? [X4: 'A_option$'] : ~ 'fun_app$aw'(X0,X4)
=> ~ 'fun_app$aw'(X0,sK95(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1329,plain,
! [X0: 'A_option_bool_fun$'] :
( ( ! [X1: 'A_option$'] : 'fun_app$aw'(X0,X1)
| ? [X2: 'A$'] : ~ 'fun_app$aw'(X0,'fun_app$q'('some$b',X2))
| ~ 'fun_app$aw'(X0,'none$b') )
& ( ( ! [X3: 'A$'] : 'fun_app$aw'(X0,'fun_app$q'('some$b',X3))
& 'fun_app$aw'(X0,'none$b') )
| ? [X4: 'A_option$'] : ~ 'fun_app$aw'(X0,X4) ) ),
inference(rectify,[],[f1328]) ).
tff(f1328,plain,
! [X0: 'A_option_bool_fun$'] :
( ( ! [X1: 'A_option$'] : 'fun_app$aw'(X0,X1)
| ? [X2: 'A$'] : ~ 'fun_app$aw'(X0,'fun_app$q'('some$b',X2))
| ~ 'fun_app$aw'(X0,'none$b') )
& ( ( ! [X2: 'A$'] : 'fun_app$aw'(X0,'fun_app$q'('some$b',X2))
& 'fun_app$aw'(X0,'none$b') )
| ? [X1: 'A_option$'] : ~ 'fun_app$aw'(X0,X1) ) ),
inference(flattening,[],[f1327]) ).
tff(f1327,plain,
! [X0: 'A_option_bool_fun$'] :
( ( ! [X1: 'A_option$'] : 'fun_app$aw'(X0,X1)
| ? [X2: 'A$'] : ~ 'fun_app$aw'(X0,'fun_app$q'('some$b',X2))
| ~ 'fun_app$aw'(X0,'none$b') )
& ( ( ! [X2: 'A$'] : 'fun_app$aw'(X0,'fun_app$q'('some$b',X2))
& 'fun_app$aw'(X0,'none$b') )
| ? [X1: 'A_option$'] : ~ 'fun_app$aw'(X0,X1) ) ),
inference(nnf_transformation,[],[f804]) ).
tff(f804,plain,
! [X0: 'A_option_bool_fun$'] :
( ! [X1: 'A_option$'] : 'fun_app$aw'(X0,X1)
<=> ( ! [X2: 'A$'] : 'fun_app$aw'(X0,'fun_app$q'('some$b',X2))
& 'fun_app$aw'(X0,'none$b') ) ),
inference(rectify,[],[f162]) ).
tff(f162,axiom,
! [X0: 'A_option_bool_fun$'] :
( ! [X1: 'A_option$'] : 'fun_app$aw'(X0,X1)
<=> ( ! [X1: 'A$'] : 'fun_app$aw'(X0,'fun_app$q'('some$b',X1))
& 'fun_app$aw'(X0,'none$b') ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom160) ).
tff(f7912,plain,
spl249_614,
inference(avatar_split_clause,[],[f2139,f7910]) ).
tff(f7910,plain,
( spl249_614
<=> ! [X0: 'B_option_set$'] :
( ( 'bot$d' != 'these$a'(X0) )
| ( 'insert$b'('none$a','bot$a') = X0 )
| ( 'bot$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_614])]) ).
tff(f2139,plain,
! [X0: 'B_option_set$'] :
( ( 'bot$d' != 'these$a'(X0) )
| ( 'insert$b'('none$a','bot$a') = X0 )
| ( 'bot$a' = X0 ) ),
inference(cnf_transformation,[],[f1269]) ).
tff(f1269,plain,
! [X0: 'B_option_set$'] :
( ( ( 'bot$d' != 'these$a'(X0) )
| ( 'insert$b'('none$a','bot$a') = X0 )
| ( 'bot$a' = X0 ) )
& ( ( ( 'insert$b'('none$a','bot$a') != X0 )
& ( 'bot$a' != X0 ) )
| ( 'bot$d' = 'these$a'(X0) ) ) ),
inference(flattening,[],[f1268]) ).
tff(f1268,plain,
! [X0: 'B_option_set$'] :
( ( ( 'bot$d' != 'these$a'(X0) )
| ( 'insert$b'('none$a','bot$a') = X0 )
| ( 'bot$a' = X0 ) )
& ( ( ( 'insert$b'('none$a','bot$a') != X0 )
& ( 'bot$a' != X0 ) )
| ( 'bot$d' = 'these$a'(X0) ) ) ),
inference(nnf_transformation,[],[f703]) ).
tff(f703,axiom,
! [X0: 'B_option_set$'] :
( ( 'bot$d' != 'these$a'(X0) )
<=> ( ( 'insert$b'('none$a','bot$a') != X0 )
& ( 'bot$a' != X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom701) ).
tff(f7908,plain,
spl249_613,
inference(avatar_split_clause,[],[f2136,f7906]) ).
tff(f7906,plain,
( spl249_613
<=> ! [X0: 'C_option_set$'] :
( ( 'bot$c' != 'these$'(X0) )
| ( 'insert$c'('none$','bot$b') = X0 )
| ( 'bot$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_613])]) ).
tff(f2136,plain,
! [X0: 'C_option_set$'] :
( ( 'bot$c' != 'these$'(X0) )
| ( 'insert$c'('none$','bot$b') = X0 )
| ( 'bot$b' = X0 ) ),
inference(cnf_transformation,[],[f1267]) ).
tff(f1267,plain,
! [X0: 'C_option_set$'] :
( ( ( 'bot$c' != 'these$'(X0) )
| ( 'insert$c'('none$','bot$b') = X0 )
| ( 'bot$b' = X0 ) )
& ( ( ( 'insert$c'('none$','bot$b') != X0 )
& ( 'bot$b' != X0 ) )
| ( 'bot$c' = 'these$'(X0) ) ) ),
inference(flattening,[],[f1266]) ).
tff(f1266,plain,
! [X0: 'C_option_set$'] :
( ( ( 'bot$c' != 'these$'(X0) )
| ( 'insert$c'('none$','bot$b') = X0 )
| ( 'bot$b' = X0 ) )
& ( ( ( 'insert$c'('none$','bot$b') != X0 )
& ( 'bot$b' != X0 ) )
| ( 'bot$c' = 'these$'(X0) ) ) ),
inference(nnf_transformation,[],[f702]) ).
tff(f702,axiom,
! [X0: 'C_option_set$'] :
( ( 'bot$c' != 'these$'(X0) )
<=> ( ( 'insert$c'('none$','bot$b') != X0 )
& ( 'bot$b' != X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom700) ).
tff(f7418,plain,
spl249_612,
inference(avatar_split_clause,[],[f3581,f7416]) ).
tff(f7416,plain,
( spl249_612
<=> ! [X0: 'B_b_fun$',X1: 'B$'] : ( 'fun_app$g'('uve$'(X0),X1) = 'fun_app$s'('map_option$b'(X0),'fun_app$g'('some$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_612])]) ).
tff(f3581,plain,
! [X0: 'B_b_fun$',X1: 'B$'] : ( 'fun_app$g'('uve$'(X0),X1) = 'fun_app$s'('map_option$b'(X0),'fun_app$g'('some$',X1)) ),
inference(forward_demodulation,[],[f2273,f2245]) ).
tff(f2273,plain,
! [X0: 'B_b_fun$',X1: 'B$'] : ( 'fun_app$g'('some$','fun_app$h'(X0,X1)) = 'fun_app$s'('map_option$b'(X0),'fun_app$g'('some$',X1)) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,axiom,
! [X0: 'B_b_fun$',X1: 'B$'] : ( 'fun_app$g'('some$','fun_app$h'(X0,X1)) = 'fun_app$s'('map_option$b'(X0),'fun_app$g'('some$',X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom288) ).
tff(f7414,plain,
spl249_611,
inference(avatar_split_clause,[],[f3580,f7412]) ).
tff(f7412,plain,
( spl249_611
<=> ! [X0: 'A_b_fun$',X1: 'A$'] : ( 'fun_app$f'('uvh$'(X0),X1) = 'fun_app$av'('map_option$e'(X0),'fun_app$q'('some$b',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_611])]) ).
tff(f3580,plain,
! [X0: 'A_b_fun$',X1: 'A$'] : ( 'fun_app$f'('uvh$'(X0),X1) = 'fun_app$av'('map_option$e'(X0),'fun_app$q'('some$b',X1)) ),
inference(forward_demodulation,[],[f2271,f2237]) ).
tff(f2237,plain,
! [X0: 'A_b_fun$',X1: 'A$'] : ( 'fun_app$f'('uvh$'(X0),X1) = 'fun_app$g'('some$','fun_app$p'(X0,X1)) ),
inference(cnf_transformation,[],[f18]) ).
tff(f18,axiom,
! [X0: 'A_b_fun$',X1: 'A$'] : ( 'fun_app$f'('uvh$'(X0),X1) = 'fun_app$g'('some$','fun_app$p'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom17) ).
tff(f2271,plain,
! [X0: 'A_b_fun$',X1: 'A$'] : ( 'fun_app$g'('some$','fun_app$p'(X0,X1)) = 'fun_app$av'('map_option$e'(X0),'fun_app$q'('some$b',X1)) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,axiom,
! [X0: 'A_b_fun$',X1: 'A$'] : ( 'fun_app$g'('some$','fun_app$p'(X0,X1)) = 'fun_app$av'('map_option$e'(X0),'fun_app$q'('some$b',X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom283) ).
tff(f7410,plain,
spl249_610,
inference(avatar_split_clause,[],[f3579,f7408]) ).
tff(f7408,plain,
( spl249_610
<=> ! [X0: 'C_c_fun$',X1: 'C$'] : ( 'fun_app$j'('uvf$'(X0),X1) = 'fun_app$u'('map_option$c'(X0),'fun_app$j'('some$a',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_610])]) ).
tff(f3579,plain,
! [X0: 'C_c_fun$',X1: 'C$'] : ( 'fun_app$j'('uvf$'(X0),X1) = 'fun_app$u'('map_option$c'(X0),'fun_app$j'('some$a',X1)) ),
inference(forward_demodulation,[],[f2270,f2244]) ).
tff(f2270,plain,
! [X0: 'C_c_fun$',X1: 'C$'] : ( 'fun_app$j'('some$a','fun_app$k'(X0,X1)) = 'fun_app$u'('map_option$c'(X0),'fun_app$j'('some$a',X1)) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,axiom,
! [X0: 'C_c_fun$',X1: 'C$'] : ( 'fun_app$j'('some$a','fun_app$k'(X0,X1)) = 'fun_app$u'('map_option$c'(X0),'fun_app$j'('some$a',X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom285) ).
tff(f7406,plain,
spl249_609,
inference(avatar_split_clause,[],[f3578,f7404]) ).
tff(f7404,plain,
( spl249_609
<=> ! [X0: 'A_a_fun$',X1: 'A$'] : ( 'fun_app$q'('uvd$'(X0),X1) = 'fun_app$be'('map_option$a'(X0),'fun_app$q'('some$b',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_609])]) ).
tff(f3578,plain,
! [X0: 'A_a_fun$',X1: 'A$'] : ( 'fun_app$q'('uvd$'(X0),X1) = 'fun_app$be'('map_option$a'(X0),'fun_app$q'('some$b',X1)) ),
inference(forward_demodulation,[],[f2268,f2243]) ).
tff(f2268,plain,
! [X0: 'A_a_fun$',X1: 'A$'] : ( 'fun_app$q'('some$b','fun_app$r'(X0,X1)) = 'fun_app$be'('map_option$a'(X0),'fun_app$q'('some$b',X1)) ),
inference(cnf_transformation,[],[f286]) ).
tff(f286,axiom,
! [X0: 'A_a_fun$',X1: 'A$'] : ( 'fun_app$q'('some$b','fun_app$r'(X0,X1)) = 'fun_app$be'('map_option$a'(X0),'fun_app$q'('some$b',X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom284) ).
tff(f7402,plain,
spl249_608,
inference(avatar_split_clause,[],[f3483,f7400]) ).
tff(f7400,plain,
( spl249_608
<=> ! [X4: 'B$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'fun_app$g'(X0,X4))
| ~ sP31(X0,X1,'fun_app$g'('some$',X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_608])]) ).
tff(f3483,plain,
! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$',X4: 'B$'] :
( 'fun_app$a'(X1,'fun_app$g'(X0,X4))
| ~ sP31(X0,X1,'fun_app$g'('some$',X4)) ),
inference(equality_resolution,[],[f2968]) ).
tff(f2968,plain,
! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$',X4: 'B$'] :
( 'fun_app$a'(X1,'fun_app$g'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 )
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f1729]) ).
tff(f7398,plain,
spl249_607,
inference(avatar_split_clause,[],[f3481,f7396]) ).
tff(f7396,plain,
( spl249_607
<=> ! [X4: 'B$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'fun_app$g'(X0,X4))
| ~ sP30(X0,X1,'fun_app$g'('some$',X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_607])]) ).
tff(f3481,plain,
! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$',X4: 'B$'] :
( 'fun_app$a'(X1,'fun_app$g'(X0,X4))
| ~ sP30(X0,X1,'fun_app$g'('some$',X4)) ),
inference(equality_resolution,[],[f2960]) ).
tff(f2960,plain,
! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$',X4: 'B$'] :
( 'fun_app$a'(X1,'fun_app$g'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 )
| ~ sP30(X0,X1,X2) ),
inference(cnf_transformation,[],[f1723]) ).
tff(f7394,plain,
spl249_606,
inference(avatar_split_clause,[],[f3479,f7392]) ).
tff(f7392,plain,
( spl249_606
<=> ! [X4: 'C$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'fun_app$j'(X0,X4))
| ~ sP29(X0,X1,'fun_app$j'('some$a',X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_606])]) ).
tff(f3479,plain,
! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$',X4: 'C$'] :
( 'fun_app$'(X1,'fun_app$j'(X0,X4))
| ~ sP29(X0,X1,'fun_app$j'('some$a',X4)) ),
inference(equality_resolution,[],[f2952]) ).
tff(f2952,plain,
! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$',X4: 'C$'] :
( 'fun_app$'(X1,'fun_app$j'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 )
| ~ sP29(X0,X1,X2) ),
inference(cnf_transformation,[],[f1717]) ).
tff(f7390,plain,
spl249_605,
inference(avatar_split_clause,[],[f3477,f7388]) ).
tff(f7388,plain,
( spl249_605
<=> ! [X4: 'C$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'fun_app$j'(X0,X4))
| ~ sP28(X0,X1,'fun_app$j'('some$a',X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_605])]) ).
tff(f3477,plain,
! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$',X4: 'C$'] :
( 'fun_app$'(X1,'fun_app$j'(X0,X4))
| ~ sP28(X0,X1,'fun_app$j'('some$a',X4)) ),
inference(equality_resolution,[],[f2944]) ).
tff(f2944,plain,
! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$',X4: 'C$'] :
( 'fun_app$'(X1,'fun_app$j'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 )
| ~ sP28(X0,X1,X2) ),
inference(cnf_transformation,[],[f1711]) ).
tff(f7386,plain,
spl249_604,
inference(avatar_split_clause,[],[f3475,f7384]) ).
tff(f7384,plain,
( spl249_604
<=> ! [X4: 'A$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'fun_app$q'(X0,X4))
| ~ sP27(X0,X1,'fun_app$q'('some$b',X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_604])]) ).
tff(f3475,plain,
! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$',X4: 'A$'] :
( 'fun_app$aw'(X1,'fun_app$q'(X0,X4))
| ~ sP27(X0,X1,'fun_app$q'('some$b',X4)) ),
inference(equality_resolution,[],[f2936]) ).
tff(f2936,plain,
! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$',X4: 'A$'] :
( 'fun_app$aw'(X1,'fun_app$q'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 )
| ~ sP27(X0,X1,X2) ),
inference(cnf_transformation,[],[f1705]) ).
tff(f7382,plain,
spl249_603,
inference(avatar_split_clause,[],[f3473,f7380]) ).
tff(f7380,plain,
( spl249_603
<=> ! [X4: 'A$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'fun_app$q'(X0,X4))
| ~ sP26(X0,X1,'fun_app$q'('some$b',X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_603])]) ).
tff(f3473,plain,
! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$',X4: 'A$'] :
( 'fun_app$aw'(X1,'fun_app$q'(X0,X4))
| ~ sP26(X0,X1,'fun_app$q'('some$b',X4)) ),
inference(equality_resolution,[],[f2928]) ).
tff(f2928,plain,
! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$',X4: 'A$'] :
( 'fun_app$aw'(X1,'fun_app$q'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 )
| ~ sP26(X0,X1,X2) ),
inference(cnf_transformation,[],[f1699]) ).
tff(f7378,plain,
spl249_602,
inference(avatar_split_clause,[],[f3462,f7376]) ).
tff(f7376,plain,
( spl249_602
<=> ! [X4: 'A$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'fun_app$f'(X0,X4))
| ~ sP22(X0,X1,'fun_app$q'('some$b',X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_602])]) ).
tff(f3462,plain,
! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$',X4: 'A$'] :
( 'fun_app$a'(X1,'fun_app$f'(X0,X4))
| ~ sP22(X0,X1,'fun_app$q'('some$b',X4)) ),
inference(equality_resolution,[],[f2878]) ).
tff(f2878,plain,
! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$',X4: 'A$'] :
( 'fun_app$a'(X1,'fun_app$f'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 )
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f1668]) ).
tff(f7374,plain,
spl249_601,
inference(avatar_split_clause,[],[f3460,f7372]) ).
tff(f7372,plain,
( spl249_601
<=> ! [X4: 'A$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'fun_app$f'(X0,X4))
| ~ sP21(X0,X1,'fun_app$q'('some$b',X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_601])]) ).
tff(f3460,plain,
! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$',X4: 'A$'] :
( 'fun_app$a'(X1,'fun_app$f'(X0,X4))
| ~ sP21(X0,X1,'fun_app$q'('some$b',X4)) ),
inference(equality_resolution,[],[f2870]) ).
tff(f2870,plain,
! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$',X4: 'A$'] :
( 'fun_app$a'(X1,'fun_app$f'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 )
| ~ sP21(X0,X1,X2) ),
inference(cnf_transformation,[],[f1662]) ).
tff(f7370,plain,
spl249_600,
inference(avatar_split_clause,[],[f3449,f7368]) ).
tff(f7368,plain,
( spl249_600
<=> ! [X4: 'A$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'fun_app$bm'(X0,X4))
| ~ sP17(X0,X1,'fun_app$q'('some$b',X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_600])]) ).
tff(f3449,plain,
! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$',X4: 'A$'] :
( 'fun_app$'(X1,'fun_app$bm'(X0,X4))
| ~ sP17(X0,X1,'fun_app$q'('some$b',X4)) ),
inference(equality_resolution,[],[f2838]) ).
tff(f2838,plain,
! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$',X4: 'A$'] :
( 'fun_app$'(X1,'fun_app$bm'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 )
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f1640]) ).
tff(f7366,plain,
( spl249_599
| ~ spl249_20
| ~ spl249_442 ),
inference(avatar_split_clause,[],[f6339,f5794,f3692,f7364]) ).
tff(f7364,plain,
( spl249_599
<=> ! [X0: 'B_option$'] : sP25(X0,'uug$',tltrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_599])]) ).
tff(f6339,plain,
( ! [X0: 'B_option$'] : sP25(X0,'uug$',tltrue)
| ~ spl249_20
| ~ spl249_442 ),
inference(resolution,[],[f5795,f3693]) ).
tff(f7362,plain,
spl249_598,
inference(avatar_split_clause,[],[f3447,f7360]) ).
tff(f7360,plain,
( spl249_598
<=> ! [X4: 'A$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'fun_app$bm'(X0,X4))
| ~ sP16(X0,X1,'fun_app$q'('some$b',X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_598])]) ).
tff(f3447,plain,
! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$',X4: 'A$'] :
( 'fun_app$'(X1,'fun_app$bm'(X0,X4))
| ~ sP16(X0,X1,'fun_app$q'('some$b',X4)) ),
inference(equality_resolution,[],[f2830]) ).
tff(f2830,plain,
! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$',X4: 'A$'] :
( 'fun_app$'(X1,'fun_app$bm'(X0,X4))
| ( 'fun_app$q'('some$b',X4) != X2 )
| ~ sP16(X0,X1,X2) ),
inference(cnf_transformation,[],[f1634]) ).
tff(f7358,plain,
spl249_597,
inference(avatar_split_clause,[],[f3445,f7356]) ).
tff(f7356,plain,
( spl249_597
<=> ! [X4: 'B$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'fun_app$bo'(X0,X4))
| ~ sP15(X0,X1,'fun_app$g'('some$',X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_597])]) ).
tff(f3445,plain,
! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$',X4: 'B$'] :
( 'fun_app$aw'(X1,'fun_app$bo'(X0,X4))
| ~ sP15(X0,X1,'fun_app$g'('some$',X4)) ),
inference(equality_resolution,[],[f2822]) ).
tff(f2822,plain,
! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$',X4: 'B$'] :
( 'fun_app$aw'(X1,'fun_app$bo'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 )
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f1628]) ).
tff(f7354,plain,
spl249_596,
inference(avatar_split_clause,[],[f3443,f7352]) ).
tff(f7352,plain,
( spl249_596
<=> ! [X4: 'C$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'fun_app$bn'(X0,X4))
| ~ sP14(X0,X1,'fun_app$j'('some$a',X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_596])]) ).
tff(f3443,plain,
! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$',X4: 'C$'] :
( 'fun_app$aw'(X1,'fun_app$bn'(X0,X4))
| ~ sP14(X0,X1,'fun_app$j'('some$a',X4)) ),
inference(equality_resolution,[],[f2814]) ).
tff(f2814,plain,
! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$',X4: 'C$'] :
( 'fun_app$aw'(X1,'fun_app$bn'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 )
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f1622]) ).
tff(f7350,plain,
spl249_595,
inference(avatar_split_clause,[],[f3441,f7348]) ).
tff(f7348,plain,
( spl249_595
<=> ! [X4: 'B$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'fun_app$bo'(X0,X4))
| ~ sP13(X0,X1,'fun_app$g'('some$',X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_595])]) ).
tff(f3441,plain,
! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$',X4: 'B$'] :
( 'fun_app$aw'(X1,'fun_app$bo'(X0,X4))
| ~ sP13(X0,X1,'fun_app$g'('some$',X4)) ),
inference(equality_resolution,[],[f2806]) ).
tff(f2806,plain,
! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$',X4: 'B$'] :
( 'fun_app$aw'(X1,'fun_app$bo'(X0,X4))
| ( 'fun_app$g'('some$',X4) != X2 )
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f1616]) ).
tff(f7346,plain,
spl249_594,
inference(avatar_split_clause,[],[f3439,f7344]) ).
tff(f7344,plain,
( spl249_594
<=> ! [X4: 'C$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'fun_app$bn'(X0,X4))
| ~ sP12(X0,X1,'fun_app$j'('some$a',X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_594])]) ).
tff(f3439,plain,
! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$',X4: 'C$'] :
( 'fun_app$aw'(X1,'fun_app$bn'(X0,X4))
| ~ sP12(X0,X1,'fun_app$j'('some$a',X4)) ),
inference(equality_resolution,[],[f2798]) ).
tff(f2798,plain,
! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$',X4: 'C$'] :
( 'fun_app$aw'(X1,'fun_app$bn'(X0,X4))
| ( 'fun_app$j'('some$a',X4) != X2 )
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f1610]) ).
tff(f7342,plain,
spl249_593,
inference(avatar_split_clause,[],[f3432,f7340]) ).
tff(f7340,plain,
( spl249_593
<=> ! [X2: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,X2)
| 'member$a'(sK156('some$c'(X2),X1),'set_option$'('some$c'(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_593])]) ).
tff(f3432,plain,
! [X2: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,X2)
| 'member$a'(sK156('some$c'(X2),X1),'set_option$'('some$c'(X2))) ),
inference(equality_resolution,[],[f2763]) ).
tff(f2763,plain,
! [X2: 'B_option$',X0: 'B_option_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,X2)
| ( 'some$c'(X2) != X0 )
| 'member$a'(sK156(X0,X1),'set_option$'(X0)) ),
inference(cnf_transformation,[],[f1578]) ).
tff(f1578,plain,
! [X0: 'B_option_option$',X1: 'B_option_bool_fun$',X2: 'B_option$'] :
( 'fun_app$a'(X1,X2)
| ( 'some$c'(X2) != X0 )
| ( ~ 'fun_app$a'(X1,sK156(X0,X1))
& 'member$a'(sK156(X0,X1),'set_option$'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK156])],[f985,f1577]) ).
tff(f1577,plain,
! [X0: 'B_option_option$',X1: 'B_option_bool_fun$'] :
( ? [X3: 'B_option$'] :
( ~ 'fun_app$a'(X1,X3)
& 'member$a'(X3,'set_option$'(X0)) )
=> ( ~ 'fun_app$a'(X1,sK156(X0,X1))
& 'member$a'(sK156(X0,X1),'set_option$'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f985,plain,
! [X0: 'B_option_option$',X1: 'B_option_bool_fun$',X2: 'B_option$'] :
( 'fun_app$a'(X1,X2)
| ( 'some$c'(X2) != X0 )
| ? [X3: 'B_option$'] :
( ~ 'fun_app$a'(X1,X3)
& 'member$a'(X3,'set_option$'(X0)) ) ),
inference(flattening,[],[f984]) ).
tff(f984,plain,
! [X0: 'B_option_option$',X1: 'B_option_bool_fun$',X2: 'B_option$'] :
( 'fun_app$a'(X1,X2)
| ( 'some$c'(X2) != X0 )
| ? [X3: 'B_option$'] :
( ~ 'fun_app$a'(X1,X3)
& 'member$a'(X3,'set_option$'(X0)) ) ),
inference(ennf_transformation,[],[f427]) ).
tff(f427,axiom,
! [X0: 'B_option_option$',X1: 'B_option_bool_fun$',X2: 'B_option$'] :
( ( ( 'some$c'(X2) = X0 )
& ! [X3: 'B_option$'] :
( 'member$a'(X3,'set_option$'(X0))
=> 'fun_app$a'(X1,X3) ) )
=> 'fun_app$a'(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom425) ).
tff(f7338,plain,
spl249_592,
inference(avatar_split_clause,[],[f3430,f7336]) ).
tff(f7336,plain,
( spl249_592
<=> ! [X2: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,X2)
| 'member$'(sK155('some$d'(X2),X1),'set_option$a'('some$d'(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_592])]) ).
tff(f3430,plain,
! [X2: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,X2)
| 'member$'(sK155('some$d'(X2),X1),'set_option$a'('some$d'(X2))) ),
inference(equality_resolution,[],[f2761]) ).
tff(f2761,plain,
! [X2: 'C_option$',X0: 'C_option_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,X2)
| ( 'some$d'(X2) != X0 )
| 'member$'(sK155(X0,X1),'set_option$a'(X0)) ),
inference(cnf_transformation,[],[f1576]) ).
tff(f1576,plain,
! [X0: 'C_option_option$',X1: 'C_option_bool_fun$',X2: 'C_option$'] :
( 'fun_app$'(X1,X2)
| ( 'some$d'(X2) != X0 )
| ( ~ 'fun_app$'(X1,sK155(X0,X1))
& 'member$'(sK155(X0,X1),'set_option$a'(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK155])],[f983,f1575]) ).
tff(f1575,plain,
! [X0: 'C_option_option$',X1: 'C_option_bool_fun$'] :
( ? [X3: 'C_option$'] :
( ~ 'fun_app$'(X1,X3)
& 'member$'(X3,'set_option$a'(X0)) )
=> ( ~ 'fun_app$'(X1,sK155(X0,X1))
& 'member$'(sK155(X0,X1),'set_option$a'(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f983,plain,
! [X0: 'C_option_option$',X1: 'C_option_bool_fun$',X2: 'C_option$'] :
( 'fun_app$'(X1,X2)
| ( 'some$d'(X2) != X0 )
| ? [X3: 'C_option$'] :
( ~ 'fun_app$'(X1,X3)
& 'member$'(X3,'set_option$a'(X0)) ) ),
inference(flattening,[],[f982]) ).
tff(f982,plain,
! [X0: 'C_option_option$',X1: 'C_option_bool_fun$',X2: 'C_option$'] :
( 'fun_app$'(X1,X2)
| ( 'some$d'(X2) != X0 )
| ? [X3: 'C_option$'] :
( ~ 'fun_app$'(X1,X3)
& 'member$'(X3,'set_option$a'(X0)) ) ),
inference(ennf_transformation,[],[f428]) ).
tff(f428,axiom,
! [X0: 'C_option_option$',X1: 'C_option_bool_fun$',X2: 'C_option$'] :
( ( ( 'some$d'(X2) = X0 )
& ! [X3: 'C_option$'] :
( 'member$'(X3,'set_option$a'(X0))
=> 'fun_app$'(X1,X3) ) )
=> 'fun_app$'(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom426) ).
tff(f7334,plain,
spl249_591,
inference(avatar_split_clause,[],[f3156,f7332]) ).
tff(f7332,plain,
( spl249_591
<=> ! [X0: 'Bool_bool_fun$',X3: 'B_option$',X2: 'B_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,def_16(X1,X2,X3))
| ~ sP35(X3,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_591])]) ).
tff(f3156,plain,
! [X2: 'B_bool_fun$',X3: 'B_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,def_16(X1,X2,X3))
| ~ sP35(X3,X2,X0,X1) ),
inference(cnf_transformation,[],[f1878]) ).
tff(f1878,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( ( 'fun_app$ag'(X0,def_16(X1,X2,X3))
| ~ sP35(X3,X2,X0,X1) )
& ( sP35(X3,X2,X0,X1)
| ~ 'fun_app$ag'(X0,def_16(X1,X2,X3)) ) ),
inference(nnf_transformation,[],[f1170]) ).
tff(f1170,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( 'fun_app$ag'(X0,def_16(X1,X2,X3))
<=> sP35(X3,X2,X0,X1) ),
inference(definition_folding,[],[f1086,f1169]) ).
tff(f1086,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( 'fun_app$ag'(X0,def_16(X1,X2,X3))
<=> ( ( 'fun_app$ag'(X0,def_17(X2,X3))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$a' != X3 ) ) ) ),
inference(ennf_transformation,[],[f180]) ).
tff(f180,axiom,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( 'fun_app$ag'(X0,def_16(X1,X2,X3))
<=> ~ ( ( ~ 'fun_app$ag'(X0,def_17(X2,X3))
& ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 ) )
| ( ~ 'fun_app$ag'(X0,X1)
& ( 'none$a' = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom178) ).
tff(f7330,plain,
spl249_590,
inference(avatar_split_clause,[],[f3155,f7328]) ).
tff(f7328,plain,
( spl249_590
<=> ! [X0: 'Bool_bool_fun$',X3: 'B_option$',X2: 'B_bool_fun$',X1: tlbool] :
( sP35(X3,X2,X0,X1)
| ~ 'fun_app$ag'(X0,def_16(X1,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_590])]) ).
tff(f3155,plain,
! [X2: 'B_bool_fun$',X3: 'B_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
( sP35(X3,X2,X0,X1)
| ~ 'fun_app$ag'(X0,def_16(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1878]) ).
tff(f7326,plain,
spl249_589,
inference(avatar_split_clause,[],[f3148,f7324]) ).
tff(f7324,plain,
( spl249_589
<=> ! [X0: 'Bool_bool_fun$',X3: 'C_option$',X2: 'C_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,def_18(X1,X2,X3))
| ~ sP34(X3,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_589])]) ).
tff(f3148,plain,
! [X2: 'C_bool_fun$',X3: 'C_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,def_18(X1,X2,X3))
| ~ sP34(X3,X2,X0,X1) ),
inference(cnf_transformation,[],[f1874]) ).
tff(f1874,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] :
( ( 'fun_app$ag'(X0,def_18(X1,X2,X3))
| ~ sP34(X3,X2,X0,X1) )
& ( sP34(X3,X2,X0,X1)
| ~ 'fun_app$ag'(X0,def_18(X1,X2,X3)) ) ),
inference(nnf_transformation,[],[f1168]) ).
tff(f1168,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] :
( 'fun_app$ag'(X0,def_18(X1,X2,X3))
<=> sP34(X3,X2,X0,X1) ),
inference(definition_folding,[],[f1085,f1167]) ).
tff(f1085,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] :
( 'fun_app$ag'(X0,def_18(X1,X2,X3))
<=> ( ( 'fun_app$ag'(X0,def_19(X2,X3))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$' != X3 ) ) ) ),
inference(ennf_transformation,[],[f181]) ).
tff(f181,axiom,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] :
( 'fun_app$ag'(X0,def_18(X1,X2,X3))
<=> ~ ( ( ~ 'fun_app$ag'(X0,def_19(X2,X3))
& ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) = X3 ) )
| ( ~ 'fun_app$ag'(X0,X1)
& ( 'none$' = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom179) ).
tff(f7322,plain,
( spl249_588
| ~ spl249_18
| ~ spl249_441 ),
inference(avatar_split_clause,[],[f6334,f5790,f3684,f7320]) ).
tff(f7320,plain,
( spl249_588
<=> ! [X0: 'C_option$'] : sP20(X0,'uuf$',tltrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_588])]) ).
tff(f6334,plain,
( ! [X0: 'C_option$'] : sP20(X0,'uuf$',tltrue)
| ~ spl249_18
| ~ spl249_441 ),
inference(resolution,[],[f5791,f3685]) ).
tff(f7318,plain,
spl249_587,
inference(avatar_split_clause,[],[f3147,f7316]) ).
tff(f7316,plain,
( spl249_587
<=> ! [X0: 'Bool_bool_fun$',X3: 'C_option$',X2: 'C_bool_fun$',X1: tlbool] :
( sP34(X3,X2,X0,X1)
| ~ 'fun_app$ag'(X0,def_18(X1,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_587])]) ).
tff(f3147,plain,
! [X2: 'C_bool_fun$',X3: 'C_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
( sP34(X3,X2,X0,X1)
| ~ 'fun_app$ag'(X0,def_18(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1874]) ).
tff(f7314,plain,
spl249_586,
inference(avatar_split_clause,[],[f3140,f7312]) ).
tff(f7312,plain,
( spl249_586
<=> ! [X0: 'Bool_bool_fun$',X3: 'B_option$',X2: 'B_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,def_20(X1,X2,X3))
| ~ sP33(X3,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_586])]) ).
tff(f3140,plain,
! [X2: 'B_bool_fun$',X3: 'B_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,def_20(X1,X2,X3))
| ~ sP33(X3,X2,X0,X1) ),
inference(cnf_transformation,[],[f1870]) ).
tff(f1870,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( ( 'fun_app$ag'(X0,def_20(X1,X2,X3))
| ~ sP33(X3,X2,X0,X1) )
& ( sP33(X3,X2,X0,X1)
| ~ 'fun_app$ag'(X0,def_20(X1,X2,X3)) ) ),
inference(nnf_transformation,[],[f1166]) ).
tff(f1166,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( 'fun_app$ag'(X0,def_20(X1,X2,X3))
<=> sP33(X3,X2,X0,X1) ),
inference(definition_folding,[],[f1084,f1165]) ).
tff(f1084,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( 'fun_app$ag'(X0,def_20(X1,X2,X3))
<=> ( ( 'fun_app$ag'(X0,def_21(X2,X3))
| ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$a' != X3 ) ) ) ),
inference(ennf_transformation,[],[f186]) ).
tff(f186,axiom,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( 'fun_app$ag'(X0,def_20(X1,X2,X3))
<=> ( ( ( 'fun_app$g'('some$','fun_app$al'('the$',X3)) = X3 )
=> 'fun_app$ag'(X0,def_21(X2,X3)) )
& ( ( 'none$a' = X3 )
=> 'fun_app$ag'(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom184) ).
tff(f7310,plain,
spl249_585,
inference(avatar_split_clause,[],[f3139,f7308]) ).
tff(f7308,plain,
( spl249_585
<=> ! [X0: 'Bool_bool_fun$',X3: 'B_option$',X2: 'B_bool_fun$',X1: tlbool] :
( sP33(X3,X2,X0,X1)
| ~ 'fun_app$ag'(X0,def_20(X1,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_585])]) ).
tff(f3139,plain,
! [X2: 'B_bool_fun$',X3: 'B_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
( sP33(X3,X2,X0,X1)
| ~ 'fun_app$ag'(X0,def_20(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1870]) ).
tff(f7306,plain,
spl249_584,
inference(avatar_split_clause,[],[f3132,f7304]) ).
tff(f7304,plain,
( spl249_584
<=> ! [X0: 'Bool_bool_fun$',X3: 'C_option$',X2: 'C_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,def_22(X1,X2,X3))
| ~ sP32(X3,X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_584])]) ).
tff(f3132,plain,
! [X2: 'C_bool_fun$',X3: 'C_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,def_22(X1,X2,X3))
| ~ sP32(X3,X2,X0,X1) ),
inference(cnf_transformation,[],[f1866]) ).
tff(f1866,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] :
( ( 'fun_app$ag'(X0,def_22(X1,X2,X3))
| ~ sP32(X3,X2,X0,X1) )
& ( sP32(X3,X2,X0,X1)
| ~ 'fun_app$ag'(X0,def_22(X1,X2,X3)) ) ),
inference(nnf_transformation,[],[f1164]) ).
tff(f1164,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] :
( 'fun_app$ag'(X0,def_22(X1,X2,X3))
<=> sP32(X3,X2,X0,X1) ),
inference(definition_folding,[],[f1083,f1163]) ).
tff(f1083,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] :
( 'fun_app$ag'(X0,def_22(X1,X2,X3))
<=> ( ( 'fun_app$ag'(X0,def_23(X2,X3))
| ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) != X3 ) )
& ( 'fun_app$ag'(X0,X1)
| ( 'none$' != X3 ) ) ) ),
inference(ennf_transformation,[],[f187]) ).
tff(f187,axiom,
! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] :
( 'fun_app$ag'(X0,def_22(X1,X2,X3))
<=> ( ( ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X3)) = X3 )
=> 'fun_app$ag'(X0,def_23(X2,X3)) )
& ( ( 'none$' = X3 )
=> 'fun_app$ag'(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom185) ).
tff(f7302,plain,
spl249_583,
inference(avatar_split_clause,[],[f3131,f7300]) ).
tff(f7300,plain,
( spl249_583
<=> ! [X0: 'Bool_bool_fun$',X3: 'C_option$',X2: 'C_bool_fun$',X1: tlbool] :
( sP32(X3,X2,X0,X1)
| ~ 'fun_app$ag'(X0,def_22(X1,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_583])]) ).
tff(f3131,plain,
! [X2: 'C_bool_fun$',X3: 'C_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
( sP32(X3,X2,X0,X1)
| ~ 'fun_app$ag'(X0,def_22(X1,X2,X3)) ),
inference(cnf_transformation,[],[f1866]) ).
tff(f7298,plain,
spl249_582,
inference(avatar_split_clause,[],[f2926,f7296]) ).
tff(f2926,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ( tltrue = def_16(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1694]) ).
tff(f1694,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( ( ( tltrue = def_16(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) )
& ( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_16(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f842]) ).
tff(f842,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( ( tltrue = def_16(X0,X1,X2) )
<=> 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(rectify,[],[f727]) ).
tff(f727,axiom,
! [X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( ( tltrue = def_16(X1,X2,X3) )
<=> 'fun_app$a'('case_option$e'(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_726) ).
tff(f7294,plain,
spl249_581,
inference(avatar_split_clause,[],[f2925,f7292]) ).
tff(f7292,plain,
( spl249_581
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_16(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_581])]) ).
tff(f2925,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_16(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f1694]) ).
tff(f7290,plain,
spl249_580,
inference(avatar_split_clause,[],[f2924,f7288]) ).
tff(f2924,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ( tltrue = def_20(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1693]) ).
tff(f1693,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( ( ( tltrue = def_20(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) )
& ( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_20(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f841]) ).
tff(f841,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( ( tltrue = def_20(X0,X1,X2) )
<=> 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(rectify,[],[f731]) ).
tff(f731,axiom,
! [X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( ( tltrue = def_20(X1,X2,X3) )
<=> 'fun_app$a'('case_option$e'(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_730) ).
tff(f7286,plain,
spl249_579,
inference(avatar_split_clause,[],[f2923,f7284]) ).
tff(f7284,plain,
( spl249_579
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_20(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_579])]) ).
tff(f2923,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_20(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f1693]) ).
tff(f7282,plain,
spl249_578,
inference(avatar_split_clause,[],[f2922,f7280]) ).
tff(f2922,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ( tltrue = def_12(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1692]) ).
tff(f1692,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( ( ( tltrue = def_12(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) )
& ( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_12(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f840]) ).
tff(f840,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( ( tltrue = def_12(X0,X1,X2) )
<=> 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(rectify,[],[f723]) ).
tff(f723,axiom,
! [X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( ( tltrue = def_12(X1,X2,X3) )
<=> 'fun_app$a'('case_option$e'(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_722) ).
tff(f7278,plain,
( ~ spl249_577
| spl249_100
| ~ spl249_437 ),
inference(avatar_split_clause,[],[f6316,f5772,f4045,f7275]) ).
tff(f7275,plain,
( spl249_577
<=> sP25('none$a','uug$',tlfalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_577])]) ).
tff(f4045,plain,
( spl249_100
<=> 'fun_app$a'('case_option$e'(tlfalse,'uug$'),'none$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_100])]) ).
tff(f6316,plain,
( ~ sP25('none$a','uug$',tlfalse)
| spl249_100
| ~ spl249_437 ),
inference(resolution,[],[f5773,f4047]) ).
tff(f4047,plain,
( ~ 'fun_app$a'('case_option$e'(tlfalse,'uug$'),'none$a')
| spl249_100 ),
inference(avatar_component_clause,[],[f4045]) ).
tff(f7273,plain,
spl249_576,
inference(avatar_split_clause,[],[f2921,f7271]) ).
tff(f7271,plain,
( spl249_576
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_12(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_576])]) ).
tff(f2921,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_12(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f1692]) ).
tff(f7269,plain,
spl249_575,
inference(avatar_split_clause,[],[f2920,f7267]) ).
tff(f2920,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ( tltrue = def_6(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1691]) ).
tff(f1691,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( ( ( tltrue = def_6(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) )
& ( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_6(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f839]) ).
tff(f839,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( ( tltrue = def_6(X0,X1,X2) )
<=> 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(rectify,[],[f717]) ).
tff(f717,axiom,
! [X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( ( tltrue = def_6(X1,X2,X3) )
<=> 'fun_app$a'('case_option$e'(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_716) ).
tff(f7265,plain,
spl249_574,
inference(avatar_split_clause,[],[f2919,f7263]) ).
tff(f7263,plain,
( spl249_574
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_6(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_574])]) ).
tff(f2919,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_6(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f1691]) ).
tff(f7261,plain,
spl249_573,
inference(avatar_split_clause,[],[f2918,f7259]) ).
tff(f2918,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( ( tltrue = def_11(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1690]) ).
tff(f1690,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( ( ( tltrue = def_11(X0,X1,X2) )
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) )
& ( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_11(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f838]) ).
tff(f838,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( ( tltrue = def_11(X0,X1,X2) )
<=> 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(rectify,[],[f722]) ).
tff(f722,axiom,
! [X1: tlbool,X2: 'B_bool_fun$',X3: 'B_option$'] :
( ( tltrue = def_11(X1,X2,X3) )
<=> 'fun_app$a'('case_option$e'(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_721) ).
tff(f7257,plain,
spl249_572,
inference(avatar_split_clause,[],[f2917,f7255]) ).
tff(f7255,plain,
( spl249_572
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_11(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_572])]) ).
tff(f2917,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ( tltrue != def_11(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f1690]) ).
tff(f7253,plain,
spl249_571,
inference(avatar_split_clause,[],[f2916,f7251]) ).
tff(f2916,plain,
! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ( tltrue = def_8(X0,X1,X2) )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1689]) ).
tff(f1689,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( ( ( tltrue = def_8(X0,X1,X2) )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) )
& ( 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue != def_8(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f837]) ).
tff(f837,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( ( tltrue = def_8(X0,X1,X2) )
<=> 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(rectify,[],[f719]) ).
tff(f719,axiom,
! [X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] :
( ( tltrue = def_8(X1,X2,X3) )
<=> 'fun_app$'('case_option$f'(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_718) ).
tff(f7249,plain,
spl249_570,
inference(avatar_split_clause,[],[f2915,f7247]) ).
tff(f7247,plain,
( spl249_570
<=> ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue != def_8(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_570])]) ).
tff(f2915,plain,
! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue != def_8(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f1689]) ).
tff(f7245,plain,
spl249_569,
inference(avatar_split_clause,[],[f2914,f7243]) ).
tff(f2914,plain,
! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ( tltrue = def_22(X0,X1,X2) )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1688]) ).
tff(f1688,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( ( ( tltrue = def_22(X0,X1,X2) )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) )
& ( 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue != def_22(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f836]) ).
tff(f836,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( ( tltrue = def_22(X0,X1,X2) )
<=> 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(rectify,[],[f733]) ).
tff(f733,axiom,
! [X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] :
( ( tltrue = def_22(X1,X2,X3) )
<=> 'fun_app$'('case_option$f'(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_732) ).
tff(f7241,plain,
spl249_568,
inference(avatar_split_clause,[],[f2913,f7239]) ).
tff(f7239,plain,
( spl249_568
<=> ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue != def_22(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_568])]) ).
tff(f2913,plain,
! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue != def_22(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f1688]) ).
tff(f7237,plain,
spl249_567,
inference(avatar_split_clause,[],[f2912,f7235]) ).
tff(f2912,plain,
! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ( tltrue = def_13(X0,X1,X2) )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1687]) ).
tff(f1687,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( ( ( tltrue = def_13(X0,X1,X2) )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) )
& ( 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue != def_13(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f835]) ).
tff(f835,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( ( tltrue = def_13(X0,X1,X2) )
<=> 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(rectify,[],[f724]) ).
tff(f724,axiom,
! [X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] :
( ( tltrue = def_13(X1,X2,X3) )
<=> 'fun_app$'('case_option$f'(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_723) ).
tff(f7233,plain,
spl249_566,
inference(avatar_split_clause,[],[f2911,f7231]) ).
tff(f7231,plain,
( spl249_566
<=> ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue != def_13(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_566])]) ).
tff(f2911,plain,
! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue != def_13(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f1687]) ).
tff(f7229,plain,
spl249_565,
inference(avatar_split_clause,[],[f2910,f7227]) ).
tff(f2910,plain,
! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( ( tltrue = def_18(X0,X1,X2) )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1686]) ).
tff(f1686,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( ( ( tltrue = def_18(X0,X1,X2) )
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) )
& ( 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue != def_18(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f834]) ).
tff(f834,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( ( tltrue = def_18(X0,X1,X2) )
<=> 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(rectify,[],[f729]) ).
tff(f729,axiom,
! [X1: tlbool,X2: 'C_bool_fun$',X3: 'C_option$'] :
( ( tltrue = def_18(X1,X2,X3) )
<=> 'fun_app$'('case_option$f'(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_728) ).
tff(f7225,plain,
spl249_564,
inference(avatar_split_clause,[],[f2909,f7223]) ).
tff(f7223,plain,
( spl249_564
<=> ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue != def_18(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_564])]) ).
tff(f2909,plain,
! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),X2)
| ( tltrue != def_18(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f1686]) ).
tff(f7221,plain,
spl249_563,
inference(avatar_split_clause,[],[f2671,f7219]) ).
tff(f7219,plain,
( spl249_563
<=> ! [X2: 'B$',X0: 'B$',X1: 'B$'] :
( ( 'none$a' = 'fun_app$g'('fun_app$t'('update1$b'(X0),X1),X2) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_563])]) ).
tff(f2671,plain,
! [X2: 'B$',X0: 'B$',X1: 'B$'] :
( ( 'none$a' = 'fun_app$g'('fun_app$t'('update1$b'(X0),X1),X2) )
| ( X0 = X2 ) ),
inference(cnf_transformation,[],[f950]) ).
tff(f950,plain,
! [X0: 'B$',X1: 'B$',X2: 'B$'] :
( ( ( 'none$a' = 'fun_app$g'('fun_app$t'('update1$b'(X0),X1),X2) )
| ( X0 = X2 ) )
& ( ( 'fun_app$g'('some$',X1) = 'fun_app$g'('fun_app$t'('update1$b'(X0),X1),X2) )
| ( X0 != X2 ) ) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,axiom,
! [X0: 'B$',X1: 'B$',X2: 'B$'] :
( ( ( X0 != X2 )
=> ( 'none$a' = 'fun_app$g'('fun_app$t'('update1$b'(X0),X1),X2) ) )
& ( ( X0 = X2 )
=> ( 'fun_app$g'('some$',X1) = 'fun_app$g'('fun_app$t'('update1$b'(X0),X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom170) ).
tff(f7217,plain,
spl249_562,
inference(avatar_split_clause,[],[f2669,f7215]) ).
tff(f7215,plain,
( spl249_562
<=> ! [X2: 'C$',X0: 'C$',X1: 'C$'] :
( ( 'none$' = 'fun_app$j'('fun_app$v'('update1$a'(X0),X1),X2) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_562])]) ).
tff(f2669,plain,
! [X2: 'C$',X0: 'C$',X1: 'C$'] :
( ( 'none$' = 'fun_app$j'('fun_app$v'('update1$a'(X0),X1),X2) )
| ( X0 = X2 ) ),
inference(cnf_transformation,[],[f949]) ).
tff(f949,plain,
! [X0: 'C$',X1: 'C$',X2: 'C$'] :
( ( ( 'none$' = 'fun_app$j'('fun_app$v'('update1$a'(X0),X1),X2) )
| ( X0 = X2 ) )
& ( ( 'fun_app$j'('some$a',X1) = 'fun_app$j'('fun_app$v'('update1$a'(X0),X1),X2) )
| ( X0 != X2 ) ) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,axiom,
! [X0: 'C$',X1: 'C$',X2: 'C$'] :
( ( ( X0 != X2 )
=> ( 'none$' = 'fun_app$j'('fun_app$v'('update1$a'(X0),X1),X2) ) )
& ( ( X0 = X2 )
=> ( 'fun_app$j'('some$a',X1) = 'fun_app$j'('fun_app$v'('update1$a'(X0),X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom169) ).
tff(f7213,plain,
spl249_561,
inference(avatar_split_clause,[],[f2588,f7211]) ).
tff(f7211,plain,
( spl249_561
<=> ! [X2: 'B$',X0: 'Bool_b_option_fun$',X1: 'B_bool_fun$'] : ( 'fun_app$g'('uun$'(X0,X1),X2) = 'fun_app$af'(X0,def_3(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_561])]) ).
tff(f2588,plain,
! [X2: 'B$',X0: 'Bool_b_option_fun$',X1: 'B_bool_fun$'] : ( 'fun_app$g'('uun$'(X0,X1),X2) = 'fun_app$af'(X0,def_3(X1,X2)) ),
inference(cnf_transformation,[],[f44]) ).
tff(f44,axiom,
! [X0: 'Bool_b_option_fun$',X1: 'B_bool_fun$',X2: 'B$'] : ( 'fun_app$g'('uun$'(X0,X1),X2) = 'fun_app$af'(X0,def_3(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom43) ).
tff(f7209,plain,
spl249_560,
inference(avatar_split_clause,[],[f2586,f7207]) ).
tff(f7207,plain,
( spl249_560
<=> ! [X2: 'C$',X0: 'Bool_c_option_fun$',X1: 'C_bool_fun$'] : ( 'fun_app$j'('uuo$'(X0,X1),X2) = 'fun_app$ae'(X0,def_1(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_560])]) ).
tff(f2586,plain,
! [X2: 'C$',X0: 'Bool_c_option_fun$',X1: 'C_bool_fun$'] : ( 'fun_app$j'('uuo$'(X0,X1),X2) = 'fun_app$ae'(X0,def_1(X1,X2)) ),
inference(cnf_transformation,[],[f42]) ).
tff(f42,axiom,
! [X0: 'Bool_c_option_fun$',X1: 'C_bool_fun$',X2: 'C$'] : ( 'fun_app$j'('uuo$'(X0,X1),X2) = 'fun_app$ae'(X0,def_1(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom41) ).
tff(f7205,plain,
spl249_559,
inference(avatar_split_clause,[],[f2584,f7203]) ).
tff(f2584,plain,
! [X2: 'B$',X0: 'B_option_b_fun$',X1: 'B_b_option_fun$'] : ( 'fun_app$h'('comp$m'(X0,X1),X2) = 'fun_app$al'(X0,'fun_app$g'(X1,X2)) ),
inference(cnf_transformation,[],[f613]) ).
tff(f613,axiom,
! [X0: 'B_option_b_fun$',X1: 'B_b_option_fun$',X2: 'B$'] : ( 'fun_app$h'('comp$m'(X0,X1),X2) = 'fun_app$al'(X0,'fun_app$g'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom611) ).
tff(f7201,plain,
spl249_558,
inference(avatar_split_clause,[],[f2576,f7199]) ).
tff(f2576,plain,
! [X2: 'C$',X0: 'C_option_c_fun$',X1: 'C_c_option_fun$'] : ( 'fun_app$k'('comp$n'(X0,X1),X2) = 'fun_app$ak'(X0,'fun_app$j'(X1,X2)) ),
inference(cnf_transformation,[],[f564]) ).
tff(f564,axiom,
! [X0: 'C_option_c_fun$',X1: 'C_c_option_fun$',X2: 'C$'] : ( 'fun_app$k'('comp$n'(X0,X1),X2) = 'fun_app$ak'(X0,'fun_app$j'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom562) ).
tff(f7197,plain,
spl249_557,
inference(avatar_split_clause,[],[f2574,f7195]) ).
tff(f7195,plain,
( spl249_557
<=> ! [X2: 'A$',X0: 'A_b_option_fun$',X1: 'A_a_fun$'] : ( 'fun_app$f'('comp$g'(X0,X1),X2) = 'fun_app$f'(X0,'fun_app$r'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_557])]) ).
tff(f2574,plain,
! [X2: 'A$',X0: 'A_b_option_fun$',X1: 'A_a_fun$'] : ( 'fun_app$f'('comp$g'(X0,X1),X2) = 'fun_app$f'(X0,'fun_app$r'(X1,X2)) ),
inference(cnf_transformation,[],[f561]) ).
tff(f561,axiom,
! [X0: 'A_b_option_fun$',X1: 'A_a_fun$',X2: 'A$'] : ( 'fun_app$f'('comp$g'(X0,X1),X2) = 'fun_app$f'(X0,'fun_app$r'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom559) ).
tff(f7193,plain,
( spl249_556
| ~ spl249_23
| ~ spl249_435 ),
inference(avatar_split_clause,[],[f6298,f5764,f3704,f7191]) ).
tff(f7191,plain,
( spl249_556
<=> ! [X0: 'C_b_option_fun$',X1: 'C_option$'] : ~ sP24(X0,'uwf$',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_556])]) ).
tff(f6298,plain,
( ! [X0: 'C_b_option_fun$',X1: 'C_option$'] : ~ sP24(X0,'uwf$',X1)
| ~ spl249_23
| ~ spl249_435 ),
inference(resolution,[],[f5765,f3705]) ).
tff(f7189,plain,
spl249_555,
inference(avatar_split_clause,[],[f2573,f7187]) ).
tff(f7187,plain,
( spl249_555
<=> ! [X2: 'A$',X0: 'A_b_b_option_fun_fun$',X1: 'B$'] : ( 'fun_app$f'('uuv$'(X0,X1),X2) = 'fun_app$g'('fun_app$x'(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_555])]) ).
tff(f2573,plain,
! [X2: 'A$',X0: 'A_b_b_option_fun_fun$',X1: 'B$'] : ( 'fun_app$f'('uuv$'(X0,X1),X2) = 'fun_app$g'('fun_app$x'(X0,X2),X1) ),
inference(cnf_transformation,[],[f26]) ).
tff(f26,axiom,
! [X0: 'A_b_b_option_fun_fun$',X1: 'B$',X2: 'A$'] : ( 'fun_app$f'('uuv$'(X0,X1),X2) = 'fun_app$g'('fun_app$x'(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom25) ).
tff(f7185,plain,
spl249_554,
inference(avatar_split_clause,[],[f2572,f7183]) ).
tff(f7183,plain,
( spl249_554
<=> ! [X2: 'A$',X0: 'B_option_b_option_fun$',X1: 'A_b_option_fun$'] : ( 'fun_app$f'('uui$'(X0,X1),X2) = 'fun_app$s'(X0,'fun_app$f'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_554])]) ).
tff(f2572,plain,
! [X2: 'A$',X0: 'B_option_b_option_fun$',X1: 'A_b_option_fun$'] : ( 'fun_app$f'('uui$'(X0,X1),X2) = 'fun_app$s'(X0,'fun_app$f'(X1,X2)) ),
inference(cnf_transformation,[],[f40]) ).
tff(f40,axiom,
! [X0: 'B_option_b_option_fun$',X1: 'A_b_option_fun$',X2: 'A$'] : ( 'fun_app$f'('uui$'(X0,X1),X2) = 'fun_app$s'(X0,'fun_app$f'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom39) ).
tff(f7181,plain,
spl249_553,
inference(avatar_split_clause,[],[f2570,f7179]) ).
tff(f7179,plain,
( spl249_553
<=> ! [X2: 'B_b_fun$',X0: 'B_option_b_fun$',X1: 'B_b_option_fun$'] : ( 'comp$m'(X0,'comp$c'(X1,X2)) = 'comp$ai'('comp$m'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_553])]) ).
tff(f2570,plain,
! [X2: 'B_b_fun$',X0: 'B_option_b_fun$',X1: 'B_b_option_fun$'] : ( 'comp$m'(X0,'comp$c'(X1,X2)) = 'comp$ai'('comp$m'(X0,X1),X2) ),
inference(cnf_transformation,[],[f605]) ).
tff(f605,axiom,
! [X0: 'B_option_b_fun$',X1: 'B_b_option_fun$',X2: 'B_b_fun$'] : ( 'comp$m'(X0,'comp$c'(X1,X2)) = 'comp$ai'('comp$m'(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom603) ).
tff(f7177,plain,
spl249_552,
inference(avatar_split_clause,[],[f2568,f7175]) ).
tff(f2568,plain,
! [X2: 'B_b_option_fun$',X0: 'B_c_option_fun$',X1: 'B_option_b_fun$'] : ( 'comp$f'(X0,'comp$m'(X1,X2)) = 'comp$av'('comp$bg'(X0,X1),X2) ),
inference(cnf_transformation,[],[f609]) ).
tff(f609,axiom,
! [X0: 'B_c_option_fun$',X1: 'B_option_b_fun$',X2: 'B_b_option_fun$'] : ( 'comp$f'(X0,'comp$m'(X1,X2)) = 'comp$av'('comp$bg'(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom607) ).
tff(f7173,plain,
spl249_551,
inference(avatar_split_clause,[],[f2566,f7171]) ).
tff(f7171,plain,
( spl249_551
<=> ! [X2: 'B_b_fun$',X0: 'B_c_option_fun$',X1: 'B_b_fun$'] : ( 'comp$f'(X0,'comp$ai'(X1,X2)) = 'comp$f'('comp$f'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_551])]) ).
tff(f2566,plain,
! [X2: 'B_b_fun$',X0: 'B_c_option_fun$',X1: 'B_b_fun$'] : ( 'comp$f'(X0,'comp$ai'(X1,X2)) = 'comp$f'('comp$f'(X0,X1),X2) ),
inference(cnf_transformation,[],[f618]) ).
tff(f618,axiom,
! [X0: 'B_c_option_fun$',X1: 'B_b_fun$',X2: 'B_b_fun$'] : ( 'comp$f'(X0,'comp$ai'(X1,X2)) = 'comp$f'('comp$f'(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom616) ).
tff(f7169,plain,
spl249_550,
inference(avatar_split_clause,[],[f2564,f7167]) ).
tff(f7167,plain,
( spl249_550
<=> ! [X2: 'A_a_fun$',X0: 'A_b_option_fun$',X1: 'A_a_fun$'] : ( 'comp$g'(X0,'comp$be'(X1,X2)) = 'comp$g'('comp$g'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_550])]) ).
tff(f2564,plain,
! [X2: 'A_a_fun$',X0: 'A_b_option_fun$',X1: 'A_a_fun$'] : ( 'comp$g'(X0,'comp$be'(X1,X2)) = 'comp$g'('comp$g'(X0,X1),X2) ),
inference(cnf_transformation,[],[f617]) ).
tff(f617,axiom,
! [X0: 'A_b_option_fun$',X1: 'A_a_fun$',X2: 'A_a_fun$'] : ( 'comp$g'(X0,'comp$be'(X1,X2)) = 'comp$g'('comp$g'(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom615) ).
tff(f7165,plain,
spl249_549,
inference(avatar_split_clause,[],[f2562,f7163]) ).
tff(f7163,plain,
( spl249_549
<=> ! [X2: 'C_c_fun$',X0: 'C_option_c_fun$',X1: 'C_c_option_fun$'] : ( 'comp$n'(X0,'comp$'(X1,X2)) = 'comp$bc'('comp$n'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_549])]) ).
tff(f2562,plain,
! [X2: 'C_c_fun$',X0: 'C_option_c_fun$',X1: 'C_c_option_fun$'] : ( 'comp$n'(X0,'comp$'(X1,X2)) = 'comp$bc'('comp$n'(X0,X1),X2) ),
inference(cnf_transformation,[],[f616]) ).
tff(f616,axiom,
! [X0: 'C_option_c_fun$',X1: 'C_c_option_fun$',X2: 'C_c_fun$'] : ( 'comp$n'(X0,'comp$'(X1,X2)) = 'comp$bc'('comp$n'(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom614) ).
tff(f7161,plain,
spl249_548,
inference(avatar_split_clause,[],[f2559,f7159]) ).
tff(f7159,plain,
( spl249_548
<=> ! [X2: 'B_b_option_fun$',X0: 'B_b_fun$',X1: 'B_option_b_fun$'] : ( 'comp$ai'(X0,'comp$m'(X1,X2)) = 'comp$m'('comp$bb'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_548])]) ).
tff(f2559,plain,
! [X2: 'B_b_option_fun$',X0: 'B_b_fun$',X1: 'B_option_b_fun$'] : ( 'comp$ai'(X0,'comp$m'(X1,X2)) = 'comp$m'('comp$bb'(X0,X1),X2) ),
inference(cnf_transformation,[],[f619]) ).
tff(f619,axiom,
! [X0: 'B_b_fun$',X1: 'B_option_b_fun$',X2: 'B_b_option_fun$'] : ( 'comp$ai'(X0,'comp$m'(X1,X2)) = 'comp$m'('comp$bb'(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom617) ).
tff(f7157,plain,
spl249_547,
inference(avatar_split_clause,[],[f2557,f7155]) ).
tff(f7155,plain,
( spl249_547
<=> ! [X2: 'B_b_fun$',X0: 'C_option_c_option_fun$',X1: 'B_c_option_fun$'] : ( 'comp$ar'(X0,'comp$f'(X1,X2)) = 'comp$f'('comp$ar'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_547])]) ).
tff(f2557,plain,
! [X2: 'B_b_fun$',X0: 'C_option_c_option_fun$',X1: 'B_c_option_fun$'] : ( 'comp$ar'(X0,'comp$f'(X1,X2)) = 'comp$f'('comp$ar'(X0,X1),X2) ),
inference(cnf_transformation,[],[f623]) ).
tff(f623,axiom,
! [X0: 'C_option_c_option_fun$',X1: 'B_c_option_fun$',X2: 'B_b_fun$'] : ( 'comp$ar'(X0,'comp$f'(X1,X2)) = 'comp$f'('comp$ar'(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom621) ).
tff(f7153,plain,
spl249_546,
inference(avatar_split_clause,[],[f2555,f7151]) ).
tff(f7151,plain,
( spl249_546
<=> ! [X2: 'A_a_fun$',X0: 'B_option_b_option_fun$',X1: 'A_b_option_fun$'] : ( 'comp$bf'(X0,'comp$g'(X1,X2)) = 'comp$g'('comp$bf'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_546])]) ).
tff(f2555,plain,
! [X2: 'A_a_fun$',X0: 'B_option_b_option_fun$',X1: 'A_b_option_fun$'] : ( 'comp$bf'(X0,'comp$g'(X1,X2)) = 'comp$g'('comp$bf'(X0,X1),X2) ),
inference(cnf_transformation,[],[f622]) ).
tff(f622,axiom,
! [X0: 'B_option_b_option_fun$',X1: 'A_b_option_fun$',X2: 'A_a_fun$'] : ( 'comp$bf'(X0,'comp$g'(X1,X2)) = 'comp$g'('comp$bf'(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom620) ).
tff(f7149,plain,
spl249_545,
inference(avatar_split_clause,[],[f2553,f7147]) ).
tff(f7147,plain,
( spl249_545
<=> ! [X2: 'C_c_option_fun$',X0: 'C_c_fun$',X1: 'C_option_c_fun$'] : ( 'comp$bc'(X0,'comp$n'(X1,X2)) = 'comp$n'('comp$bd'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_545])]) ).
tff(f2553,plain,
! [X2: 'C_c_option_fun$',X0: 'C_c_fun$',X1: 'C_option_c_fun$'] : ( 'comp$bc'(X0,'comp$n'(X1,X2)) = 'comp$n'('comp$bd'(X0,X1),X2) ),
inference(cnf_transformation,[],[f620]) ).
tff(f620,axiom,
! [X0: 'C_c_fun$',X1: 'C_option_c_fun$',X2: 'C_c_option_fun$'] : ( 'comp$bc'(X0,'comp$n'(X1,X2)) = 'comp$n'('comp$bd'(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom618) ).
tff(f7145,plain,
spl249_544,
inference(avatar_split_clause,[],[f2552,f7143]) ).
tff(f7143,plain,
( spl249_544
<=> ! [X2: 'B$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ( 'fun_app$g'(X1,X2) = 'fun_app$s'('case_option$'(X0,X1),'fun_app$g'('some$',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_544])]) ).
tff(f2552,plain,
! [X2: 'B$',X0: 'B_option$',X1: 'B_b_option_fun$'] : ( 'fun_app$g'(X1,X2) = 'fun_app$s'('case_option$'(X0,X1),'fun_app$g'('some$',X2)) ),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
! [X0: 'B_option$',X1: 'B_b_option_fun$',X2: 'B$'] : ( 'fun_app$g'(X1,X2) = 'fun_app$s'('case_option$'(X0,X1),'fun_app$g'('some$',X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom100) ).
tff(f7141,plain,
spl249_543,
inference(avatar_split_clause,[],[f2551,f7139]) ).
tff(f7139,plain,
( spl249_543
<=> ! [X2: 'C$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ( 'fun_app$j'(X1,X2) = 'fun_app$u'('case_option$a'(X0,X1),'fun_app$j'('some$a',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_543])]) ).
tff(f2551,plain,
! [X2: 'C$',X0: 'C_option$',X1: 'C_c_option_fun$'] : ( 'fun_app$j'(X1,X2) = 'fun_app$u'('case_option$a'(X0,X1),'fun_app$j'('some$a',X2)) ),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
! [X0: 'C_option$',X1: 'C_c_option_fun$',X2: 'C$'] : ( 'fun_app$j'(X1,X2) = 'fun_app$u'('case_option$a'(X0,X1),'fun_app$j'('some$a',X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom101) ).
tff(f7137,plain,
spl249_542,
inference(avatar_split_clause,[],[f2549,f7135]) ).
tff(f7135,plain,
( spl249_542
<=> ! [X2: 'A$',X0: 'B_option$',X1: 'A_b_option_fun$'] : ( 'fun_app$f'(X1,X2) = 'fun_app$av'('case_option$d'(X0,X1),'fun_app$q'('some$b',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_542])]) ).
tff(f2549,plain,
! [X2: 'A$',X0: 'B_option$',X1: 'A_b_option_fun$'] : ( 'fun_app$f'(X1,X2) = 'fun_app$av'('case_option$d'(X0,X1),'fun_app$q'('some$b',X2)) ),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
! [X0: 'B_option$',X1: 'A_b_option_fun$',X2: 'A$'] : ( 'fun_app$f'(X1,X2) = 'fun_app$av'('case_option$d'(X0,X1),'fun_app$q'('some$b',X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom103) ).
tff(f7133,plain,
spl249_541,
inference(avatar_split_clause,[],[f2334,f7131]) ).
tff(f7131,plain,
( spl249_541
<=> ! [X0: 'B_option_option$',X1: 'B_option_b_option_fun$'] :
( ( 'map_option$i'(X1,X0) = X0 )
| 'member$a'(sK118(X0,X1),'set_option$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_541])]) ).
tff(f2334,plain,
! [X0: 'B_option_option$',X1: 'B_option_b_option_fun$'] :
( ( 'map_option$i'(X1,X0) = X0 )
| 'member$a'(sK118(X0,X1),'set_option$'(X0)) ),
inference(cnf_transformation,[],[f1407]) ).
tff(f7129,plain,
spl249_540,
inference(avatar_split_clause,[],[f2332,f7127]) ).
tff(f7127,plain,
( spl249_540
<=> ! [X0: 'C_option_option$',X1: 'C_option_c_option_fun$'] :
( ( 'map_option$j'(X1,X0) = X0 )
| 'member$'(sK117(X0,X1),'set_option$a'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_540])]) ).
tff(f2332,plain,
! [X0: 'C_option_option$',X1: 'C_option_c_option_fun$'] :
( ( 'map_option$j'(X1,X0) = X0 )
| 'member$'(sK117(X0,X1),'set_option$a'(X0)) ),
inference(cnf_transformation,[],[f1405]) ).
tff(f7125,plain,
spl249_539,
inference(avatar_split_clause,[],[f2266,f7123]) ).
tff(f7123,plain,
( spl249_539
<=> ! [X0: 'B$',X1: 'B_option_set$'] : ( 'these$a'('insert$b'('fun_app$g'('some$',X0),X1)) = 'insert$'(X0,'these$a'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_539])]) ).
tff(f2266,plain,
! [X0: 'B$',X1: 'B_option_set$'] : ( 'these$a'('insert$b'('fun_app$g'('some$',X0),X1)) = 'insert$'(X0,'these$a'(X1)) ),
inference(cnf_transformation,[],[f697]) ).
tff(f697,axiom,
! [X0: 'B$',X1: 'B_option_set$'] : ( 'these$a'('insert$b'('fun_app$g'('some$',X0),X1)) = 'insert$'(X0,'these$a'(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom695) ).
tff(f7121,plain,
spl249_538,
inference(avatar_split_clause,[],[f2265,f7119]) ).
tff(f7119,plain,
( spl249_538
<=> ! [X0: 'C$',X1: 'C_option_set$'] : ( 'these$'('insert$c'('fun_app$j'('some$a',X0),X1)) = 'insert$a'(X0,'these$'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_538])]) ).
tff(f2265,plain,
! [X0: 'C$',X1: 'C_option_set$'] : ( 'these$'('insert$c'('fun_app$j'('some$a',X0),X1)) = 'insert$a'(X0,'these$'(X1)) ),
inference(cnf_transformation,[],[f696]) ).
tff(f696,axiom,
! [X0: 'C$',X1: 'C_option_set$'] : ( 'these$'('insert$c'('fun_app$j'('some$a',X0),X1)) = 'insert$a'(X0,'these$'(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom694) ).
tff(f7117,plain,
spl249_537,
inference(avatar_split_clause,[],[f2264,f7115]) ).
tff(f7115,plain,
( spl249_537
<=> ! [X0: 'B_b_fun$',X1: 'B_option$'] : ( 'fun_app$s'('map_option$b'(X0),X1) = 'fun_app$s'('case_option$'('none$a','uve$'(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_537])]) ).
tff(f2264,plain,
! [X0: 'B_b_fun$',X1: 'B_option$'] : ( 'fun_app$s'('map_option$b'(X0),X1) = 'fun_app$s'('case_option$'('none$a','uve$'(X0)),X1) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,axiom,
! [X0: 'B_b_fun$',X1: 'B_option$'] : ( 'fun_app$s'('map_option$b'(X0),X1) = 'fun_app$s'('case_option$'('none$a','uve$'(X0)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom192) ).
tff(f7113,plain,
spl249_536,
inference(avatar_split_clause,[],[f2263,f7111]) ).
tff(f7111,plain,
( spl249_536
<=> ! [X0: 'B_b_fun$',X1: 'B_option$'] : ( 'fun_app$s'('map_option$b'(X0),X1) = 'fun_app$ac'('bind$c'(X1),'comp$c'('some$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_536])]) ).
tff(f2263,plain,
! [X0: 'B_b_fun$',X1: 'B_option$'] : ( 'fun_app$s'('map_option$b'(X0),X1) = 'fun_app$ac'('bind$c'(X1),'comp$c'('some$',X0)) ),
inference(cnf_transformation,[],[f483]) ).
tff(f483,axiom,
! [X0: 'B_b_fun$',X1: 'B_option$'] : ( 'fun_app$s'('map_option$b'(X0),X1) = 'fun_app$ac'('bind$c'(X1),'comp$c'('some$',X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom481) ).
tff(f7109,plain,
spl249_535,
inference(avatar_split_clause,[],[f2262,f7107]) ).
tff(f7107,plain,
( spl249_535
<=> ! [X0: 'B_c_fun$',X1: 'B_option$'] : ( 'fun_app$an'('map_option$d'(X0),X1) = 'fun_app$an'('case_option$c'('none$','uvg$'(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_535])]) ).
tff(f2262,plain,
! [X0: 'B_c_fun$',X1: 'B_option$'] : ( 'fun_app$an'('map_option$d'(X0),X1) = 'fun_app$an'('case_option$c'('none$','uvg$'(X0)),X1) ),
inference(cnf_transformation,[],[f196]) ).
tff(f196,axiom,
! [X0: 'B_c_fun$',X1: 'B_option$'] : ( 'fun_app$an'('map_option$d'(X0),X1) = 'fun_app$an'('case_option$c'('none$','uvg$'(X0)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom194) ).
tff(f7105,plain,
spl249_534,
inference(avatar_split_clause,[],[f2261,f7103]) ).
tff(f7103,plain,
( spl249_534
<=> ! [X0: 'C_c_fun$',X1: 'C_option$'] : ( 'fun_app$u'('map_option$c'(X0),X1) = 'fun_app$u'('case_option$a'('none$','uvf$'(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_534])]) ).
tff(f2261,plain,
! [X0: 'C_c_fun$',X1: 'C_option$'] : ( 'fun_app$u'('map_option$c'(X0),X1) = 'fun_app$u'('case_option$a'('none$','uvf$'(X0)),X1) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,axiom,
! [X0: 'C_c_fun$',X1: 'C_option$'] : ( 'fun_app$u'('map_option$c'(X0),X1) = 'fun_app$u'('case_option$a'('none$','uvf$'(X0)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom193) ).
tff(f7101,plain,
spl249_533,
inference(avatar_split_clause,[],[f2260,f7099]) ).
tff(f7099,plain,
( spl249_533
<=> ! [X0: 'C_c_fun$',X1: 'C_option$'] : ( 'fun_app$u'('map_option$c'(X0),X1) = 'fun_app$ab'('bind$'(X1),'comp$'('some$a',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_533])]) ).
tff(f2260,plain,
! [X0: 'C_c_fun$',X1: 'C_option$'] : ( 'fun_app$u'('map_option$c'(X0),X1) = 'fun_app$ab'('bind$'(X1),'comp$'('some$a',X0)) ),
inference(cnf_transformation,[],[f480]) ).
tff(f480,axiom,
! [X0: 'C_c_fun$',X1: 'C_option$'] : ( 'fun_app$u'('map_option$c'(X0),X1) = 'fun_app$ab'('bind$'(X1),'comp$'('some$a',X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom478) ).
tff(f7097,plain,
spl249_532,
inference(avatar_split_clause,[],[f2259,f7095]) ).
tff(f7095,plain,
( spl249_532
<=> ! [X0: 'A_b_fun$',X1: 'A_option$'] : ( 'fun_app$av'('map_option$e'(X0),X1) = 'fun_app$av'('case_option$d'('none$a','uvh$'(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_532])]) ).
tff(f2259,plain,
! [X0: 'A_b_fun$',X1: 'A_option$'] : ( 'fun_app$av'('map_option$e'(X0),X1) = 'fun_app$av'('case_option$d'('none$a','uvh$'(X0)),X1) ),
inference(cnf_transformation,[],[f197]) ).
tff(f197,axiom,
! [X0: 'A_b_fun$',X1: 'A_option$'] : ( 'fun_app$av'('map_option$e'(X0),X1) = 'fun_app$av'('case_option$d'('none$a','uvh$'(X0)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom195) ).
tff(f7093,plain,
spl249_531,
inference(avatar_split_clause,[],[f2258,f7091]) ).
tff(f7091,plain,
( spl249_531
<=> ! [X0: 'A_a_fun$',X1: 'A_option$'] : ( 'fun_app$be'('map_option$a'(X0),X1) = 'fun_app$bp'('bind$h'(X1),'comp$e'('some$b',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_531])]) ).
tff(f2258,plain,
! [X0: 'A_a_fun$',X1: 'A_option$'] : ( 'fun_app$be'('map_option$a'(X0),X1) = 'fun_app$bp'('bind$h'(X1),'comp$e'('some$b',X0)) ),
inference(cnf_transformation,[],[f485]) ).
tff(f485,axiom,
! [X0: 'A_a_fun$',X1: 'A_option$'] : ( 'fun_app$be'('map_option$a'(X0),X1) = 'fun_app$bp'('bind$h'(X1),'comp$e'('some$b',X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom483) ).
tff(f6940,plain,
( spl249_530
| ~ spl249_478 ),
inference(avatar_split_clause,[],[f6765,f6457,f6938]) ).
tff(f6938,plain,
( spl249_530
<=> ! [X0: 'B_option$'] : ~ sP2(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_530])]) ).
tff(f6457,plain,
( spl249_478
<=> ! [X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$al'('the$',X0) != 'fun_app$al'('the$',X1) )
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_478])]) ).
tff(f6765,plain,
( ! [X0: 'B_option$'] : ~ sP2(X0,X0)
| ~ spl249_478 ),
inference(equality_resolution,[],[f6458]) ).
tff(f6458,plain,
( ! [X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$al'('the$',X0) != 'fun_app$al'('the$',X1) )
| ~ sP2(X0,X1) )
| ~ spl249_478 ),
inference(avatar_component_clause,[],[f6457]) ).
tff(f6857,plain,
( spl249_529
| ~ spl249_477 ),
inference(avatar_split_clause,[],[f6762,f6453,f6855]) ).
tff(f6855,plain,
( spl249_529
<=> ! [X0: 'C_option$'] : ~ sP1(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_529])]) ).
tff(f6453,plain,
( spl249_477
<=> ! [X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$ak'('the$a',X0) != 'fun_app$ak'('the$a',X1) )
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_477])]) ).
tff(f6762,plain,
( ! [X0: 'C_option$'] : ~ sP1(X0,X0)
| ~ spl249_477 ),
inference(equality_resolution,[],[f6454]) ).
tff(f6454,plain,
( ! [X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$ak'('the$a',X0) != 'fun_app$ak'('the$a',X1) )
| ~ sP1(X0,X1) )
| ~ spl249_477 ),
inference(avatar_component_clause,[],[f6453]) ).
tff(f6792,plain,
( spl249_528
| ~ spl249_476 ),
inference(avatar_split_clause,[],[f6759,f6449,f6790]) ).
tff(f6790,plain,
( spl249_528
<=> ! [X0: 'A_option$'] : ~ sP0(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_528])]) ).
tff(f6449,plain,
( spl249_476
<=> ! [X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$bf'('the$b',X0) != 'fun_app$bf'('the$b',X1) )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_476])]) ).
tff(f6759,plain,
( ! [X0: 'A_option$'] : ~ sP0(X0,X0)
| ~ spl249_476 ),
inference(equality_resolution,[],[f6450]) ).
tff(f6450,plain,
( ! [X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$bf'('the$b',X0) != 'fun_app$bf'('the$b',X1) )
| ~ sP0(X0,X1) )
| ~ spl249_476 ),
inference(avatar_component_clause,[],[f6449]) ).
tff(f6756,plain,
( spl249_527
| ~ spl249_23
| ~ spl249_433 ),
inference(avatar_split_clause,[],[f6275,f5756,f3704,f6754]) ).
tff(f6754,plain,
( spl249_527
<=> ! [X0: 'C_b_option_fun$',X1: 'C_option$'] : ~ sP23(X0,'uwf$',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_527])]) ).
tff(f6275,plain,
( ! [X0: 'C_b_option_fun$',X1: 'C_option$'] : ~ sP23(X0,'uwf$',X1)
| ~ spl249_23
| ~ spl249_433 ),
inference(resolution,[],[f5757,f3705]) ).
tff(f6726,plain,
( spl249_526
| ~ spl249_23
| ~ spl249_431 ),
inference(avatar_split_clause,[],[f6255,f5748,f3704,f6724]) ).
tff(f6724,plain,
( spl249_526
<=> ! [X0: 'A_b_option_fun$',X1: 'A_option$'] : ~ sP22(X0,'uwf$',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_526])]) ).
tff(f6255,plain,
( ! [X0: 'A_b_option_fun$',X1: 'A_option$'] : ~ sP22(X0,'uwf$',X1)
| ~ spl249_23
| ~ spl249_431 ),
inference(resolution,[],[f5749,f3705]) ).
tff(f6665,plain,
( spl249_525
| ~ spl249_23
| ~ spl249_429 ),
inference(avatar_split_clause,[],[f6234,f5740,f3704,f6663]) ).
tff(f6663,plain,
( spl249_525
<=> ! [X0: 'A_b_option_fun$',X1: 'A_option$'] : ~ sP21(X0,'uwf$',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_525])]) ).
tff(f6234,plain,
( ! [X0: 'A_b_option_fun$',X1: 'A_option$'] : ~ sP21(X0,'uwf$',X1)
| ~ spl249_23
| ~ spl249_429 ),
inference(resolution,[],[f5741,f3705]) ).
tff(f6644,plain,
spl249_524,
inference(avatar_split_clause,[],[f3437,f6642]) ).
tff(f6642,plain,
( spl249_524
<=> ! [X2: 'B$',X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,X2)
| ~ 'fun_app$c'(X1,sK159('fun_app$g'('some$',X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_524])]) ).
tff(f3437,plain,
! [X2: 'B$',X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,X2)
| ~ 'fun_app$c'(X1,sK159('fun_app$g'('some$',X2),X1)) ),
inference(equality_resolution,[],[f2770]) ).
tff(f2770,plain,
! [X2: 'B$',X0: 'B_option$',X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,X2)
| ( 'fun_app$g'('some$',X2) != X0 )
| ~ 'fun_app$c'(X1,sK159(X0,X1)) ),
inference(cnf_transformation,[],[f1584]) ).
tff(f6640,plain,
spl249_523,
inference(avatar_split_clause,[],[f3435,f6638]) ).
tff(f6638,plain,
( spl249_523
<=> ! [X2: 'C$',X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,X2)
| ~ 'fun_app$b'(X1,sK158('fun_app$j'('some$a',X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_523])]) ).
tff(f3435,plain,
! [X2: 'C$',X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,X2)
| ~ 'fun_app$b'(X1,sK158('fun_app$j'('some$a',X2),X1)) ),
inference(equality_resolution,[],[f2768]) ).
tff(f2768,plain,
! [X2: 'C$',X0: 'C_option$',X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,X2)
| ( 'fun_app$j'('some$a',X2) != X0 )
| ~ 'fun_app$b'(X1,sK158(X0,X1)) ),
inference(cnf_transformation,[],[f1582]) ).
tff(f6636,plain,
spl249_522,
inference(avatar_split_clause,[],[f3433,f6634]) ).
tff(f6634,plain,
( spl249_522
<=> ! [X2: 'A$',X1: 'A_bool_fun$'] :
( 'fun_app$z'(X1,X2)
| ~ 'fun_app$z'(X1,sK157('fun_app$q'('some$b',X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_522])]) ).
tff(f3433,plain,
! [X2: 'A$',X1: 'A_bool_fun$'] :
( 'fun_app$z'(X1,X2)
| ~ 'fun_app$z'(X1,sK157('fun_app$q'('some$b',X2),X1)) ),
inference(equality_resolution,[],[f2766]) ).
tff(f2766,plain,
! [X2: 'A$',X0: 'A_option$',X1: 'A_bool_fun$'] :
( 'fun_app$z'(X1,X2)
| ( 'fun_app$q'('some$b',X2) != X0 )
| ~ 'fun_app$z'(X1,sK157(X0,X1)) ),
inference(cnf_transformation,[],[f1580]) ).
tff(f6632,plain,
spl249_521,
inference(avatar_split_clause,[],[f3420,f6630]) ).
tff(f6630,plain,
( spl249_521
<=> ! [X2: 'B$',X1: 'B$'] : ( 'fun_app$g'('some$',X1) = 'fun_app$g'('fun_app$t'('update1$b'(X2),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_521])]) ).
tff(f3420,plain,
! [X2: 'B$',X1: 'B$'] : ( 'fun_app$g'('some$',X1) = 'fun_app$g'('fun_app$t'('update1$b'(X2),X1),X2) ),
inference(equality_resolution,[],[f2670]) ).
tff(f2670,plain,
! [X2: 'B$',X0: 'B$',X1: 'B$'] :
( ( 'fun_app$g'('some$',X1) = 'fun_app$g'('fun_app$t'('update1$b'(X0),X1),X2) )
| ( X0 != X2 ) ),
inference(cnf_transformation,[],[f950]) ).
tff(f6628,plain,
spl249_520,
inference(avatar_split_clause,[],[f3419,f6626]) ).
tff(f6626,plain,
( spl249_520
<=> ! [X2: 'C$',X1: 'C$'] : ( 'fun_app$j'('some$a',X1) = 'fun_app$j'('fun_app$v'('update1$a'(X2),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_520])]) ).
tff(f3419,plain,
! [X2: 'C$',X1: 'C$'] : ( 'fun_app$j'('some$a',X1) = 'fun_app$j'('fun_app$v'('update1$a'(X2),X1),X2) ),
inference(equality_resolution,[],[f2668]) ).
tff(f2668,plain,
! [X2: 'C$',X0: 'C$',X1: 'C$'] :
( ( 'fun_app$j'('some$a',X1) = 'fun_app$j'('fun_app$v'('update1$a'(X0),X1),X2) )
| ( X0 != X2 ) ),
inference(cnf_transformation,[],[f949]) ).
tff(f6624,plain,
spl249_519,
inference(avatar_split_clause,[],[f3254,f6622]) ).
tff(f6622,plain,
( spl249_519
<=> ! [X2: 'B$',X0: 'C_option$',X1: 'B_b_fun$'] : ( 'bind$b'('fun_app$g'('some$',X2),'comp$f'('uwi$'(X0),X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_519])]) ).
tff(f3254,plain,
! [X2: 'B$',X0: 'C_option$',X1: 'B_b_fun$'] : ( 'bind$b'('fun_app$g'('some$',X2),'comp$f'('uwi$'(X0),X1)) = X0 ),
inference(definition_unfolding,[],[f2547,f2234]) ).
tff(f2547,plain,
! [X2: 'B$',X0: 'C_option$',X1: 'B_b_fun$'] : ( 'fun_app$n'('comp$f'('uwi$'(X0),X1),X2) = X0 ),
inference(cnf_transformation,[],[f646]) ).
tff(f646,axiom,
! [X0: 'C_option$',X1: 'B_b_fun$',X2: 'B$'] : ( 'fun_app$n'('comp$f'('uwi$'(X0),X1),X2) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom644) ).
tff(f6620,plain,
( ~ spl249_518
| spl249_99
| ~ spl249_427 ),
inference(avatar_split_clause,[],[f6206,f5730,f4040,f6617]) ).
tff(f6617,plain,
( spl249_518
<=> sP20('none$','uuf$',tlfalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_518])]) ).
tff(f4040,plain,
( spl249_99
<=> 'fun_app$'('case_option$f'(tlfalse,'uuf$'),'none$') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_99])]) ).
tff(f6206,plain,
( ~ sP20('none$','uuf$',tlfalse)
| spl249_99
| ~ spl249_427 ),
inference(resolution,[],[f5731,f4042]) ).
tff(f4042,plain,
( ~ 'fun_app$'('case_option$f'(tlfalse,'uuf$'),'none$')
| spl249_99 ),
inference(avatar_component_clause,[],[f4040]) ).
tff(f6615,plain,
spl249_517,
inference(avatar_split_clause,[],[f2996,f6613]) ).
tff(f6613,plain,
( spl249_517
<=> ! [X2: 'B$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$g'('some$',X2))
| ~ 'fun_app$c'(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_517])]) ).
tff(f2996,plain,
! [X2: 'B$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$g'('some$',X2))
| ~ 'fun_app$c'(X1,X2) ),
inference(cnf_transformation,[],[f1756]) ).
tff(f1756,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B$'] :
( ( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$g'('some$',X2))
| ~ 'fun_app$c'(X1,X2) )
& ( 'fun_app$c'(X1,X2)
| ~ 'fun_app$a'('case_option$e'(X0,X1),'fun_app$g'('some$',X2)) ) ),
inference(nnf_transformation,[],[f100]) ).
tff(f100,axiom,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B$'] :
( 'fun_app$a'('case_option$e'(X0,X1),'fun_app$g'('some$',X2))
<=> 'fun_app$c'(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom98) ).
tff(f6611,plain,
spl249_516,
inference(avatar_split_clause,[],[f2995,f6609]) ).
tff(f6609,plain,
( spl249_516
<=> ! [X2: 'B$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,X2)
| ~ 'fun_app$a'('case_option$e'(X0,X1),'fun_app$g'('some$',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_516])]) ).
tff(f2995,plain,
! [X2: 'B$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,X2)
| ~ 'fun_app$a'('case_option$e'(X0,X1),'fun_app$g'('some$',X2)) ),
inference(cnf_transformation,[],[f1756]) ).
tff(f6607,plain,
spl249_515,
inference(avatar_split_clause,[],[f2994,f6605]) ).
tff(f6605,plain,
( spl249_515
<=> ! [X2: 'C$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),'fun_app$j'('some$a',X2))
| ~ 'fun_app$b'(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_515])]) ).
tff(f2994,plain,
! [X2: 'C$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),'fun_app$j'('some$a',X2))
| ~ 'fun_app$b'(X1,X2) ),
inference(cnf_transformation,[],[f1755]) ).
tff(f1755,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C$'] :
( ( 'fun_app$'('case_option$f'(X0,X1),'fun_app$j'('some$a',X2))
| ~ 'fun_app$b'(X1,X2) )
& ( 'fun_app$b'(X1,X2)
| ~ 'fun_app$'('case_option$f'(X0,X1),'fun_app$j'('some$a',X2)) ) ),
inference(nnf_transformation,[],[f101]) ).
tff(f101,axiom,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C$'] :
( 'fun_app$'('case_option$f'(X0,X1),'fun_app$j'('some$a',X2))
<=> 'fun_app$b'(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom99) ).
tff(f6603,plain,
spl249_514,
inference(avatar_split_clause,[],[f2993,f6601]) ).
tff(f6601,plain,
( spl249_514
<=> ! [X2: 'C$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,X2)
| ~ 'fun_app$'('case_option$f'(X0,X1),'fun_app$j'('some$a',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_514])]) ).
tff(f2993,plain,
! [X2: 'C$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,X2)
| ~ 'fun_app$'('case_option$f'(X0,X1),'fun_app$j'('some$a',X2)) ),
inference(cnf_transformation,[],[f1755]) ).
tff(f6599,plain,
spl249_513,
inference(avatar_split_clause,[],[f2974,f6597]) ).
tff(f2974,plain,
! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
| ~ sP31(X2,X0,X1) ),
inference(cnf_transformation,[],[f1730]) ).
tff(f1730,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$'] :
( ( 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
| ~ sP31(X2,X0,X1) )
& ( sP31(X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2)) ) ),
inference(nnf_transformation,[],[f1162]) ).
tff(f1162,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$'] :
( 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
<=> sP31(X2,X0,X1) ),
inference(definition_folding,[],[f1018,f1161]) ).
tff(f1018,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$'] :
( 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
<=> ( ! [X3: 'B$'] :
( 'fun_app$a'(X0,'fun_app$g'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$a' != X1 ) ) ) ),
inference(ennf_transformation,[],[f479]) ).
tff(f479,axiom,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$'] :
( 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
<=> ~ ( ? [X3: 'B$'] :
( ~ 'fun_app$a'(X0,'fun_app$g'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$a' = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom477) ).
tff(f6595,plain,
spl249_512,
inference(avatar_split_clause,[],[f2973,f6593]) ).
tff(f2973,plain,
! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( sP31(X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2)) ),
inference(cnf_transformation,[],[f1730]) ).
tff(f6591,plain,
spl249_511,
inference(avatar_split_clause,[],[f2966,f6589]) ).
tff(f2966,plain,
! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
| ~ sP30(X2,X0,X1) ),
inference(cnf_transformation,[],[f1724]) ).
tff(f1724,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$'] :
( ( 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
| ~ sP30(X2,X0,X1) )
& ( sP30(X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2)) ) ),
inference(nnf_transformation,[],[f1160]) ).
tff(f1160,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$'] :
( 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
<=> sP30(X2,X0,X1) ),
inference(definition_folding,[],[f1017,f1159]) ).
tff(f1017,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$'] :
( 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
<=> ( ! [X3: 'B$'] :
( 'fun_app$a'(X0,'fun_app$g'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$a' != X1 ) ) ) ),
inference(ennf_transformation,[],[f354]) ).
tff(f354,axiom,
! [X0: 'B_option_bool_fun$',X1: 'B_option$',X2: 'B_b_option_fun$'] :
( 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2))
<=> ( ! [X3: 'B$'] :
( ( 'fun_app$g'('some$',X3) = X1 )
=> 'fun_app$a'(X0,'fun_app$g'(X2,X3)) )
& ( ( 'none$a' = X1 )
=> 'fun_app$a'(X0,'none$a') ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom352) ).
tff(f6587,plain,
spl249_510,
inference(avatar_split_clause,[],[f2965,f6585]) ).
tff(f2965,plain,
! [X2: 'B_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( sP30(X2,X0,X1)
| ~ 'fun_app$a'(X0,'fun_app$ac'('bind$c'(X1),X2)) ),
inference(cnf_transformation,[],[f1724]) ).
tff(f6583,plain,
spl249_509,
inference(avatar_split_clause,[],[f2958,f6581]) ).
tff(f2958,plain,
! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
| ~ sP29(X2,X0,X1) ),
inference(cnf_transformation,[],[f1718]) ).
tff(f1718,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$'] :
( ( 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
| ~ sP29(X2,X0,X1) )
& ( sP29(X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2)) ) ),
inference(nnf_transformation,[],[f1158]) ).
tff(f1158,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$'] :
( 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
<=> sP29(X2,X0,X1) ),
inference(definition_folding,[],[f1016,f1157]) ).
tff(f1016,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$'] :
( 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
<=> ( ! [X3: 'C$'] :
( 'fun_app$'(X0,'fun_app$j'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$' != X1 ) ) ) ),
inference(ennf_transformation,[],[f476]) ).
tff(f476,axiom,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$'] :
( 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
<=> ~ ( ? [X3: 'C$'] :
( ~ 'fun_app$'(X0,'fun_app$j'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$' = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom474) ).
tff(f6579,plain,
spl249_508,
inference(avatar_split_clause,[],[f2957,f6577]) ).
tff(f2957,plain,
! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( sP29(X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2)) ),
inference(cnf_transformation,[],[f1718]) ).
tff(f6575,plain,
( spl249_507
| ~ spl249_22
| ~ spl249_425 ),
inference(avatar_split_clause,[],[f6187,f5722,f3700,f6573]) ).
tff(f6573,plain,
( spl249_507
<=> ! [X0: 'B_c_option_fun$',X1: 'B_option$'] : ~ sP19(X0,'uwg$',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_507])]) ).
tff(f6187,plain,
( ! [X0: 'B_c_option_fun$',X1: 'B_option$'] : ~ sP19(X0,'uwg$',X1)
| ~ spl249_22
| ~ spl249_425 ),
inference(resolution,[],[f5723,f3701]) ).
tff(f6571,plain,
spl249_506,
inference(avatar_split_clause,[],[f2950,f6569]) ).
tff(f2950,plain,
! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
| ~ sP28(X2,X0,X1) ),
inference(cnf_transformation,[],[f1712]) ).
tff(f1712,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$'] :
( ( 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
| ~ sP28(X2,X0,X1) )
& ( sP28(X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2)) ) ),
inference(nnf_transformation,[],[f1156]) ).
tff(f1156,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$'] :
( 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
<=> sP28(X2,X0,X1) ),
inference(definition_folding,[],[f1015,f1155]) ).
tff(f1015,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$'] :
( 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
<=> ( ! [X3: 'C$'] :
( 'fun_app$'(X0,'fun_app$j'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$' != X1 ) ) ) ),
inference(ennf_transformation,[],[f351]) ).
tff(f351,axiom,
! [X0: 'C_option_bool_fun$',X1: 'C_option$',X2: 'C_c_option_fun$'] :
( 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2))
<=> ( ! [X3: 'C$'] :
( ( 'fun_app$j'('some$a',X3) = X1 )
=> 'fun_app$'(X0,'fun_app$j'(X2,X3)) )
& ( ( 'none$' = X1 )
=> 'fun_app$'(X0,'none$') ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom349) ).
tff(f6567,plain,
spl249_505,
inference(avatar_split_clause,[],[f2949,f6565]) ).
tff(f2949,plain,
! [X2: 'C_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( sP28(X2,X0,X1)
| ~ 'fun_app$'(X0,'fun_app$ab'('bind$'(X1),X2)) ),
inference(cnf_transformation,[],[f1712]) ).
tff(f6563,plain,
spl249_504,
inference(avatar_split_clause,[],[f2942,f6561]) ).
tff(f2942,plain,
! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
| ~ sP27(X2,X0,X1) ),
inference(cnf_transformation,[],[f1706]) ).
tff(f1706,plain,
! [X0: 'A_option_bool_fun$',X1: 'A_option$',X2: 'A_a_option_fun$'] :
( ( 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
| ~ sP27(X2,X0,X1) )
& ( sP27(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2)) ) ),
inference(nnf_transformation,[],[f1154]) ).
tff(f1154,plain,
! [X0: 'A_option_bool_fun$',X1: 'A_option$',X2: 'A_a_option_fun$'] :
( 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
<=> sP27(X2,X0,X1) ),
inference(definition_folding,[],[f1014,f1153]) ).
tff(f1014,plain,
! [X0: 'A_option_bool_fun$',X1: 'A_option$',X2: 'A_a_option_fun$'] :
( 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
<=> ( ! [X3: 'A$'] :
( 'fun_app$aw'(X0,'fun_app$q'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$b' != X1 ) ) ) ),
inference(ennf_transformation,[],[f475]) ).
tff(f475,axiom,
! [X0: 'A_option_bool_fun$',X1: 'A_option$',X2: 'A_a_option_fun$'] :
( 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
<=> ~ ( ? [X3: 'A$'] :
( ~ 'fun_app$aw'(X0,'fun_app$q'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$b' = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom473) ).
tff(f6559,plain,
spl249_503,
inference(avatar_split_clause,[],[f2941,f6557]) ).
tff(f2941,plain,
! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( sP27(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2)) ),
inference(cnf_transformation,[],[f1706]) ).
tff(f6555,plain,
spl249_502,
inference(avatar_split_clause,[],[f2934,f6553]) ).
tff(f2934,plain,
! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
| ~ sP26(X2,X0,X1) ),
inference(cnf_transformation,[],[f1700]) ).
tff(f1700,plain,
! [X0: 'A_option_bool_fun$',X1: 'A_option$',X2: 'A_a_option_fun$'] :
( ( 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
| ~ sP26(X2,X0,X1) )
& ( sP26(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2)) ) ),
inference(nnf_transformation,[],[f1152]) ).
tff(f1152,plain,
! [X0: 'A_option_bool_fun$',X1: 'A_option$',X2: 'A_a_option_fun$'] :
( 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
<=> sP26(X2,X0,X1) ),
inference(definition_folding,[],[f1013,f1151]) ).
tff(f1013,plain,
! [X0: 'A_option_bool_fun$',X1: 'A_option$',X2: 'A_a_option_fun$'] :
( 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
<=> ( ! [X3: 'A$'] :
( 'fun_app$aw'(X0,'fun_app$q'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$b' != X1 ) ) ) ),
inference(ennf_transformation,[],[f350]) ).
tff(f350,axiom,
! [X0: 'A_option_bool_fun$',X1: 'A_option$',X2: 'A_a_option_fun$'] :
( 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2))
<=> ( ! [X3: 'A$'] :
( ( 'fun_app$q'('some$b',X3) = X1 )
=> 'fun_app$aw'(X0,'fun_app$q'(X2,X3)) )
& ( ( 'none$b' = X1 )
=> 'fun_app$aw'(X0,'none$b') ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom348) ).
tff(f6551,plain,
spl249_501,
inference(avatar_split_clause,[],[f2933,f6549]) ).
tff(f2933,plain,
! [X2: 'A_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'A_option$'] :
( sP26(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'fun_app$bp'('bind$h'(X1),X2)) ),
inference(cnf_transformation,[],[f1700]) ).
tff(f6547,plain,
spl249_500,
inference(avatar_split_clause,[],[f2794,f6545]) ).
tff(f6545,plain,
( spl249_500
<=> ! [X2: 'B$',X0: 'B_option_bool_fun$',X1: 'B_b_option_fun$'] :
( 'fun_app$c'('uup$'(X0,X1),X2)
| ~ 'fun_app$a'(X0,'fun_app$g'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_500])]) ).
tff(f2794,plain,
! [X2: 'B$',X0: 'B_option_bool_fun$',X1: 'B_b_option_fun$'] :
( 'fun_app$c'('uup$'(X0,X1),X2)
| ~ 'fun_app$a'(X0,'fun_app$g'(X1,X2)) ),
inference(cnf_transformation,[],[f1604]) ).
tff(f1604,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_b_option_fun$',X2: 'B$'] :
( ( 'fun_app$c'('uup$'(X0,X1),X2)
| ~ 'fun_app$a'(X0,'fun_app$g'(X1,X2)) )
& ( 'fun_app$a'(X0,'fun_app$g'(X1,X2))
| ~ 'fun_app$c'('uup$'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f41]) ).
tff(f41,axiom,
! [X0: 'B_option_bool_fun$',X1: 'B_b_option_fun$',X2: 'B$'] :
( 'fun_app$c'('uup$'(X0,X1),X2)
<=> 'fun_app$a'(X0,'fun_app$g'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom40) ).
tff(f6543,plain,
spl249_499,
inference(avatar_split_clause,[],[f2793,f6541]) ).
tff(f6541,plain,
( spl249_499
<=> ! [X2: 'B$',X0: 'B_option_bool_fun$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'(X0,'fun_app$g'(X1,X2))
| ~ 'fun_app$c'('uup$'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_499])]) ).
tff(f2793,plain,
! [X2: 'B$',X0: 'B_option_bool_fun$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'(X0,'fun_app$g'(X1,X2))
| ~ 'fun_app$c'('uup$'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1604]) ).
tff(f6539,plain,
spl249_498,
inference(avatar_split_clause,[],[f2790,f6537]) ).
tff(f6537,plain,
( spl249_498
<=> ! [X2: 'B$',X0: 'Bool_bool_fun$',X1: 'B_bool_fun$'] :
( 'fun_app$c'('uuj$'(X0,X1),X2)
| ~ 'fun_app$ag'(X0,def_5(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_498])]) ).
tff(f2790,plain,
! [X2: 'B$',X0: 'Bool_bool_fun$',X1: 'B_bool_fun$'] :
( 'fun_app$c'('uuj$'(X0,X1),X2)
| ~ 'fun_app$ag'(X0,def_5(X1,X2)) ),
inference(cnf_transformation,[],[f1602]) ).
tff(f1602,plain,
! [X0: 'Bool_bool_fun$',X1: 'B_bool_fun$',X2: 'B$'] :
( ( 'fun_app$c'('uuj$'(X0,X1),X2)
| ~ 'fun_app$ag'(X0,def_5(X1,X2)) )
& ( 'fun_app$ag'(X0,def_5(X1,X2))
| ~ 'fun_app$c'('uuj$'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f46]) ).
tff(f46,axiom,
! [X0: 'Bool_bool_fun$',X1: 'B_bool_fun$',X2: 'B$'] :
( 'fun_app$c'('uuj$'(X0,X1),X2)
<=> 'fun_app$ag'(X0,def_5(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom45) ).
tff(f6535,plain,
spl249_497,
inference(avatar_split_clause,[],[f2789,f6533]) ).
tff(f6533,plain,
( spl249_497
<=> ! [X2: 'B$',X0: 'Bool_bool_fun$',X1: 'B_bool_fun$'] :
( 'fun_app$ag'(X0,def_5(X1,X2))
| ~ 'fun_app$c'('uuj$'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_497])]) ).
tff(f2789,plain,
! [X2: 'B$',X0: 'Bool_bool_fun$',X1: 'B_bool_fun$'] :
( 'fun_app$ag'(X0,def_5(X1,X2))
| ~ 'fun_app$c'('uuj$'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1602]) ).
tff(f6531,plain,
( spl249_496
| ~ spl249_22
| ~ spl249_423 ),
inference(avatar_split_clause,[],[f6161,f5714,f3700,f6529]) ).
tff(f6529,plain,
( spl249_496
<=> ! [X0: 'B_c_option_fun$',X1: 'B_option$'] : ~ sP18(X0,'uwg$',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_496])]) ).
tff(f6161,plain,
( ! [X0: 'B_c_option_fun$',X1: 'B_option$'] : ~ sP18(X0,'uwg$',X1)
| ~ spl249_22
| ~ spl249_423 ),
inference(resolution,[],[f5715,f3701]) ).
tff(f6527,plain,
spl249_495,
inference(avatar_split_clause,[],[f2788,f6525]) ).
tff(f6525,plain,
( spl249_495
<=> ! [X2: 'C$',X0: 'C_option_bool_fun$',X1: 'C_c_option_fun$'] :
( 'fun_app$b'('uuq$'(X0,X1),X2)
| ~ 'fun_app$'(X0,'fun_app$j'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_495])]) ).
tff(f2788,plain,
! [X2: 'C$',X0: 'C_option_bool_fun$',X1: 'C_c_option_fun$'] :
( 'fun_app$b'('uuq$'(X0,X1),X2)
| ~ 'fun_app$'(X0,'fun_app$j'(X1,X2)) ),
inference(cnf_transformation,[],[f1601]) ).
tff(f1601,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_c_option_fun$',X2: 'C$'] :
( ( 'fun_app$b'('uuq$'(X0,X1),X2)
| ~ 'fun_app$'(X0,'fun_app$j'(X1,X2)) )
& ( 'fun_app$'(X0,'fun_app$j'(X1,X2))
| ~ 'fun_app$b'('uuq$'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f38]) ).
tff(f38,axiom,
! [X0: 'C_option_bool_fun$',X1: 'C_c_option_fun$',X2: 'C$'] :
( 'fun_app$b'('uuq$'(X0,X1),X2)
<=> 'fun_app$'(X0,'fun_app$j'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom37) ).
tff(f6523,plain,
spl249_494,
inference(avatar_split_clause,[],[f2787,f6521]) ).
tff(f6521,plain,
( spl249_494
<=> ! [X2: 'C$',X0: 'C_option_bool_fun$',X1: 'C_c_option_fun$'] :
( 'fun_app$'(X0,'fun_app$j'(X1,X2))
| ~ 'fun_app$b'('uuq$'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_494])]) ).
tff(f2787,plain,
! [X2: 'C$',X0: 'C_option_bool_fun$',X1: 'C_c_option_fun$'] :
( 'fun_app$'(X0,'fun_app$j'(X1,X2))
| ~ 'fun_app$b'('uuq$'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1601]) ).
tff(f6519,plain,
spl249_493,
inference(avatar_split_clause,[],[f2786,f6517]) ).
tff(f6517,plain,
( spl249_493
<=> ! [X2: 'C$',X0: 'Bool_bool_fun$',X1: 'C_bool_fun$'] :
( 'fun_app$b'('uuk$'(X0,X1),X2)
| ~ 'fun_app$ag'(X0,def_4(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_493])]) ).
tff(f2786,plain,
! [X2: 'C$',X0: 'Bool_bool_fun$',X1: 'C_bool_fun$'] :
( 'fun_app$b'('uuk$'(X0,X1),X2)
| ~ 'fun_app$ag'(X0,def_4(X1,X2)) ),
inference(cnf_transformation,[],[f1600]) ).
tff(f1600,plain,
! [X0: 'Bool_bool_fun$',X1: 'C_bool_fun$',X2: 'C$'] :
( ( 'fun_app$b'('uuk$'(X0,X1),X2)
| ~ 'fun_app$ag'(X0,def_4(X1,X2)) )
& ( 'fun_app$ag'(X0,def_4(X1,X2))
| ~ 'fun_app$b'('uuk$'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f45]) ).
tff(f45,axiom,
! [X0: 'Bool_bool_fun$',X1: 'C_bool_fun$',X2: 'C$'] :
( 'fun_app$b'('uuk$'(X0,X1),X2)
<=> 'fun_app$ag'(X0,def_4(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom44) ).
tff(f6515,plain,
spl249_492,
inference(avatar_split_clause,[],[f2785,f6513]) ).
tff(f6513,plain,
( spl249_492
<=> ! [X2: 'C$',X0: 'Bool_bool_fun$',X1: 'C_bool_fun$'] :
( 'fun_app$ag'(X0,def_4(X1,X2))
| ~ 'fun_app$b'('uuk$'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_492])]) ).
tff(f2785,plain,
! [X2: 'C$',X0: 'Bool_bool_fun$',X1: 'C_bool_fun$'] :
( 'fun_app$ag'(X0,def_4(X1,X2))
| ~ 'fun_app$b'('uuk$'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1600]) ).
tff(f6511,plain,
spl249_491,
inference(avatar_split_clause,[],[f2667,f6509]) ).
tff(f6509,plain,
( spl249_491
<=> ! [X2: 'A$',X0: 'A$',X1: 'A$'] :
( ( 'none$b' = 'fun_app$q'('update1$'(X0,X1),X2) )
| ( X0 = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_491])]) ).
tff(f2667,plain,
! [X2: 'A$',X0: 'A$',X1: 'A$'] :
( ( 'none$b' = 'fun_app$q'('update1$'(X0,X1),X2) )
| ( X0 = X2 ) ),
inference(cnf_transformation,[],[f948]) ).
tff(f948,plain,
! [X0: 'A$',X1: 'A$',X2: 'A$'] :
( ( ( 'none$b' = 'fun_app$q'('update1$'(X0,X1),X2) )
| ( X0 = X2 ) )
& ( ( 'fun_app$q'('some$b',X1) = 'fun_app$q'('update1$'(X0,X1),X2) )
| ( X0 != X2 ) ) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,axiom,
! [X0: 'A$',X1: 'A$',X2: 'A$'] :
( ( ( X0 != X2 )
=> ( 'none$b' = 'fun_app$q'('update1$'(X0,X1),X2) ) )
& ( ( X0 = X2 )
=> ( 'fun_app$q'('some$b',X1) = 'fun_app$q'('update1$'(X0,X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom168) ).
tff(f6507,plain,
spl249_490,
inference(avatar_split_clause,[],[f2543,f6505]) ).
tff(f6505,plain,
( spl249_490
<=> ! [X0: 'B$',X1: 'B$'] :
( ( X0 = X1 )
| ( 'fun_app$g'('some$',X1) != 'fun_app$g'('some$',X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_490])]) ).
tff(f2543,plain,
! [X0: 'B$',X1: 'B$'] :
( ( X0 = X1 )
| ( 'fun_app$g'('some$',X1) != 'fun_app$g'('some$',X0) ) ),
inference(cnf_transformation,[],[f1532]) ).
tff(f1532,plain,
! [X0: 'B$',X1: 'B$'] :
( ( ( 'fun_app$g'('some$',X1) = 'fun_app$g'('some$',X0) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'fun_app$g'('some$',X1) != 'fun_app$g'('some$',X0) ) ) ),
inference(nnf_transformation,[],[f99]) ).
tff(f99,axiom,
! [X0: 'B$',X1: 'B$'] :
( ( 'fun_app$g'('some$',X1) = 'fun_app$g'('some$',X0) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom97) ).
tff(f6503,plain,
spl249_489,
inference(avatar_split_clause,[],[f2541,f6501]) ).
tff(f6501,plain,
( spl249_489
<=> ! [X0: 'C$',X1: 'C$'] :
( ( X0 = X1 )
| ( 'fun_app$j'('some$a',X1) != 'fun_app$j'('some$a',X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_489])]) ).
tff(f2541,plain,
! [X0: 'C$',X1: 'C$'] :
( ( X0 = X1 )
| ( 'fun_app$j'('some$a',X1) != 'fun_app$j'('some$a',X0) ) ),
inference(cnf_transformation,[],[f1531]) ).
tff(f1531,plain,
! [X0: 'C$',X1: 'C$'] :
( ( ( 'fun_app$j'('some$a',X1) = 'fun_app$j'('some$a',X0) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'fun_app$j'('some$a',X1) != 'fun_app$j'('some$a',X0) ) ) ),
inference(nnf_transformation,[],[f98]) ).
tff(f98,axiom,
! [X0: 'C$',X1: 'C$'] :
( ( 'fun_app$j'('some$a',X1) = 'fun_app$j'('some$a',X0) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom96) ).
tff(f6499,plain,
spl249_488,
inference(avatar_split_clause,[],[f2539,f6497]) ).
tff(f6497,plain,
( spl249_488
<=> ! [X0: 'A$',X1: 'A$'] :
( ( X0 = X1 )
| ( 'fun_app$q'('some$b',X1) != 'fun_app$q'('some$b',X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_488])]) ).
tff(f2539,plain,
! [X0: 'A$',X1: 'A$'] :
( ( X0 = X1 )
| ( 'fun_app$q'('some$b',X1) != 'fun_app$q'('some$b',X0) ) ),
inference(cnf_transformation,[],[f1530]) ).
tff(f1530,plain,
! [X0: 'A$',X1: 'A$'] :
( ( ( 'fun_app$q'('some$b',X1) = 'fun_app$q'('some$b',X0) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'fun_app$q'('some$b',X1) != 'fun_app$q'('some$b',X0) ) ) ),
inference(nnf_transformation,[],[f97]) ).
tff(f97,axiom,
! [X0: 'A$',X1: 'A$'] :
( ( 'fun_app$q'('some$b',X1) = 'fun_app$q'('some$b',X0) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom95) ).
tff(f6495,plain,
spl249_487,
inference(avatar_split_clause,[],[f2405,f6493]) ).
tff(f2405,plain,
! [X0: 'B_bool_fun$',X1: 'B_option$'] :
( ( tltrue = def_21(X0,X1) )
| ~ 'fun_app$c'(X0,'fun_app$al'('the$',X1)) ),
inference(cnf_transformation,[],[f1455]) ).
tff(f1455,plain,
! [X0: 'B_bool_fun$',X1: 'B_option$'] :
( ( ( tltrue = def_21(X0,X1) )
| ~ 'fun_app$c'(X0,'fun_app$al'('the$',X1)) )
& ( 'fun_app$c'(X0,'fun_app$al'('the$',X1))
| ( tltrue != def_21(X0,X1) ) ) ),
inference(nnf_transformation,[],[f825]) ).
tff(f825,plain,
! [X0: 'B_bool_fun$',X1: 'B_option$'] :
( ( tltrue = def_21(X0,X1) )
<=> 'fun_app$c'(X0,'fun_app$al'('the$',X1)) ),
inference(rectify,[],[f732]) ).
tff(f732,axiom,
! [X2: 'B_bool_fun$',X3: 'B_option$'] :
( ( tltrue = def_21(X2,X3) )
<=> 'fun_app$c'(X2,'fun_app$al'('the$',X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_731) ).
tff(f6491,plain,
spl249_486,
inference(avatar_split_clause,[],[f2404,f6489]) ).
tff(f6489,plain,
( spl249_486
<=> ! [X0: 'B_bool_fun$',X1: 'B_option$'] :
( 'fun_app$c'(X0,'fun_app$al'('the$',X1))
| ( tltrue != def_21(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_486])]) ).
tff(f2404,plain,
! [X0: 'B_bool_fun$',X1: 'B_option$'] :
( 'fun_app$c'(X0,'fun_app$al'('the$',X1))
| ( tltrue != def_21(X0,X1) ) ),
inference(cnf_transformation,[],[f1455]) ).
tff(f6487,plain,
( spl249_485
| ~ spl249_22
| ~ spl249_421 ),
inference(avatar_split_clause,[],[f6139,f5706,f3700,f6485]) ).
tff(f6485,plain,
( spl249_485
<=> ! [X0: 'A_c_option_fun$',X1: 'A_option$'] : ~ sP17(X0,'uwg$',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_485])]) ).
tff(f6139,plain,
( ! [X0: 'A_c_option_fun$',X1: 'A_option$'] : ~ sP17(X0,'uwg$',X1)
| ~ spl249_22
| ~ spl249_421 ),
inference(resolution,[],[f5707,f3701]) ).
tff(f6483,plain,
spl249_484,
inference(avatar_split_clause,[],[f2403,f6481]) ).
tff(f2403,plain,
! [X0: 'B_bool_fun$',X1: 'B_option$'] :
( ( tltrue = def_17(X0,X1) )
| ~ 'fun_app$c'(X0,'fun_app$al'('the$',X1)) ),
inference(cnf_transformation,[],[f1454]) ).
tff(f1454,plain,
! [X0: 'B_bool_fun$',X1: 'B_option$'] :
( ( ( tltrue = def_17(X0,X1) )
| ~ 'fun_app$c'(X0,'fun_app$al'('the$',X1)) )
& ( 'fun_app$c'(X0,'fun_app$al'('the$',X1))
| ( tltrue != def_17(X0,X1) ) ) ),
inference(nnf_transformation,[],[f824]) ).
tff(f824,plain,
! [X0: 'B_bool_fun$',X1: 'B_option$'] :
( ( tltrue = def_17(X0,X1) )
<=> 'fun_app$c'(X0,'fun_app$al'('the$',X1)) ),
inference(rectify,[],[f728]) ).
tff(f728,axiom,
! [X2: 'B_bool_fun$',X3: 'B_option$'] :
( ( tltrue = def_17(X2,X3) )
<=> 'fun_app$c'(X2,'fun_app$al'('the$',X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_727) ).
tff(f6479,plain,
spl249_483,
inference(avatar_split_clause,[],[f2402,f6477]) ).
tff(f6477,plain,
( spl249_483
<=> ! [X0: 'B_bool_fun$',X1: 'B_option$'] :
( 'fun_app$c'(X0,'fun_app$al'('the$',X1))
| ( tltrue != def_17(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_483])]) ).
tff(f2402,plain,
! [X0: 'B_bool_fun$',X1: 'B_option$'] :
( 'fun_app$c'(X0,'fun_app$al'('the$',X1))
| ( tltrue != def_17(X0,X1) ) ),
inference(cnf_transformation,[],[f1454]) ).
tff(f6475,plain,
spl249_482,
inference(avatar_split_clause,[],[f2401,f6473]) ).
tff(f2401,plain,
! [X0: 'C_bool_fun$',X1: 'C_option$'] :
( ( tltrue = def_19(X0,X1) )
| ~ 'fun_app$b'(X0,'fun_app$ak'('the$a',X1)) ),
inference(cnf_transformation,[],[f1453]) ).
tff(f1453,plain,
! [X0: 'C_bool_fun$',X1: 'C_option$'] :
( ( ( tltrue = def_19(X0,X1) )
| ~ 'fun_app$b'(X0,'fun_app$ak'('the$a',X1)) )
& ( 'fun_app$b'(X0,'fun_app$ak'('the$a',X1))
| ( tltrue != def_19(X0,X1) ) ) ),
inference(nnf_transformation,[],[f823]) ).
tff(f823,plain,
! [X0: 'C_bool_fun$',X1: 'C_option$'] :
( ( tltrue = def_19(X0,X1) )
<=> 'fun_app$b'(X0,'fun_app$ak'('the$a',X1)) ),
inference(rectify,[],[f730]) ).
tff(f730,axiom,
! [X2: 'C_bool_fun$',X3: 'C_option$'] :
( ( tltrue = def_19(X2,X3) )
<=> 'fun_app$b'(X2,'fun_app$ak'('the$a',X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_729) ).
tff(f6471,plain,
spl249_481,
inference(avatar_split_clause,[],[f2400,f6469]) ).
tff(f6469,plain,
( spl249_481
<=> ! [X0: 'C_bool_fun$',X1: 'C_option$'] :
( 'fun_app$b'(X0,'fun_app$ak'('the$a',X1))
| ( tltrue != def_19(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_481])]) ).
tff(f2400,plain,
! [X0: 'C_bool_fun$',X1: 'C_option$'] :
( 'fun_app$b'(X0,'fun_app$ak'('the$a',X1))
| ( tltrue != def_19(X0,X1) ) ),
inference(cnf_transformation,[],[f1453]) ).
tff(f6467,plain,
spl249_480,
inference(avatar_split_clause,[],[f2399,f6465]) ).
tff(f2399,plain,
! [X0: 'C_bool_fun$',X1: 'C_option$'] :
( ( tltrue = def_23(X0,X1) )
| ~ 'fun_app$b'(X0,'fun_app$ak'('the$a',X1)) ),
inference(cnf_transformation,[],[f1452]) ).
tff(f1452,plain,
! [X0: 'C_bool_fun$',X1: 'C_option$'] :
( ( ( tltrue = def_23(X0,X1) )
| ~ 'fun_app$b'(X0,'fun_app$ak'('the$a',X1)) )
& ( 'fun_app$b'(X0,'fun_app$ak'('the$a',X1))
| ( tltrue != def_23(X0,X1) ) ) ),
inference(nnf_transformation,[],[f822]) ).
tff(f822,plain,
! [X0: 'C_bool_fun$',X1: 'C_option$'] :
( ( tltrue = def_23(X0,X1) )
<=> 'fun_app$b'(X0,'fun_app$ak'('the$a',X1)) ),
inference(rectify,[],[f734]) ).
tff(f734,axiom,
! [X2: 'C_bool_fun$',X3: 'C_option$'] :
( ( tltrue = def_23(X2,X3) )
<=> 'fun_app$b'(X2,'fun_app$ak'('the$a',X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_733) ).
tff(f6463,plain,
spl249_479,
inference(avatar_split_clause,[],[f2398,f6461]) ).
tff(f6461,plain,
( spl249_479
<=> ! [X0: 'C_bool_fun$',X1: 'C_option$'] :
( 'fun_app$b'(X0,'fun_app$ak'('the$a',X1))
| ( tltrue != def_23(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_479])]) ).
tff(f2398,plain,
! [X0: 'C_bool_fun$',X1: 'C_option$'] :
( 'fun_app$b'(X0,'fun_app$ak'('the$a',X1))
| ( tltrue != def_23(X0,X1) ) ),
inference(cnf_transformation,[],[f1452]) ).
tff(f6459,plain,
spl249_478,
inference(avatar_split_clause,[],[f2329,f6457]) ).
tff(f2329,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$al'('the$',X0) != 'fun_app$al'('the$',X1) )
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1402]) ).
tff(f1402,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( ( ( 'fun_app$al'('the$',X0) != 'fun_app$al'('the$',X1) )
& ( 'none$a' != X0 )
& ( 'none$a' != X1 ) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f1401]) ).
tff(f1401,plain,
! [X1: 'B_option$',X0: 'B_option$'] :
( ( ( 'fun_app$al'('the$',X0) != 'fun_app$al'('the$',X1) )
& ( 'none$a' != X1 )
& ( 'none$a' != X0 ) )
| ~ sP2(X1,X0) ),
inference(nnf_transformation,[],[f1103]) ).
tff(f6455,plain,
spl249_477,
inference(avatar_split_clause,[],[f2324,f6453]) ).
tff(f2324,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$ak'('the$a',X0) != 'fun_app$ak'('the$a',X1) )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f1399]) ).
tff(f1399,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( ( ( 'fun_app$ak'('the$a',X0) != 'fun_app$ak'('the$a',X1) )
& ( 'none$' != X0 )
& ( 'none$' != X1 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f1398]) ).
tff(f1398,plain,
! [X1: 'C_option$',X0: 'C_option$'] :
( ( ( 'fun_app$ak'('the$a',X0) != 'fun_app$ak'('the$a',X1) )
& ( 'none$' != X1 )
& ( 'none$' != X0 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f1101]) ).
tff(f6451,plain,
spl249_476,
inference(avatar_split_clause,[],[f2319,f6449]) ).
tff(f2319,plain,
! [X0: 'A_option$',X1: 'A_option$'] :
( ( 'fun_app$bf'('the$b',X0) != 'fun_app$bf'('the$b',X1) )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f1396]) ).
tff(f1396,plain,
! [X0: 'A_option$',X1: 'A_option$'] :
( ( ( 'fun_app$bf'('the$b',X0) != 'fun_app$bf'('the$b',X1) )
& ( 'none$b' != X0 )
& ( 'none$b' != X1 ) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f1395]) ).
tff(f1395,plain,
! [X1: 'A_option$',X0: 'A_option$'] :
( ( ( 'fun_app$bf'('the$b',X0) != 'fun_app$bf'('the$b',X1) )
& ( 'none$b' != X1 )
& ( 'none$b' != X0 ) )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f1099]) ).
tff(f6447,plain,
spl249_475,
inference(avatar_split_clause,[],[f2257,f6445]) ).
tff(f6445,plain,
( spl249_475
<=> ! [X0: 'B$',X1: 'B_b_option_fun$'] : ( 'fun_app$ac'('bind$c'('fun_app$g'('some$',X0)),X1) = 'fun_app$g'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_475])]) ).
tff(f2257,plain,
! [X0: 'B$',X1: 'B_b_option_fun$'] : ( 'fun_app$ac'('bind$c'('fun_app$g'('some$',X0)),X1) = 'fun_app$g'(X1,X0) ),
inference(cnf_transformation,[],[f425]) ).
tff(f425,axiom,
! [X0: 'B$',X1: 'B_b_option_fun$'] : ( 'fun_app$ac'('bind$c'('fun_app$g'('some$',X0)),X1) = 'fun_app$g'(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom423) ).
tff(f6443,plain,
( spl249_474
| ~ spl249_22
| ~ spl249_419 ),
inference(avatar_split_clause,[],[f6117,f5698,f3700,f6441]) ).
tff(f6441,plain,
( spl249_474
<=> ! [X0: 'A_c_option_fun$',X1: 'A_option$'] : ~ sP16(X0,'uwg$',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_474])]) ).
tff(f6117,plain,
( ! [X0: 'A_c_option_fun$',X1: 'A_option$'] : ~ sP16(X0,'uwg$',X1)
| ~ spl249_22
| ~ spl249_419 ),
inference(resolution,[],[f5699,f3701]) ).
tff(f6439,plain,
spl249_473,
inference(avatar_split_clause,[],[f2256,f6437]) ).
tff(f6437,plain,
( spl249_473
<=> ! [X0: 'C$',X1: 'C_c_option_fun$'] : ( 'fun_app$ab'('bind$'('fun_app$j'('some$a',X0)),X1) = 'fun_app$j'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_473])]) ).
tff(f2256,plain,
! [X0: 'C$',X1: 'C_c_option_fun$'] : ( 'fun_app$ab'('bind$'('fun_app$j'('some$a',X0)),X1) = 'fun_app$j'(X1,X0) ),
inference(cnf_transformation,[],[f424]) ).
tff(f424,axiom,
! [X0: 'C$',X1: 'C_c_option_fun$'] : ( 'fun_app$ab'('bind$'('fun_app$j'('some$a',X0)),X1) = 'fun_app$j'(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom422) ).
tff(f6435,plain,
spl249_472,
inference(avatar_split_clause,[],[f2255,f6433]) ).
tff(f6433,plain,
( spl249_472
<=> ! [X0: 'B_b_fun$',X1: 'B_b_fun$'] : ( 'comp$ah'('map_option$b'(X0),'map_option$b'(X1)) = 'map_option$b'('comp$ai'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_472])]) ).
tff(f2255,plain,
! [X0: 'B_b_fun$',X1: 'B_b_fun$'] : ( 'comp$ah'('map_option$b'(X0),'map_option$b'(X1)) = 'map_option$b'('comp$ai'(X0,X1)) ),
inference(cnf_transformation,[],[f510]) ).
tff(f510,axiom,
! [X0: 'B_b_fun$',X1: 'B_b_fun$'] : ( 'comp$ah'('map_option$b'(X0),'map_option$b'(X1)) = 'map_option$b'('comp$ai'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom508) ).
tff(f6431,plain,
spl249_471,
inference(avatar_split_clause,[],[f2254,f6429]) ).
tff(f6429,plain,
( spl249_471
<=> ! [X0: 'B_b_fun$',X1: 'C_b_fun$'] : ( 'comp$af'('map_option$b'(X0),'map_option$'(X1)) = 'map_option$'('comp$ag'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_471])]) ).
tff(f2254,plain,
! [X0: 'B_b_fun$',X1: 'C_b_fun$'] : ( 'comp$af'('map_option$b'(X0),'map_option$'(X1)) = 'map_option$'('comp$ag'(X0,X1)) ),
inference(cnf_transformation,[],[f509]) ).
tff(f509,axiom,
! [X0: 'B_b_fun$',X1: 'C_b_fun$'] : ( 'comp$af'('map_option$b'(X0),'map_option$'(X1)) = 'map_option$'('comp$ag'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom507) ).
tff(f6427,plain,
spl249_470,
inference(avatar_split_clause,[],[f2253,f6425]) ).
tff(f6425,plain,
( spl249_470
<=> ! [X0: 'B_c_fun$',X1: 'B_b_fun$'] : ( 'comp$ab'('map_option$d'(X0),'map_option$b'(X1)) = 'map_option$d'('comp$ac'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_470])]) ).
tff(f2253,plain,
! [X0: 'B_c_fun$',X1: 'B_b_fun$'] : ( 'comp$ab'('map_option$d'(X0),'map_option$b'(X1)) = 'map_option$d'('comp$ac'(X0,X1)) ),
inference(cnf_transformation,[],[f507]) ).
tff(f507,axiom,
! [X0: 'B_c_fun$',X1: 'B_b_fun$'] : ( 'comp$ab'('map_option$d'(X0),'map_option$b'(X1)) = 'map_option$d'('comp$ac'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom505) ).
tff(f6423,plain,
spl249_469,
inference(avatar_split_clause,[],[f2252,f6421]) ).
tff(f6421,plain,
( spl249_469
<=> ! [X0: 'B_c_fun$',X1: 'C_b_fun$'] : ( 'comp$z'('map_option$d'(X0),'map_option$'(X1)) = 'map_option$c'('comp$aa'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_469])]) ).
tff(f2252,plain,
! [X0: 'B_c_fun$',X1: 'C_b_fun$'] : ( 'comp$z'('map_option$d'(X0),'map_option$'(X1)) = 'map_option$c'('comp$aa'(X0,X1)) ),
inference(cnf_transformation,[],[f506]) ).
tff(f506,axiom,
! [X0: 'B_c_fun$',X1: 'C_b_fun$'] : ( 'comp$z'('map_option$d'(X0),'map_option$'(X1)) = 'map_option$c'('comp$aa'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom504) ).
tff(f6419,plain,
spl249_468,
inference(avatar_split_clause,[],[f2251,f6417]) ).
tff(f6417,plain,
( spl249_468
<=> ! [X0: 'B_c_fun$',X1: 'A_b_fun$'] : ( 'comp$ad'('map_option$d'(X0),'map_option$e'(X1)) = 'map_option$f'('comp$ae'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_468])]) ).
tff(f2251,plain,
! [X0: 'B_c_fun$',X1: 'A_b_fun$'] : ( 'comp$ad'('map_option$d'(X0),'map_option$e'(X1)) = 'map_option$f'('comp$ae'(X0,X1)) ),
inference(cnf_transformation,[],[f508]) ).
tff(f508,axiom,
! [X0: 'B_c_fun$',X1: 'A_b_fun$'] : ( 'comp$ad'('map_option$d'(X0),'map_option$e'(X1)) = 'map_option$f'('comp$ae'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom506) ).
tff(f6415,plain,
spl249_467,
inference(avatar_split_clause,[],[f2250,f6413]) ).
tff(f6413,plain,
( spl249_467
<=> ! [X0: 'C_b_fun$',X1: 'B_c_fun$'] : ( 'comp$x'('map_option$'(X0),'map_option$d'(X1)) = 'map_option$b'('comp$y'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_467])]) ).
tff(f2250,plain,
! [X0: 'C_b_fun$',X1: 'B_c_fun$'] : ( 'comp$x'('map_option$'(X0),'map_option$d'(X1)) = 'map_option$b'('comp$y'(X0,X1)) ),
inference(cnf_transformation,[],[f505]) ).
tff(f505,axiom,
! [X0: 'C_b_fun$',X1: 'B_c_fun$'] : ( 'comp$x'('map_option$'(X0),'map_option$d'(X1)) = 'map_option$b'('comp$y'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom503) ).
tff(f6411,plain,
spl249_466,
inference(avatar_split_clause,[],[f2249,f6409]) ).
tff(f6409,plain,
( spl249_466
<=> ! [X0: 'C_b_fun$',X1: 'C_c_fun$'] : ( 'comp$t'('map_option$'(X0),'map_option$c'(X1)) = 'map_option$'('comp$u'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_466])]) ).
tff(f2249,plain,
! [X0: 'C_b_fun$',X1: 'C_c_fun$'] : ( 'comp$t'('map_option$'(X0),'map_option$c'(X1)) = 'map_option$'('comp$u'(X0,X1)) ),
inference(cnf_transformation,[],[f503]) ).
tff(f503,axiom,
! [X0: 'C_b_fun$',X1: 'C_c_fun$'] : ( 'comp$t'('map_option$'(X0),'map_option$c'(X1)) = 'map_option$'('comp$u'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom501) ).
tff(f6407,plain,
spl249_465,
inference(avatar_split_clause,[],[f2248,f6405]) ).
tff(f6405,plain,
( spl249_465
<=> ! [X0: 'C_b_fun$',X1: 'A_c_fun$'] : ( 'comp$v'('map_option$'(X0),'map_option$f'(X1)) = 'map_option$e'('comp$w'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_465])]) ).
tff(f2248,plain,
! [X0: 'C_b_fun$',X1: 'A_c_fun$'] : ( 'comp$v'('map_option$'(X0),'map_option$f'(X1)) = 'map_option$e'('comp$w'(X0,X1)) ),
inference(cnf_transformation,[],[f504]) ).
tff(f504,axiom,
! [X0: 'C_b_fun$',X1: 'A_c_fun$'] : ( 'comp$v'('map_option$'(X0),'map_option$f'(X1)) = 'map_option$e'('comp$w'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom502) ).
tff(f6403,plain,
spl249_464,
inference(avatar_split_clause,[],[f2247,f6401]) ).
tff(f6401,plain,
( spl249_464
<=> ! [X0: 'C_c_fun$',X1: 'B_c_fun$'] : ( 'comp$p'('map_option$c'(X0),'map_option$d'(X1)) = 'map_option$d'('comp$q'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_464])]) ).
tff(f2247,plain,
! [X0: 'C_c_fun$',X1: 'B_c_fun$'] : ( 'comp$p'('map_option$c'(X0),'map_option$d'(X1)) = 'map_option$d'('comp$q'(X0,X1)) ),
inference(cnf_transformation,[],[f501]) ).
tff(f501,axiom,
! [X0: 'C_c_fun$',X1: 'B_c_fun$'] : ( 'comp$p'('map_option$c'(X0),'map_option$d'(X1)) = 'map_option$d'('comp$q'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom499) ).
tff(f6399,plain,
spl249_463,
inference(avatar_split_clause,[],[f2246,f6397]) ).
tff(f6397,plain,
( spl249_463
<=> ! [X0: 'B_a_fun$',X1: 'A_b_fun$'] : ( 'comp$r'('map_option$h'(X0),'map_option$e'(X1)) = 'map_option$a'('comp$s'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_463])]) ).
tff(f2246,plain,
! [X0: 'B_a_fun$',X1: 'A_b_fun$'] : ( 'comp$r'('map_option$h'(X0),'map_option$e'(X1)) = 'map_option$a'('comp$s'(X0,X1)) ),
inference(cnf_transformation,[],[f502]) ).
tff(f502,axiom,
! [X0: 'B_a_fun$',X1: 'A_b_fun$'] : ( 'comp$r'('map_option$h'(X0),'map_option$e'(X1)) = 'map_option$a'('comp$s'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom500) ).
tff(f6395,plain,
spl249_462,
inference(avatar_split_clause,[],[f2245,f6393]) ).
tff(f6391,plain,
spl249_461,
inference(avatar_split_clause,[],[f2244,f6389]) ).
tff(f6387,plain,
spl249_460,
inference(avatar_split_clause,[],[f2243,f6385]) ).
tff(f6383,plain,
spl249_459,
inference(avatar_split_clause,[],[f2242,f6381]) ).
tff(f6381,plain,
( spl249_459
<=> ! [X0: 'B_c_fun$',X1: 'B_option$'] : ( 'fun_app$an'('map_option$d'(X0),X1) = 'bind$b'(X1,'comp$b'('some$a',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_459])]) ).
tff(f2242,plain,
! [X0: 'B_c_fun$',X1: 'B_option$'] : ( 'fun_app$an'('map_option$d'(X0),X1) = 'bind$b'(X1,'comp$b'('some$a',X0)) ),
inference(cnf_transformation,[],[f482]) ).
tff(f482,axiom,
! [X0: 'B_c_fun$',X1: 'B_option$'] : ( 'fun_app$an'('map_option$d'(X0),X1) = 'bind$b'(X1,'comp$b'('some$a',X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom480) ).
tff(f6379,plain,
spl249_458,
inference(avatar_split_clause,[],[f2241,f6377]) ).
tff(f6377,plain,
( spl249_458
<=> ! [X0: 'A_b_fun$',X1: 'A_option$'] : ( 'fun_app$av'('map_option$e'(X0),X1) = 'bind$e'(X1,'comp$d'('some$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_458])]) ).
tff(f2241,plain,
! [X0: 'A_b_fun$',X1: 'A_option$'] : ( 'fun_app$av'('map_option$e'(X0),X1) = 'bind$e'(X1,'comp$d'('some$',X0)) ),
inference(cnf_transformation,[],[f484]) ).
tff(f484,axiom,
! [X0: 'A_b_fun$',X1: 'A_option$'] : ( 'fun_app$av'('map_option$e'(X0),X1) = 'bind$e'(X1,'comp$d'('some$',X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom482) ).
tff(f6375,plain,
spl249_457,
inference(avatar_split_clause,[],[f2239,f6373]) ).
tff(f6373,plain,
( spl249_457
<=> ! [X0: 'C_b_fun$',X1: 'C_option$'] : ( 'fun_app$bg'('map_option$'(X0),X1) = 'case_option$h'('none$a','uvc$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_457])]) ).
tff(f2239,plain,
! [X0: 'C_b_fun$',X1: 'C_option$'] : ( 'fun_app$bg'('map_option$'(X0),X1) = 'case_option$h'('none$a','uvc$'(X0),X1) ),
inference(cnf_transformation,[],[f192]) ).
tff(f192,axiom,
! [X0: 'C_b_fun$',X1: 'C_option$'] : ( 'fun_app$bg'('map_option$'(X0),X1) = 'case_option$h'('none$a','uvc$'(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom190) ).
tff(f6371,plain,
spl249_456,
inference(avatar_split_clause,[],[f2238,f6369]) ).
tff(f6369,plain,
( spl249_456
<=> ! [X0: 'C_b_fun$',X1: 'C_option$'] : ( 'fun_app$bg'('map_option$'(X0),X1) = 'bind$a'(X1,'comp$a'('some$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_456])]) ).
tff(f2238,plain,
! [X0: 'C_b_fun$',X1: 'C_option$'] : ( 'fun_app$bg'('map_option$'(X0),X1) = 'bind$a'(X1,'comp$a'('some$',X0)) ),
inference(cnf_transformation,[],[f481]) ).
tff(f481,axiom,
! [X0: 'C_b_fun$',X1: 'C_option$'] : ( 'fun_app$bg'('map_option$'(X0),X1) = 'bind$a'(X1,'comp$a'('some$',X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom479) ).
tff(f6367,plain,
spl249_455,
inference(avatar_split_clause,[],[f2237,f6365]) ).
tff(f6363,plain,
spl249_454,
inference(avatar_split_clause,[],[f2236,f6361]) ).
tff(f6361,plain,
( spl249_454
<=> ! [X0: 'A_a_fun$',X1: 'A_option$'] : ( 'fun_app$be'('map_option$a'(X0),X1) = 'case_option$b'('none$b','uvd$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_454])]) ).
tff(f2236,plain,
! [X0: 'A_a_fun$',X1: 'A_option$'] : ( 'fun_app$be'('map_option$a'(X0),X1) = 'case_option$b'('none$b','uvd$'(X0),X1) ),
inference(cnf_transformation,[],[f193]) ).
tff(f193,axiom,
! [X0: 'A_a_fun$',X1: 'A_option$'] : ( 'fun_app$be'('map_option$a'(X0),X1) = 'case_option$b'('none$b','uvd$'(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom191) ).
tff(f6359,plain,
( spl249_453
| ~ spl249_106
| ~ spl249_409 ),
inference(avatar_split_clause,[],[f6057,f5656,f4071,f6357]) ).
tff(f6357,plain,
( spl249_453
<=> ! [X0: 'B_option$'] : ~ sP11(X0,X0,'uwr$') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_453])]) ).
tff(f5656,plain,
( spl249_409
<=> ! [X2: 'B_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ~ 'fun_app$a'('fun_app$e'(X2,X1),X0)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_409])]) ).
tff(f6057,plain,
( ! [X0: 'B_option$'] : ~ sP11(X0,X0,'uwr$')
| ~ spl249_106
| ~ spl249_409 ),
inference(resolution,[],[f5657,f4072]) ).
tff(f5657,plain,
( ! [X2: 'B_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ~ 'fun_app$a'('fun_app$e'(X2,X1),X0)
| ~ sP11(X0,X1,X2) )
| ~ spl249_409 ),
inference(avatar_component_clause,[],[f5656]) ).
tff(f6355,plain,
spl249_452,
inference(avatar_split_clause,[],[f2052,f6353]) ).
tff(f6353,plain,
( spl249_452
<=> ! [X0: 'B_option$'] :
( ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_452])]) ).
tff(f2052,plain,
! [X0: 'B_option$'] :
( ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f879]) ).
tff(f879,plain,
! [X0: 'B_option$'] :
( ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 )
| ( 'none$a' = X0 ) ),
inference(ennf_transformation,[],[f200]) ).
tff(f200,axiom,
! [X0: 'B_option$'] :
( ( 'none$a' != X0 )
=> ( 'fun_app$g'('some$','fun_app$al'('the$',X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom198) ).
tff(f6351,plain,
spl249_451,
inference(avatar_split_clause,[],[f2050,f6349]) ).
tff(f6349,plain,
( spl249_451
<=> ! [X0: 'C_option$'] :
( ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 )
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_451])]) ).
tff(f2050,plain,
! [X0: 'C_option$'] :
( ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 )
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f877]) ).
tff(f877,plain,
! [X0: 'C_option$'] :
( ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 )
| ( 'none$' = X0 ) ),
inference(ennf_transformation,[],[f199]) ).
tff(f199,axiom,
! [X0: 'C_option$'] :
( ( 'none$' != X0 )
=> ( 'fun_app$j'('some$a','fun_app$ak'('the$a',X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom197) ).
tff(f6347,plain,
spl249_450,
inference(avatar_split_clause,[],[f2048,f6345]) ).
tff(f6345,plain,
( spl249_450
<=> ! [X0: 'A_option$'] :
( ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) = X0 )
| ( 'none$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_450])]) ).
tff(f2048,plain,
! [X0: 'A_option$'] :
( ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) = X0 )
| ( 'none$b' = X0 ) ),
inference(cnf_transformation,[],[f875]) ).
tff(f875,plain,
! [X0: 'A_option$'] :
( ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) = X0 )
| ( 'none$b' = X0 ) ),
inference(ennf_transformation,[],[f198]) ).
tff(f198,axiom,
! [X0: 'A_option$'] :
( ( 'none$b' != X0 )
=> ( 'fun_app$q'('some$b','fun_app$bf'('the$b',X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom196) ).
tff(f6306,plain,
( spl249_449
| ~ spl249_105
| ~ spl249_409 ),
inference(avatar_split_clause,[],[f6056,f5656,f4067,f6304]) ).
tff(f6304,plain,
( spl249_449
<=> ! [X0: 'B_option$'] : ~ sP11(X0,X0,'uwn$') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_449])]) ).
tff(f6056,plain,
( ! [X0: 'B_option$'] : ~ sP11(X0,X0,'uwn$')
| ~ spl249_105
| ~ spl249_409 ),
inference(resolution,[],[f5657,f4068]) ).
tff(f6093,plain,
( spl249_448
| ~ spl249_103
| ~ spl249_405 ),
inference(avatar_split_clause,[],[f6041,f5638,f4059,f6091]) ).
tff(f6091,plain,
( spl249_448
<=> ! [X0: 'C_option$'] : ~ sP7(X0,X0,'uws$') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_448])]) ).
tff(f5638,plain,
( spl249_405
<=> ! [X2: 'C_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ~ 'fun_app$'('fun_app$d'(X2,X1),X0)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_405])]) ).
tff(f6041,plain,
( ! [X0: 'C_option$'] : ~ sP7(X0,X0,'uws$')
| ~ spl249_103
| ~ spl249_405 ),
inference(resolution,[],[f5639,f4060]) ).
tff(f5639,plain,
( ! [X2: 'C_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ~ 'fun_app$'('fun_app$d'(X2,X1),X0)
| ~ sP7(X0,X1,X2) )
| ~ spl249_405 ),
inference(avatar_component_clause,[],[f5638]) ).
tff(f6048,plain,
( spl249_447
| ~ spl249_102
| ~ spl249_405 ),
inference(avatar_split_clause,[],[f6040,f5638,f4055,f6046]) ).
tff(f6046,plain,
( spl249_447
<=> ! [X0: 'C_option$'] : ~ sP7(X0,X0,'uwo$') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_447])]) ).
tff(f6040,plain,
( ! [X0: 'C_option$'] : ~ sP7(X0,X0,'uwo$')
| ~ spl249_102
| ~ spl249_405 ),
inference(resolution,[],[f5639,f4056]) ).
tff(f6009,plain,
( spl249_446
| ~ spl249_55
| ~ spl249_297 ),
inference(avatar_split_clause,[],[f5281,f4991,f3852,f6007]) ).
tff(f6007,plain,
( spl249_446
<=> ! [X0: 'C$'] : ( tltrue = def_1('uwm$'(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_446])]) ).
tff(f4991,plain,
( spl249_297
<=> ! [X0: 'C_bool_fun$',X1: 'C$'] :
( ( tltrue = def_1(X0,X1) )
| ~ 'fun_app$b'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_297])]) ).
tff(f5281,plain,
( ! [X0: 'C$'] : ( tltrue = def_1('uwm$'(X0),X0) )
| ~ spl249_55
| ~ spl249_297 ),
inference(resolution,[],[f4992,f3853]) ).
tff(f4992,plain,
( ! [X0: 'C_bool_fun$',X1: 'C$'] :
( ~ 'fun_app$b'(X0,X1)
| ( tltrue = def_1(X0,X1) ) )
| ~ spl249_297 ),
inference(avatar_component_clause,[],[f4991]) ).
tff(f5962,plain,
( spl249_445
| ~ spl249_54
| ~ spl249_297 ),
inference(avatar_split_clause,[],[f5280,f4991,f3848,f5960]) ).
tff(f5960,plain,
( spl249_445
<=> ! [X0: 'C$'] : ( tltrue = def_1('uwq$'(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_445])]) ).
tff(f5280,plain,
( ! [X0: 'C$'] : ( tltrue = def_1('uwq$'(X0),X0) )
| ~ spl249_54
| ~ spl249_297 ),
inference(resolution,[],[f4992,f3849]) ).
tff(f5931,plain,
( spl249_444
| ~ spl249_55
| ~ spl249_295 ),
inference(avatar_split_clause,[],[f5268,f4983,f3852,f5929]) ).
tff(f5929,plain,
( spl249_444
<=> ! [X0: 'C$'] : ( tltrue = def_4('uwm$'(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_444])]) ).
tff(f4983,plain,
( spl249_295
<=> ! [X0: 'C_bool_fun$',X1: 'C$'] :
( ( tltrue = def_4(X0,X1) )
| ~ 'fun_app$b'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_295])]) ).
tff(f5268,plain,
( ! [X0: 'C$'] : ( tltrue = def_4('uwm$'(X0),X0) )
| ~ spl249_55
| ~ spl249_295 ),
inference(resolution,[],[f4984,f3853]) ).
tff(f4984,plain,
( ! [X0: 'C_bool_fun$',X1: 'C$'] :
( ~ 'fun_app$b'(X0,X1)
| ( tltrue = def_4(X0,X1) ) )
| ~ spl249_295 ),
inference(avatar_component_clause,[],[f4983]) ).
tff(f5888,plain,
( spl249_443
| ~ spl249_54
| ~ spl249_295 ),
inference(avatar_split_clause,[],[f5267,f4983,f3848,f5886]) ).
tff(f5886,plain,
( spl249_443
<=> ! [X0: 'C$'] : ( tltrue = def_4('uwq$'(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_443])]) ).
tff(f5267,plain,
( ! [X0: 'C$'] : ( tltrue = def_4('uwq$'(X0),X0) )
| ~ spl249_54
| ~ spl249_295 ),
inference(resolution,[],[f4984,f3849]) ).
tff(f5796,plain,
spl249_442,
inference(avatar_split_clause,[],[f3468,f5794]) ).
tff(f3468,plain,
! [X0: 'B_option$',X1: 'B_bool_fun$'] :
( sP25(X0,X1,tltrue)
| ~ 'fun_app$c'(X1,'fun_app$al'('the$',X0)) ),
inference(equality_resolution,[],[f2906]) ).
tff(f2906,plain,
! [X2: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( sP25(X0,X1,X2)
| ~ 'fun_app$c'(X1,'fun_app$al'('the$',X0))
| ( tltrue != X2 ) ),
inference(cnf_transformation,[],[f1684]) ).
tff(f5792,plain,
spl249_441,
inference(avatar_split_clause,[],[f3455,f5790]) ).
tff(f3455,plain,
! [X0: 'C_option$',X1: 'C_bool_fun$'] :
( sP20(X0,X1,tltrue)
| ~ 'fun_app$b'(X1,'fun_app$ak'('the$a',X0)) ),
inference(equality_resolution,[],[f2866]) ).
tff(f2866,plain,
! [X2: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( sP20(X0,X1,X2)
| ~ 'fun_app$b'(X1,'fun_app$ak'('the$a',X0))
| ( tltrue != X2 ) ),
inference(cnf_transformation,[],[f1656]) ).
tff(f5788,plain,
spl249_440,
inference(avatar_split_clause,[],[f3431,f5786]) ).
tff(f5786,plain,
( spl249_440
<=> ! [X2: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,X2)
| ~ 'fun_app$a'(X1,sK156('some$c'(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_440])]) ).
tff(f3431,plain,
! [X2: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,X2)
| ~ 'fun_app$a'(X1,sK156('some$c'(X2),X1)) ),
inference(equality_resolution,[],[f2764]) ).
tff(f2764,plain,
! [X2: 'B_option$',X0: 'B_option_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,X2)
| ( 'some$c'(X2) != X0 )
| ~ 'fun_app$a'(X1,sK156(X0,X1)) ),
inference(cnf_transformation,[],[f1578]) ).
tff(f5784,plain,
spl249_439,
inference(avatar_split_clause,[],[f3429,f5782]) ).
tff(f5782,plain,
( spl249_439
<=> ! [X2: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,X2)
| ~ 'fun_app$'(X1,sK155('some$d'(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_439])]) ).
tff(f3429,plain,
! [X2: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,X2)
| ~ 'fun_app$'(X1,sK155('some$d'(X2),X1)) ),
inference(equality_resolution,[],[f2762]) ).
tff(f2762,plain,
! [X2: 'C_option$',X0: 'C_option_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,X2)
| ( 'some$d'(X2) != X0 )
| ~ 'fun_app$'(X1,sK155(X0,X1)) ),
inference(cnf_transformation,[],[f1576]) ).
tff(f5780,plain,
spl249_438,
inference(avatar_split_clause,[],[f3418,f5778]) ).
tff(f5778,plain,
( spl249_438
<=> ! [X2: 'A$',X1: 'A$'] : ( 'fun_app$q'('some$b',X1) = 'fun_app$q'('update1$'(X2,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_438])]) ).
tff(f3418,plain,
! [X2: 'A$',X1: 'A$'] : ( 'fun_app$q'('some$b',X1) = 'fun_app$q'('update1$'(X2,X1),X2) ),
inference(equality_resolution,[],[f2666]) ).
tff(f2666,plain,
! [X2: 'A$',X0: 'A$',X1: 'A$'] :
( ( 'fun_app$q'('some$b',X1) = 'fun_app$q'('update1$'(X0,X1),X2) )
| ( X0 != X2 ) ),
inference(cnf_transformation,[],[f948]) ).
tff(f5774,plain,
spl249_437,
inference(avatar_split_clause,[],[f2908,f5772]) ).
tff(f2908,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ~ sP25(X2,X1,X0) ),
inference(cnf_transformation,[],[f1685]) ).
tff(f1685,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( ( 'fun_app$a'('case_option$e'(X0,X1),X2)
| ~ sP25(X2,X1,X0) )
& ( sP25(X2,X1,X0)
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f1150]) ).
tff(f1150,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
<=> sP25(X2,X1,X0) ),
inference(definition_folding,[],[f1012,f1149]) ).
tff(f1012,plain,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
<=> ( ( 'fun_app$c'(X1,'fun_app$al'('the$',X2))
| ( 'none$a' = X2 ) )
& ( ( tltrue = X0 )
| ( 'none$a' != X2 ) ) ) ),
inference(ennf_transformation,[],[f305]) ).
tff(f305,axiom,
! [X0: tlbool,X1: 'B_bool_fun$',X2: 'B_option$'] :
( 'fun_app$a'('case_option$e'(X0,X1),X2)
<=> ( ( ( 'none$a' != X2 )
=> 'fun_app$c'(X1,'fun_app$al'('the$',X2)) )
& ( ( 'none$a' = X2 )
=> ( tltrue = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom303) ).
tff(f5770,plain,
spl249_436,
inference(avatar_split_clause,[],[f2907,f5768]) ).
tff(f5768,plain,
( spl249_436
<=> ! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( sP25(X2,X1,X0)
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_436])]) ).
tff(f2907,plain,
! [X2: 'B_option$',X0: tlbool,X1: 'B_bool_fun$'] :
( sP25(X2,X1,X0)
| ~ 'fun_app$a'('case_option$e'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1685]) ).
tff(f5766,plain,
spl249_435,
inference(avatar_split_clause,[],[f2900,f5764]) ).
tff(f2900,plain,
! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$a'(X0,'bind$a'(X1,X2))
| ~ sP24(X2,X0,X1) ),
inference(cnf_transformation,[],[f1681]) ).
tff(f1681,plain,
! [X0: 'B_option_bool_fun$',X1: 'C_option$',X2: 'C_b_option_fun$'] :
( ( 'fun_app$a'(X0,'bind$a'(X1,X2))
| ~ sP24(X2,X0,X1) )
& ( sP24(X2,X0,X1)
| ~ 'fun_app$a'(X0,'bind$a'(X1,X2)) ) ),
inference(nnf_transformation,[],[f1148]) ).
tff(f1148,plain,
! [X0: 'B_option_bool_fun$',X1: 'C_option$',X2: 'C_b_option_fun$'] :
( 'fun_app$a'(X0,'bind$a'(X1,X2))
<=> sP24(X2,X0,X1) ),
inference(definition_folding,[],[f1011,f1147]) ).
tff(f1011,plain,
! [X0: 'B_option_bool_fun$',X1: 'C_option$',X2: 'C_b_option_fun$'] :
( 'fun_app$a'(X0,'bind$a'(X1,X2))
<=> ( ! [X3: 'C$'] :
( 'fun_app$a'(X0,'fun_app$l'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$' != X1 ) ) ) ),
inference(ennf_transformation,[],[f477]) ).
tff(f477,axiom,
! [X0: 'B_option_bool_fun$',X1: 'C_option$',X2: 'C_b_option_fun$'] :
( 'fun_app$a'(X0,'bind$a'(X1,X2))
<=> ~ ( ? [X3: 'C$'] :
( ~ 'fun_app$a'(X0,'fun_app$l'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$' = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom475) ).
tff(f5762,plain,
spl249_434,
inference(avatar_split_clause,[],[f2899,f5760]) ).
tff(f2899,plain,
! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( sP24(X2,X0,X1)
| ~ 'fun_app$a'(X0,'bind$a'(X1,X2)) ),
inference(cnf_transformation,[],[f1681]) ).
tff(f5758,plain,
spl249_433,
inference(avatar_split_clause,[],[f2892,f5756]) ).
tff(f2892,plain,
! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$a'(X0,'bind$a'(X1,X2))
| ~ sP23(X2,X0,X1) ),
inference(cnf_transformation,[],[f1675]) ).
tff(f1675,plain,
! [X0: 'B_option_bool_fun$',X1: 'C_option$',X2: 'C_b_option_fun$'] :
( ( 'fun_app$a'(X0,'bind$a'(X1,X2))
| ~ sP23(X2,X0,X1) )
& ( sP23(X2,X0,X1)
| ~ 'fun_app$a'(X0,'bind$a'(X1,X2)) ) ),
inference(nnf_transformation,[],[f1146]) ).
tff(f1146,plain,
! [X0: 'B_option_bool_fun$',X1: 'C_option$',X2: 'C_b_option_fun$'] :
( 'fun_app$a'(X0,'bind$a'(X1,X2))
<=> sP23(X2,X0,X1) ),
inference(definition_folding,[],[f1010,f1145]) ).
tff(f1010,plain,
! [X0: 'B_option_bool_fun$',X1: 'C_option$',X2: 'C_b_option_fun$'] :
( 'fun_app$a'(X0,'bind$a'(X1,X2))
<=> ( ! [X3: 'C$'] :
( 'fun_app$a'(X0,'fun_app$l'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$' != X1 ) ) ) ),
inference(ennf_transformation,[],[f352]) ).
tff(f352,axiom,
! [X0: 'B_option_bool_fun$',X1: 'C_option$',X2: 'C_b_option_fun$'] :
( 'fun_app$a'(X0,'bind$a'(X1,X2))
<=> ( ! [X3: 'C$'] :
( ( 'fun_app$j'('some$a',X3) = X1 )
=> 'fun_app$a'(X0,'fun_app$l'(X2,X3)) )
& ( ( 'none$' = X1 )
=> 'fun_app$a'(X0,'none$a') ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom350) ).
tff(f5754,plain,
spl249_432,
inference(avatar_split_clause,[],[f2891,f5752]) ).
tff(f2891,plain,
! [X2: 'C_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'C_option$'] :
( sP23(X2,X0,X1)
| ~ 'fun_app$a'(X0,'bind$a'(X1,X2)) ),
inference(cnf_transformation,[],[f1675]) ).
tff(f5750,plain,
spl249_431,
inference(avatar_split_clause,[],[f2884,f5748]) ).
tff(f2884,plain,
! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$a'(X0,'bind$e'(X1,X2))
| ~ sP22(X2,X0,X1) ),
inference(cnf_transformation,[],[f1669]) ).
tff(f1669,plain,
! [X0: 'B_option_bool_fun$',X1: 'A_option$',X2: 'A_b_option_fun$'] :
( ( 'fun_app$a'(X0,'bind$e'(X1,X2))
| ~ sP22(X2,X0,X1) )
& ( sP22(X2,X0,X1)
| ~ 'fun_app$a'(X0,'bind$e'(X1,X2)) ) ),
inference(nnf_transformation,[],[f1144]) ).
tff(f1144,plain,
! [X0: 'B_option_bool_fun$',X1: 'A_option$',X2: 'A_b_option_fun$'] :
( 'fun_app$a'(X0,'bind$e'(X1,X2))
<=> sP22(X2,X0,X1) ),
inference(definition_folding,[],[f1009,f1143]) ).
tff(f1009,plain,
! [X0: 'B_option_bool_fun$',X1: 'A_option$',X2: 'A_b_option_fun$'] :
( 'fun_app$a'(X0,'bind$e'(X1,X2))
<=> ( ! [X3: 'A$'] :
( 'fun_app$a'(X0,'fun_app$f'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$b' != X1 ) ) ) ),
inference(ennf_transformation,[],[f474]) ).
tff(f474,axiom,
! [X0: 'B_option_bool_fun$',X1: 'A_option$',X2: 'A_b_option_fun$'] :
( 'fun_app$a'(X0,'bind$e'(X1,X2))
<=> ~ ( ? [X3: 'A$'] :
( ~ 'fun_app$a'(X0,'fun_app$f'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$a'(X0,'none$a')
& ( 'none$b' = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom472) ).
tff(f5746,plain,
spl249_430,
inference(avatar_split_clause,[],[f2883,f5744]) ).
tff(f2883,plain,
! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( sP22(X2,X0,X1)
| ~ 'fun_app$a'(X0,'bind$e'(X1,X2)) ),
inference(cnf_transformation,[],[f1669]) ).
tff(f5742,plain,
spl249_429,
inference(avatar_split_clause,[],[f2876,f5740]) ).
tff(f2876,plain,
! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$a'(X0,'bind$e'(X1,X2))
| ~ sP21(X2,X0,X1) ),
inference(cnf_transformation,[],[f1663]) ).
tff(f1663,plain,
! [X0: 'B_option_bool_fun$',X1: 'A_option$',X2: 'A_b_option_fun$'] :
( ( 'fun_app$a'(X0,'bind$e'(X1,X2))
| ~ sP21(X2,X0,X1) )
& ( sP21(X2,X0,X1)
| ~ 'fun_app$a'(X0,'bind$e'(X1,X2)) ) ),
inference(nnf_transformation,[],[f1142]) ).
tff(f1142,plain,
! [X0: 'B_option_bool_fun$',X1: 'A_option$',X2: 'A_b_option_fun$'] :
( 'fun_app$a'(X0,'bind$e'(X1,X2))
<=> sP21(X2,X0,X1) ),
inference(definition_folding,[],[f1008,f1141]) ).
tff(f1008,plain,
! [X0: 'B_option_bool_fun$',X1: 'A_option$',X2: 'A_b_option_fun$'] :
( 'fun_app$a'(X0,'bind$e'(X1,X2))
<=> ( ! [X3: 'A$'] :
( 'fun_app$a'(X0,'fun_app$f'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$a'(X0,'none$a')
| ( 'none$b' != X1 ) ) ) ),
inference(ennf_transformation,[],[f349]) ).
tff(f349,axiom,
! [X0: 'B_option_bool_fun$',X1: 'A_option$',X2: 'A_b_option_fun$'] :
( 'fun_app$a'(X0,'bind$e'(X1,X2))
<=> ( ! [X3: 'A$'] :
( ( 'fun_app$q'('some$b',X3) = X1 )
=> 'fun_app$a'(X0,'fun_app$f'(X2,X3)) )
& ( ( 'none$b' = X1 )
=> 'fun_app$a'(X0,'none$a') ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom347) ).
tff(f5738,plain,
spl249_428,
inference(avatar_split_clause,[],[f2875,f5736]) ).
tff(f2875,plain,
! [X2: 'A_b_option_fun$',X0: 'B_option_bool_fun$',X1: 'A_option$'] :
( sP21(X2,X0,X1)
| ~ 'fun_app$a'(X0,'bind$e'(X1,X2)) ),
inference(cnf_transformation,[],[f1663]) ).
tff(f5732,plain,
spl249_427,
inference(avatar_split_clause,[],[f2868,f5730]) ).
tff(f2868,plain,
! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),X2)
| ~ sP20(X2,X1,X0) ),
inference(cnf_transformation,[],[f1657]) ).
tff(f1657,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( ( 'fun_app$'('case_option$f'(X0,X1),X2)
| ~ sP20(X2,X1,X0) )
& ( sP20(X2,X1,X0)
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f1140]) ).
tff(f1140,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( 'fun_app$'('case_option$f'(X0,X1),X2)
<=> sP20(X2,X1,X0) ),
inference(definition_folding,[],[f1007,f1139]) ).
tff(f1007,plain,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( 'fun_app$'('case_option$f'(X0,X1),X2)
<=> ( ( 'fun_app$b'(X1,'fun_app$ak'('the$a',X2))
| ( 'none$' = X2 ) )
& ( ( tltrue = X0 )
| ( 'none$' != X2 ) ) ) ),
inference(ennf_transformation,[],[f306]) ).
tff(f306,axiom,
! [X0: tlbool,X1: 'C_bool_fun$',X2: 'C_option$'] :
( 'fun_app$'('case_option$f'(X0,X1),X2)
<=> ( ( ( 'none$' != X2 )
=> 'fun_app$b'(X1,'fun_app$ak'('the$a',X2)) )
& ( ( 'none$' = X2 )
=> ( tltrue = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom304) ).
tff(f5728,plain,
spl249_426,
inference(avatar_split_clause,[],[f2867,f5726]) ).
tff(f5726,plain,
( spl249_426
<=> ! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( sP20(X2,X1,X0)
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_426])]) ).
tff(f2867,plain,
! [X2: 'C_option$',X0: tlbool,X1: 'C_bool_fun$'] :
( sP20(X2,X1,X0)
| ~ 'fun_app$'('case_option$f'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1657]) ).
tff(f5724,plain,
spl249_425,
inference(avatar_split_clause,[],[f2860,f5722]) ).
tff(f2860,plain,
! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$'(X0,'bind$b'(X1,X2))
| ~ sP19(X2,X0,X1) ),
inference(cnf_transformation,[],[f1653]) ).
tff(f1653,plain,
! [X0: 'C_option_bool_fun$',X1: 'B_option$',X2: 'B_c_option_fun$'] :
( ( 'fun_app$'(X0,'bind$b'(X1,X2))
| ~ sP19(X2,X0,X1) )
& ( sP19(X2,X0,X1)
| ~ 'fun_app$'(X0,'bind$b'(X1,X2)) ) ),
inference(nnf_transformation,[],[f1138]) ).
tff(f1138,plain,
! [X0: 'C_option_bool_fun$',X1: 'B_option$',X2: 'B_c_option_fun$'] :
( 'fun_app$'(X0,'bind$b'(X1,X2))
<=> sP19(X2,X0,X1) ),
inference(definition_folding,[],[f1006,f1137]) ).
tff(f1006,plain,
! [X0: 'C_option_bool_fun$',X1: 'B_option$',X2: 'B_c_option_fun$'] :
( 'fun_app$'(X0,'bind$b'(X1,X2))
<=> ( ! [X3: 'B$'] :
( 'fun_app$'(X0,'fun_app$n'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$a' != X1 ) ) ) ),
inference(ennf_transformation,[],[f478]) ).
tff(f478,axiom,
! [X0: 'C_option_bool_fun$',X1: 'B_option$',X2: 'B_c_option_fun$'] :
( 'fun_app$'(X0,'bind$b'(X1,X2))
<=> ~ ( ? [X3: 'B$'] :
( ~ 'fun_app$'(X0,'fun_app$n'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$a' = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom476) ).
tff(f5720,plain,
spl249_424,
inference(avatar_split_clause,[],[f2859,f5718]) ).
tff(f2859,plain,
! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( sP19(X2,X0,X1)
| ~ 'fun_app$'(X0,'bind$b'(X1,X2)) ),
inference(cnf_transformation,[],[f1653]) ).
tff(f5716,plain,
spl249_423,
inference(avatar_split_clause,[],[f2852,f5714]) ).
tff(f2852,plain,
! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$'(X0,'bind$b'(X1,X2))
| ~ sP18(X2,X0,X1) ),
inference(cnf_transformation,[],[f1647]) ).
tff(f1647,plain,
! [X0: 'C_option_bool_fun$',X1: 'B_option$',X2: 'B_c_option_fun$'] :
( ( 'fun_app$'(X0,'bind$b'(X1,X2))
| ~ sP18(X2,X0,X1) )
& ( sP18(X2,X0,X1)
| ~ 'fun_app$'(X0,'bind$b'(X1,X2)) ) ),
inference(nnf_transformation,[],[f1136]) ).
tff(f1136,plain,
! [X0: 'C_option_bool_fun$',X1: 'B_option$',X2: 'B_c_option_fun$'] :
( 'fun_app$'(X0,'bind$b'(X1,X2))
<=> sP18(X2,X0,X1) ),
inference(definition_folding,[],[f1005,f1135]) ).
tff(f1005,plain,
! [X0: 'C_option_bool_fun$',X1: 'B_option$',X2: 'B_c_option_fun$'] :
( 'fun_app$'(X0,'bind$b'(X1,X2))
<=> ( ! [X3: 'B$'] :
( 'fun_app$'(X0,'fun_app$n'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$a' != X1 ) ) ) ),
inference(ennf_transformation,[],[f353]) ).
tff(f353,axiom,
! [X0: 'C_option_bool_fun$',X1: 'B_option$',X2: 'B_c_option_fun$'] :
( 'fun_app$'(X0,'bind$b'(X1,X2))
<=> ( ! [X3: 'B$'] :
( ( 'fun_app$g'('some$',X3) = X1 )
=> 'fun_app$'(X0,'fun_app$n'(X2,X3)) )
& ( ( 'none$a' = X1 )
=> 'fun_app$'(X0,'none$') ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom351) ).
tff(f5712,plain,
spl249_422,
inference(avatar_split_clause,[],[f2851,f5710]) ).
tff(f2851,plain,
! [X2: 'B_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'B_option$'] :
( sP18(X2,X0,X1)
| ~ 'fun_app$'(X0,'bind$b'(X1,X2)) ),
inference(cnf_transformation,[],[f1647]) ).
tff(f5708,plain,
spl249_421,
inference(avatar_split_clause,[],[f2844,f5706]) ).
tff(f2844,plain,
! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$'(X0,'bind$d'(X1,X2))
| ~ sP17(X2,X0,X1) ),
inference(cnf_transformation,[],[f1641]) ).
tff(f1641,plain,
! [X0: 'C_option_bool_fun$',X1: 'A_option$',X2: 'A_c_option_fun$'] :
( ( 'fun_app$'(X0,'bind$d'(X1,X2))
| ~ sP17(X2,X0,X1) )
& ( sP17(X2,X0,X1)
| ~ 'fun_app$'(X0,'bind$d'(X1,X2)) ) ),
inference(nnf_transformation,[],[f1134]) ).
tff(f1134,plain,
! [X0: 'C_option_bool_fun$',X1: 'A_option$',X2: 'A_c_option_fun$'] :
( 'fun_app$'(X0,'bind$d'(X1,X2))
<=> sP17(X2,X0,X1) ),
inference(definition_folding,[],[f1004,f1133]) ).
tff(f1004,plain,
! [X0: 'C_option_bool_fun$',X1: 'A_option$',X2: 'A_c_option_fun$'] :
( 'fun_app$'(X0,'bind$d'(X1,X2))
<=> ( ! [X3: 'A$'] :
( 'fun_app$'(X0,'fun_app$bm'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$b' != X1 ) ) ) ),
inference(ennf_transformation,[],[f473]) ).
tff(f473,axiom,
! [X0: 'C_option_bool_fun$',X1: 'A_option$',X2: 'A_c_option_fun$'] :
( 'fun_app$'(X0,'bind$d'(X1,X2))
<=> ~ ( ? [X3: 'A$'] :
( ~ 'fun_app$'(X0,'fun_app$bm'(X2,X3))
& ( 'fun_app$q'('some$b',X3) = X1 ) )
| ( ~ 'fun_app$'(X0,'none$')
& ( 'none$b' = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom471) ).
tff(f5704,plain,
spl249_420,
inference(avatar_split_clause,[],[f2843,f5702]) ).
tff(f2843,plain,
! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( sP17(X2,X0,X1)
| ~ 'fun_app$'(X0,'bind$d'(X1,X2)) ),
inference(cnf_transformation,[],[f1641]) ).
tff(f5700,plain,
spl249_419,
inference(avatar_split_clause,[],[f2836,f5698]) ).
tff(f2836,plain,
! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( 'fun_app$'(X0,'bind$d'(X1,X2))
| ~ sP16(X2,X0,X1) ),
inference(cnf_transformation,[],[f1635]) ).
tff(f1635,plain,
! [X0: 'C_option_bool_fun$',X1: 'A_option$',X2: 'A_c_option_fun$'] :
( ( 'fun_app$'(X0,'bind$d'(X1,X2))
| ~ sP16(X2,X0,X1) )
& ( sP16(X2,X0,X1)
| ~ 'fun_app$'(X0,'bind$d'(X1,X2)) ) ),
inference(nnf_transformation,[],[f1132]) ).
tff(f1132,plain,
! [X0: 'C_option_bool_fun$',X1: 'A_option$',X2: 'A_c_option_fun$'] :
( 'fun_app$'(X0,'bind$d'(X1,X2))
<=> sP16(X2,X0,X1) ),
inference(definition_folding,[],[f1003,f1131]) ).
tff(f1003,plain,
! [X0: 'C_option_bool_fun$',X1: 'A_option$',X2: 'A_c_option_fun$'] :
( 'fun_app$'(X0,'bind$d'(X1,X2))
<=> ( ! [X3: 'A$'] :
( 'fun_app$'(X0,'fun_app$bm'(X2,X3))
| ( 'fun_app$q'('some$b',X3) != X1 ) )
& ( 'fun_app$'(X0,'none$')
| ( 'none$b' != X1 ) ) ) ),
inference(ennf_transformation,[],[f348]) ).
tff(f348,axiom,
! [X0: 'C_option_bool_fun$',X1: 'A_option$',X2: 'A_c_option_fun$'] :
( 'fun_app$'(X0,'bind$d'(X1,X2))
<=> ( ! [X3: 'A$'] :
( ( 'fun_app$q'('some$b',X3) = X1 )
=> 'fun_app$'(X0,'fun_app$bm'(X2,X3)) )
& ( ( 'none$b' = X1 )
=> 'fun_app$'(X0,'none$') ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom346) ).
tff(f5696,plain,
spl249_418,
inference(avatar_split_clause,[],[f2835,f5694]) ).
tff(f2835,plain,
! [X2: 'A_c_option_fun$',X0: 'C_option_bool_fun$',X1: 'A_option$'] :
( sP16(X2,X0,X1)
| ~ 'fun_app$'(X0,'bind$d'(X1,X2)) ),
inference(cnf_transformation,[],[f1635]) ).
tff(f5690,plain,
spl249_417,
inference(avatar_split_clause,[],[f2828,f5688]) ).
tff(f5688,plain,
( spl249_417
<=> ! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$aw'(X0,'bind$g'(X1,X2))
| ~ sP15(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_417])]) ).
tff(f2828,plain,
! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$aw'(X0,'bind$g'(X1,X2))
| ~ sP15(X2,X0,X1) ),
inference(cnf_transformation,[],[f1629]) ).
tff(f1629,plain,
! [X0: 'A_option_bool_fun$',X1: 'B_option$',X2: 'B_a_option_fun$'] :
( ( 'fun_app$aw'(X0,'bind$g'(X1,X2))
| ~ sP15(X2,X0,X1) )
& ( sP15(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'bind$g'(X1,X2)) ) ),
inference(nnf_transformation,[],[f1130]) ).
tff(f1130,plain,
! [X0: 'A_option_bool_fun$',X1: 'B_option$',X2: 'B_a_option_fun$'] :
( 'fun_app$aw'(X0,'bind$g'(X1,X2))
<=> sP15(X2,X0,X1) ),
inference(definition_folding,[],[f1002,f1129]) ).
tff(f1002,plain,
! [X0: 'A_option_bool_fun$',X1: 'B_option$',X2: 'B_a_option_fun$'] :
( 'fun_app$aw'(X0,'bind$g'(X1,X2))
<=> ( ! [X3: 'B$'] :
( 'fun_app$aw'(X0,'fun_app$bo'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$a' != X1 ) ) ) ),
inference(ennf_transformation,[],[f472]) ).
tff(f472,axiom,
! [X0: 'A_option_bool_fun$',X1: 'B_option$',X2: 'B_a_option_fun$'] :
( 'fun_app$aw'(X0,'bind$g'(X1,X2))
<=> ~ ( ? [X3: 'B$'] :
( ~ 'fun_app$aw'(X0,'fun_app$bo'(X2,X3))
& ( 'fun_app$g'('some$',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$a' = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom470) ).
tff(f5686,plain,
spl249_416,
inference(avatar_split_clause,[],[f2827,f5684]) ).
tff(f2827,plain,
! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( sP15(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'bind$g'(X1,X2)) ),
inference(cnf_transformation,[],[f1629]) ).
tff(f5682,plain,
spl249_415,
inference(avatar_split_clause,[],[f2820,f5680]) ).
tff(f5680,plain,
( spl249_415
<=> ! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$aw'(X0,'bind$f'(X1,X2))
| ~ sP14(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_415])]) ).
tff(f2820,plain,
! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$aw'(X0,'bind$f'(X1,X2))
| ~ sP14(X2,X0,X1) ),
inference(cnf_transformation,[],[f1623]) ).
tff(f1623,plain,
! [X0: 'A_option_bool_fun$',X1: 'C_option$',X2: 'C_a_option_fun$'] :
( ( 'fun_app$aw'(X0,'bind$f'(X1,X2))
| ~ sP14(X2,X0,X1) )
& ( sP14(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'bind$f'(X1,X2)) ) ),
inference(nnf_transformation,[],[f1128]) ).
tff(f1128,plain,
! [X0: 'A_option_bool_fun$',X1: 'C_option$',X2: 'C_a_option_fun$'] :
( 'fun_app$aw'(X0,'bind$f'(X1,X2))
<=> sP14(X2,X0,X1) ),
inference(definition_folding,[],[f1001,f1127]) ).
tff(f1001,plain,
! [X0: 'A_option_bool_fun$',X1: 'C_option$',X2: 'C_a_option_fun$'] :
( 'fun_app$aw'(X0,'bind$f'(X1,X2))
<=> ( ! [X3: 'C$'] :
( 'fun_app$aw'(X0,'fun_app$bn'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$' != X1 ) ) ) ),
inference(ennf_transformation,[],[f471]) ).
tff(f471,axiom,
! [X0: 'A_option_bool_fun$',X1: 'C_option$',X2: 'C_a_option_fun$'] :
( 'fun_app$aw'(X0,'bind$f'(X1,X2))
<=> ~ ( ? [X3: 'C$'] :
( ~ 'fun_app$aw'(X0,'fun_app$bn'(X2,X3))
& ( 'fun_app$j'('some$a',X3) = X1 ) )
| ( ~ 'fun_app$aw'(X0,'none$b')
& ( 'none$' = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom469) ).
tff(f5678,plain,
spl249_414,
inference(avatar_split_clause,[],[f2819,f5676]) ).
tff(f2819,plain,
! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( sP14(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'bind$f'(X1,X2)) ),
inference(cnf_transformation,[],[f1623]) ).
tff(f5674,plain,
spl249_413,
inference(avatar_split_clause,[],[f2812,f5672]) ).
tff(f5672,plain,
( spl249_413
<=> ! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$aw'(X0,'bind$g'(X1,X2))
| ~ sP13(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_413])]) ).
tff(f2812,plain,
! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$aw'(X0,'bind$g'(X1,X2))
| ~ sP13(X2,X0,X1) ),
inference(cnf_transformation,[],[f1617]) ).
tff(f1617,plain,
! [X0: 'A_option_bool_fun$',X1: 'B_option$',X2: 'B_a_option_fun$'] :
( ( 'fun_app$aw'(X0,'bind$g'(X1,X2))
| ~ sP13(X2,X0,X1) )
& ( sP13(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'bind$g'(X1,X2)) ) ),
inference(nnf_transformation,[],[f1126]) ).
tff(f1126,plain,
! [X0: 'A_option_bool_fun$',X1: 'B_option$',X2: 'B_a_option_fun$'] :
( 'fun_app$aw'(X0,'bind$g'(X1,X2))
<=> sP13(X2,X0,X1) ),
inference(definition_folding,[],[f1000,f1125]) ).
tff(f1000,plain,
! [X0: 'A_option_bool_fun$',X1: 'B_option$',X2: 'B_a_option_fun$'] :
( 'fun_app$aw'(X0,'bind$g'(X1,X2))
<=> ( ! [X3: 'B$'] :
( 'fun_app$aw'(X0,'fun_app$bo'(X2,X3))
| ( 'fun_app$g'('some$',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$a' != X1 ) ) ) ),
inference(ennf_transformation,[],[f347]) ).
tff(f347,axiom,
! [X0: 'A_option_bool_fun$',X1: 'B_option$',X2: 'B_a_option_fun$'] :
( 'fun_app$aw'(X0,'bind$g'(X1,X2))
<=> ( ! [X3: 'B$'] :
( ( 'fun_app$g'('some$',X3) = X1 )
=> 'fun_app$aw'(X0,'fun_app$bo'(X2,X3)) )
& ( ( 'none$a' = X1 )
=> 'fun_app$aw'(X0,'none$b') ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom345) ).
tff(f5670,plain,
spl249_412,
inference(avatar_split_clause,[],[f2811,f5668]) ).
tff(f2811,plain,
! [X2: 'B_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'B_option$'] :
( sP13(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'bind$g'(X1,X2)) ),
inference(cnf_transformation,[],[f1617]) ).
tff(f5666,plain,
spl249_411,
inference(avatar_split_clause,[],[f2804,f5664]) ).
tff(f5664,plain,
( spl249_411
<=> ! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$aw'(X0,'bind$f'(X1,X2))
| ~ sP12(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_411])]) ).
tff(f2804,plain,
! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$aw'(X0,'bind$f'(X1,X2))
| ~ sP12(X2,X0,X1) ),
inference(cnf_transformation,[],[f1611]) ).
tff(f1611,plain,
! [X0: 'A_option_bool_fun$',X1: 'C_option$',X2: 'C_a_option_fun$'] :
( ( 'fun_app$aw'(X0,'bind$f'(X1,X2))
| ~ sP12(X2,X0,X1) )
& ( sP12(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'bind$f'(X1,X2)) ) ),
inference(nnf_transformation,[],[f1124]) ).
tff(f1124,plain,
! [X0: 'A_option_bool_fun$',X1: 'C_option$',X2: 'C_a_option_fun$'] :
( 'fun_app$aw'(X0,'bind$f'(X1,X2))
<=> sP12(X2,X0,X1) ),
inference(definition_folding,[],[f999,f1123]) ).
tff(f999,plain,
! [X0: 'A_option_bool_fun$',X1: 'C_option$',X2: 'C_a_option_fun$'] :
( 'fun_app$aw'(X0,'bind$f'(X1,X2))
<=> ( ! [X3: 'C$'] :
( 'fun_app$aw'(X0,'fun_app$bn'(X2,X3))
| ( 'fun_app$j'('some$a',X3) != X1 ) )
& ( 'fun_app$aw'(X0,'none$b')
| ( 'none$' != X1 ) ) ) ),
inference(ennf_transformation,[],[f346]) ).
tff(f346,axiom,
! [X0: 'A_option_bool_fun$',X1: 'C_option$',X2: 'C_a_option_fun$'] :
( 'fun_app$aw'(X0,'bind$f'(X1,X2))
<=> ( ! [X3: 'C$'] :
( ( 'fun_app$j'('some$a',X3) = X1 )
=> 'fun_app$aw'(X0,'fun_app$bn'(X2,X3)) )
& ( ( 'none$' = X1 )
=> 'fun_app$aw'(X0,'none$b') ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom344) ).
tff(f5662,plain,
spl249_410,
inference(avatar_split_clause,[],[f2803,f5660]) ).
tff(f2803,plain,
! [X2: 'C_a_option_fun$',X0: 'A_option_bool_fun$',X1: 'C_option$'] :
( sP12(X2,X0,X1)
| ~ 'fun_app$aw'(X0,'bind$f'(X1,X2)) ),
inference(cnf_transformation,[],[f1611]) ).
tff(f5658,plain,
spl249_409,
inference(avatar_split_clause,[],[f2756,f5656]) ).
tff(f2756,plain,
! [X2: 'B_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'B_option$'] :
( ~ 'fun_app$a'('fun_app$e'(X2,X1),X0)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f1574]) ).
tff(f5654,plain,
spl249_408,
inference(avatar_split_clause,[],[f2749,f5652]) ).
tff(f5652,plain,
( spl249_408
<=> ! [X2: 'B_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'B_option$'] :
( ~ 'fun_app$'('fun_app$bd'(X2,X1),X0)
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_408])]) ).
tff(f2749,plain,
! [X2: 'B_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'B_option$'] :
( ~ 'fun_app$'('fun_app$bd'(X2,X1),X0)
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f1570]) ).
tff(f5648,plain,
spl249_407,
inference(avatar_split_clause,[],[f2742,f5646]) ).
tff(f5646,plain,
( spl249_407
<=> ! [X2: 'B_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'B_option$'] :
( ~ 'fun_app$aw'('fun_app$ay'(X2,X1),X0)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_407])]) ).
tff(f2742,plain,
! [X2: 'B_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'B_option$'] :
( ~ 'fun_app$aw'('fun_app$ay'(X2,X1),X0)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f1566]) ).
tff(f5644,plain,
spl249_406,
inference(avatar_split_clause,[],[f2735,f5642]) ).
tff(f5642,plain,
( spl249_406
<=> ! [X2: 'C_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'C_option$'] :
( ~ 'fun_app$a'('fun_app$bc'(X2,X1),X0)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_406])]) ).
tff(f2735,plain,
! [X2: 'C_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'C_option$'] :
( ~ 'fun_app$a'('fun_app$bc'(X2,X1),X0)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f1562]) ).
tff(f5640,plain,
spl249_405,
inference(avatar_split_clause,[],[f2728,f5638]) ).
tff(f2728,plain,
! [X2: 'C_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'C_option$'] :
( ~ 'fun_app$'('fun_app$d'(X2,X1),X0)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f1558]) ).
tff(f5636,plain,
spl249_404,
inference(avatar_split_clause,[],[f2721,f5634]) ).
tff(f5634,plain,
( spl249_404
<=> ! [X2: 'C_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'C_option$'] :
( ~ 'fun_app$aw'('fun_app$ax'(X2,X1),X0)
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_404])]) ).
tff(f2721,plain,
! [X2: 'C_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'C_option$'] :
( ~ 'fun_app$aw'('fun_app$ax'(X2,X1),X0)
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f1554]) ).
tff(f5632,plain,
spl249_403,
inference(avatar_split_clause,[],[f2714,f5630]) ).
tff(f5630,plain,
( spl249_403
<=> ! [X2: 'A_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'A_option$'] :
( ~ 'fun_app$a'('fun_app$ba'(X2,X1),X0)
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_403])]) ).
tff(f2714,plain,
! [X2: 'A_option_b_option_bool_fun_fun$',X0: 'B_option$',X1: 'A_option$'] :
( ~ 'fun_app$a'('fun_app$ba'(X2,X1),X0)
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f1550]) ).
tff(f5628,plain,
spl249_402,
inference(avatar_split_clause,[],[f2707,f5626]) ).
tff(f5626,plain,
( spl249_402
<=> ! [X2: 'A_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'A_option$'] :
( ~ 'fun_app$'('fun_app$az'(X2,X1),X0)
| ~ sP4(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_402])]) ).
tff(f2707,plain,
! [X2: 'A_option_c_option_bool_fun_fun$',X0: 'C_option$',X1: 'A_option$'] :
( ~ 'fun_app$'('fun_app$az'(X2,X1),X0)
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f1546]) ).
tff(f5624,plain,
spl249_401,
inference(avatar_split_clause,[],[f2700,f5622]) ).
tff(f5622,plain,
( spl249_401
<=> ! [X2: 'A_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ~ 'fun_app$aw'('fun_app$bb'(X2,X1),X0)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_401])]) ).
tff(f2700,plain,
! [X2: 'A_option_a_option_bool_fun_fun$',X0: 'A_option$',X1: 'A_option$'] :
( ~ 'fun_app$aw'('fun_app$bb'(X2,X1),X0)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f1542]) ).
tff(f5620,plain,
spl249_400,
inference(avatar_split_clause,[],[f2538,f5618]) ).
tff(f5618,plain,
( spl249_400
<=> ! [X0: 'B_b_fun$',X1: 'B_option$'] :
( 'fun_app$a'('is_none$','fun_app$s'('map_option$b'(X0),X1))
| ~ 'fun_app$a'('is_none$',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_400])]) ).
tff(f2538,plain,
! [X0: 'B_b_fun$',X1: 'B_option$'] :
( 'fun_app$a'('is_none$','fun_app$s'('map_option$b'(X0),X1))
| ~ 'fun_app$a'('is_none$',X1) ),
inference(cnf_transformation,[],[f1529]) ).
tff(f1529,plain,
! [X0: 'B_b_fun$',X1: 'B_option$'] :
( ( 'fun_app$a'('is_none$','fun_app$s'('map_option$b'(X0),X1))
| ~ 'fun_app$a'('is_none$',X1) )
& ( 'fun_app$a'('is_none$',X1)
| ~ 'fun_app$a'('is_none$','fun_app$s'('map_option$b'(X0),X1)) ) ),
inference(nnf_transformation,[],[f380]) ).
tff(f380,axiom,
! [X0: 'B_b_fun$',X1: 'B_option$'] :
( 'fun_app$a'('is_none$','fun_app$s'('map_option$b'(X0),X1))
<=> 'fun_app$a'('is_none$',X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom378) ).
tff(f5616,plain,
spl249_399,
inference(avatar_split_clause,[],[f2537,f5614]) ).
tff(f5614,plain,
( spl249_399
<=> ! [X0: 'B_b_fun$',X1: 'B_option$'] :
( 'fun_app$a'('is_none$',X1)
| ~ 'fun_app$a'('is_none$','fun_app$s'('map_option$b'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_399])]) ).
tff(f2537,plain,
! [X0: 'B_b_fun$',X1: 'B_option$'] :
( 'fun_app$a'('is_none$',X1)
| ~ 'fun_app$a'('is_none$','fun_app$s'('map_option$b'(X0),X1)) ),
inference(cnf_transformation,[],[f1529]) ).
tff(f5612,plain,
spl249_398,
inference(avatar_split_clause,[],[f2536,f5610]) ).
tff(f5610,plain,
( spl249_398
<=> ! [X0: 'A_b_fun$',X1: 'A_option$'] :
( 'fun_app$a'('is_none$','fun_app$av'('map_option$e'(X0),X1))
| ~ 'fun_app$aw'('is_none$b',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_398])]) ).
tff(f2536,plain,
! [X0: 'A_b_fun$',X1: 'A_option$'] :
( 'fun_app$a'('is_none$','fun_app$av'('map_option$e'(X0),X1))
| ~ 'fun_app$aw'('is_none$b',X1) ),
inference(cnf_transformation,[],[f1528]) ).
tff(f1528,plain,
! [X0: 'A_b_fun$',X1: 'A_option$'] :
( ( 'fun_app$a'('is_none$','fun_app$av'('map_option$e'(X0),X1))
| ~ 'fun_app$aw'('is_none$b',X1) )
& ( 'fun_app$aw'('is_none$b',X1)
| ~ 'fun_app$a'('is_none$','fun_app$av'('map_option$e'(X0),X1)) ) ),
inference(nnf_transformation,[],[f381]) ).
tff(f381,axiom,
! [X0: 'A_b_fun$',X1: 'A_option$'] :
( 'fun_app$a'('is_none$','fun_app$av'('map_option$e'(X0),X1))
<=> 'fun_app$aw'('is_none$b',X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom379) ).
tff(f5606,plain,
spl249_397,
inference(avatar_split_clause,[],[f2535,f5604]) ).
tff(f5604,plain,
( spl249_397
<=> ! [X0: 'A_b_fun$',X1: 'A_option$'] :
( 'fun_app$aw'('is_none$b',X1)
| ~ 'fun_app$a'('is_none$','fun_app$av'('map_option$e'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_397])]) ).
tff(f2535,plain,
! [X0: 'A_b_fun$',X1: 'A_option$'] :
( 'fun_app$aw'('is_none$b',X1)
| ~ 'fun_app$a'('is_none$','fun_app$av'('map_option$e'(X0),X1)) ),
inference(cnf_transformation,[],[f1528]) ).
tff(f5602,plain,
spl249_396,
inference(avatar_split_clause,[],[f2534,f5600]) ).
tff(f5600,plain,
( spl249_396
<=> ! [X0: 'C_b_fun$',X1: 'C_option$'] :
( 'fun_app$a'('is_none$','fun_app$bg'('map_option$'(X0),X1))
| ~ 'fun_app$'('is_none$a',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_396])]) ).
tff(f2534,plain,
! [X0: 'C_b_fun$',X1: 'C_option$'] :
( 'fun_app$a'('is_none$','fun_app$bg'('map_option$'(X0),X1))
| ~ 'fun_app$'('is_none$a',X1) ),
inference(cnf_transformation,[],[f1527]) ).
tff(f1527,plain,
! [X0: 'C_b_fun$',X1: 'C_option$'] :
( ( 'fun_app$a'('is_none$','fun_app$bg'('map_option$'(X0),X1))
| ~ 'fun_app$'('is_none$a',X1) )
& ( 'fun_app$'('is_none$a',X1)
| ~ 'fun_app$a'('is_none$','fun_app$bg'('map_option$'(X0),X1)) ) ),
inference(nnf_transformation,[],[f378]) ).
tff(f378,axiom,
! [X0: 'C_b_fun$',X1: 'C_option$'] :
( 'fun_app$a'('is_none$','fun_app$bg'('map_option$'(X0),X1))
<=> 'fun_app$'('is_none$a',X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom376) ).
tff(f5598,plain,
spl249_395,
inference(avatar_split_clause,[],[f2533,f5596]) ).
tff(f5596,plain,
( spl249_395
<=> ! [X0: 'C_b_fun$',X1: 'C_option$'] :
( 'fun_app$'('is_none$a',X1)
| ~ 'fun_app$a'('is_none$','fun_app$bg'('map_option$'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_395])]) ).
tff(f2533,plain,
! [X0: 'C_b_fun$',X1: 'C_option$'] :
( 'fun_app$'('is_none$a',X1)
| ~ 'fun_app$a'('is_none$','fun_app$bg'('map_option$'(X0),X1)) ),
inference(cnf_transformation,[],[f1527]) ).
tff(f5594,plain,
spl249_394,
inference(avatar_split_clause,[],[f2531,f5592]) ).
tff(f2531,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'('is_none$','fun_app$ac'('bind$c'(X0),X1))
| ~ 'fun_app$a'('is_none$',X0) ),
inference(cnf_transformation,[],[f1526]) ).
tff(f5590,plain,
spl249_393,
inference(avatar_split_clause,[],[f2529,f5588]) ).
tff(f5588,plain,
( spl249_393
<=> ! [X0: 'B_c_fun$',X1: 'B_option$'] :
( 'fun_app$'('is_none$a','fun_app$an'('map_option$d'(X0),X1))
| ~ 'fun_app$a'('is_none$',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_393])]) ).
tff(f2529,plain,
! [X0: 'B_c_fun$',X1: 'B_option$'] :
( 'fun_app$'('is_none$a','fun_app$an'('map_option$d'(X0),X1))
| ~ 'fun_app$a'('is_none$',X1) ),
inference(cnf_transformation,[],[f1524]) ).
tff(f1524,plain,
! [X0: 'B_c_fun$',X1: 'B_option$'] :
( ( 'fun_app$'('is_none$a','fun_app$an'('map_option$d'(X0),X1))
| ~ 'fun_app$a'('is_none$',X1) )
& ( 'fun_app$a'('is_none$',X1)
| ~ 'fun_app$'('is_none$a','fun_app$an'('map_option$d'(X0),X1)) ) ),
inference(nnf_transformation,[],[f379]) ).
tff(f379,axiom,
! [X0: 'B_c_fun$',X1: 'B_option$'] :
( 'fun_app$'('is_none$a','fun_app$an'('map_option$d'(X0),X1))
<=> 'fun_app$a'('is_none$',X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom377) ).
tff(f5586,plain,
spl249_392,
inference(avatar_split_clause,[],[f2528,f5584]) ).
tff(f5584,plain,
( spl249_392
<=> ! [X0: 'B_c_fun$',X1: 'B_option$'] :
( 'fun_app$a'('is_none$',X1)
| ~ 'fun_app$'('is_none$a','fun_app$an'('map_option$d'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_392])]) ).
tff(f2528,plain,
! [X0: 'B_c_fun$',X1: 'B_option$'] :
( 'fun_app$a'('is_none$',X1)
| ~ 'fun_app$'('is_none$a','fun_app$an'('map_option$d'(X0),X1)) ),
inference(cnf_transformation,[],[f1524]) ).
tff(f5582,plain,
spl249_391,
inference(avatar_split_clause,[],[f2527,f5580]) ).
tff(f5580,plain,
( spl249_391
<=> ! [X0: 'C_c_fun$',X1: 'C_option$'] :
( 'fun_app$'('is_none$a','fun_app$u'('map_option$c'(X0),X1))
| ~ 'fun_app$'('is_none$a',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_391])]) ).
tff(f2527,plain,
! [X0: 'C_c_fun$',X1: 'C_option$'] :
( 'fun_app$'('is_none$a','fun_app$u'('map_option$c'(X0),X1))
| ~ 'fun_app$'('is_none$a',X1) ),
inference(cnf_transformation,[],[f1523]) ).
tff(f1523,plain,
! [X0: 'C_c_fun$',X1: 'C_option$'] :
( ( 'fun_app$'('is_none$a','fun_app$u'('map_option$c'(X0),X1))
| ~ 'fun_app$'('is_none$a',X1) )
& ( 'fun_app$'('is_none$a',X1)
| ~ 'fun_app$'('is_none$a','fun_app$u'('map_option$c'(X0),X1)) ) ),
inference(nnf_transformation,[],[f377]) ).
tff(f377,axiom,
! [X0: 'C_c_fun$',X1: 'C_option$'] :
( 'fun_app$'('is_none$a','fun_app$u'('map_option$c'(X0),X1))
<=> 'fun_app$'('is_none$a',X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom375) ).
tff(f5578,plain,
spl249_390,
inference(avatar_split_clause,[],[f2526,f5576]) ).
tff(f5576,plain,
( spl249_390
<=> ! [X0: 'C_c_fun$',X1: 'C_option$'] :
( 'fun_app$'('is_none$a',X1)
| ~ 'fun_app$'('is_none$a','fun_app$u'('map_option$c'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_390])]) ).
tff(f2526,plain,
! [X0: 'C_c_fun$',X1: 'C_option$'] :
( 'fun_app$'('is_none$a',X1)
| ~ 'fun_app$'('is_none$a','fun_app$u'('map_option$c'(X0),X1)) ),
inference(cnf_transformation,[],[f1523]) ).
tff(f5574,plain,
spl249_389,
inference(avatar_split_clause,[],[f2524,f5572]) ).
tff(f2524,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$'] :
( 'fun_app$'('is_none$a','fun_app$ab'('bind$'(X0),X1))
| ~ 'fun_app$'('is_none$a',X0) ),
inference(cnf_transformation,[],[f1522]) ).
tff(f5570,plain,
spl249_388,
inference(avatar_split_clause,[],[f2522,f5568]) ).
tff(f5568,plain,
( spl249_388
<=> ! [X0: 'A_a_fun$',X1: 'A_option$'] :
( 'fun_app$aw'('is_none$b','fun_app$be'('map_option$a'(X0),X1))
| ~ 'fun_app$aw'('is_none$b',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_388])]) ).
tff(f2522,plain,
! [X0: 'A_a_fun$',X1: 'A_option$'] :
( 'fun_app$aw'('is_none$b','fun_app$be'('map_option$a'(X0),X1))
| ~ 'fun_app$aw'('is_none$b',X1) ),
inference(cnf_transformation,[],[f1520]) ).
tff(f1520,plain,
! [X0: 'A_a_fun$',X1: 'A_option$'] :
( ( 'fun_app$aw'('is_none$b','fun_app$be'('map_option$a'(X0),X1))
| ~ 'fun_app$aw'('is_none$b',X1) )
& ( 'fun_app$aw'('is_none$b',X1)
| ~ 'fun_app$aw'('is_none$b','fun_app$be'('map_option$a'(X0),X1)) ) ),
inference(nnf_transformation,[],[f382]) ).
tff(f382,axiom,
! [X0: 'A_a_fun$',X1: 'A_option$'] :
( 'fun_app$aw'('is_none$b','fun_app$be'('map_option$a'(X0),X1))
<=> 'fun_app$aw'('is_none$b',X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom380) ).
tff(f5566,plain,
( spl249_387
| ~ spl249_20
| ~ spl249_304 ),
inference(avatar_split_clause,[],[f5303,f5020,f3692,f5564]) ).
tff(f5564,plain,
( spl249_387
<=> ! [X0: 'B$'] : ( tltrue = def_3('uug$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_387])]) ).
tff(f5303,plain,
( ! [X0: 'B$'] : ( tltrue = def_3('uug$',X0) )
| ~ spl249_20
| ~ spl249_304 ),
inference(resolution,[],[f5021,f3693]) ).
tff(f5562,plain,
spl249_386,
inference(avatar_split_clause,[],[f2521,f5560]) ).
tff(f5560,plain,
( spl249_386
<=> ! [X0: 'A_a_fun$',X1: 'A_option$'] :
( 'fun_app$aw'('is_none$b',X1)
| ~ 'fun_app$aw'('is_none$b','fun_app$be'('map_option$a'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_386])]) ).
tff(f2521,plain,
! [X0: 'A_a_fun$',X1: 'A_option$'] :
( 'fun_app$aw'('is_none$b',X1)
| ~ 'fun_app$aw'('is_none$b','fun_app$be'('map_option$a'(X0),X1)) ),
inference(cnf_transformation,[],[f1520]) ).
tff(f5558,plain,
spl249_385,
inference(avatar_split_clause,[],[f2515,f5556]) ).
tff(f5556,plain,
( spl249_385
<=> ! [X0: 'B_b_fun$',X1: 'B_option$'] :
( ( 'none$a' = X1 )
| ( 'none$a' != 'fun_app$s'('map_option$b'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_385])]) ).
tff(f2515,plain,
! [X0: 'B_b_fun$',X1: 'B_option$'] :
( ( 'none$a' = X1 )
| ( 'none$a' != 'fun_app$s'('map_option$b'(X0),X1) ) ),
inference(cnf_transformation,[],[f1517]) ).
tff(f1517,plain,
! [X0: 'B_b_fun$',X1: 'B_option$'] :
( ( ( 'none$a' = 'fun_app$s'('map_option$b'(X0),X1) )
| ( 'none$a' != X1 ) )
& ( ( 'none$a' = X1 )
| ( 'none$a' != 'fun_app$s'('map_option$b'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f227]) ).
tff(f227,axiom,
! [X0: 'B_b_fun$',X1: 'B_option$'] :
( ( 'none$a' = 'fun_app$s'('map_option$b'(X0),X1) )
<=> ( 'none$a' = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom225) ).
tff(f5554,plain,
spl249_384,
inference(avatar_split_clause,[],[f2509,f5552]) ).
tff(f5552,plain,
( spl249_384
<=> ! [X0: 'A_b_fun$',X1: 'A_option$'] :
( ( 'none$b' = X1 )
| ( 'none$a' != 'fun_app$av'('map_option$e'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_384])]) ).
tff(f2509,plain,
! [X0: 'A_b_fun$',X1: 'A_option$'] :
( ( 'none$b' = X1 )
| ( 'none$a' != 'fun_app$av'('map_option$e'(X0),X1) ) ),
inference(cnf_transformation,[],[f1514]) ).
tff(f1514,plain,
! [X0: 'A_b_fun$',X1: 'A_option$'] :
( ( ( 'none$a' = 'fun_app$av'('map_option$e'(X0),X1) )
| ( 'none$b' != X1 ) )
& ( ( 'none$b' = X1 )
| ( 'none$a' != 'fun_app$av'('map_option$e'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f213]) ).
tff(f213,axiom,
! [X0: 'A_b_fun$',X1: 'A_option$'] :
( ( 'none$a' = 'fun_app$av'('map_option$e'(X0),X1) )
<=> ( 'none$b' = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom211) ).
tff(f5550,plain,
spl249_383,
inference(avatar_split_clause,[],[f2503,f5548]) ).
tff(f5548,plain,
( spl249_383
<=> ! [X0: 'C_b_fun$',X1: 'C_option$'] :
( ( 'none$' = X1 )
| ( 'none$a' != 'fun_app$bg'('map_option$'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_383])]) ).
tff(f2503,plain,
! [X0: 'C_b_fun$',X1: 'C_option$'] :
( ( 'none$' = X1 )
| ( 'none$a' != 'fun_app$bg'('map_option$'(X0),X1) ) ),
inference(cnf_transformation,[],[f1511]) ).
tff(f1511,plain,
! [X0: 'C_b_fun$',X1: 'C_option$'] :
( ( ( 'none$a' = 'fun_app$bg'('map_option$'(X0),X1) )
| ( 'none$' != X1 ) )
& ( ( 'none$' = X1 )
| ( 'none$a' != 'fun_app$bg'('map_option$'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f217]) ).
tff(f217,axiom,
! [X0: 'C_b_fun$',X1: 'C_option$'] :
( ( 'none$a' = 'fun_app$bg'('map_option$'(X0),X1) )
<=> ( 'none$' = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom215) ).
tff(f5546,plain,
spl249_382,
inference(avatar_split_clause,[],[f2494,f5544]) ).
tff(f5544,plain,
( spl249_382
<=> ! [X0: 'B_c_fun$',X1: 'B_option$'] :
( ( 'none$a' = X1 )
| ( 'none$' != 'fun_app$an'('map_option$d'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_382])]) ).
tff(f2494,plain,
! [X0: 'B_c_fun$',X1: 'B_option$'] :
( ( 'none$a' = X1 )
| ( 'none$' != 'fun_app$an'('map_option$d'(X0),X1) ) ),
inference(cnf_transformation,[],[f1506]) ).
tff(f1506,plain,
! [X0: 'B_c_fun$',X1: 'B_option$'] :
( ( ( 'none$' = 'fun_app$an'('map_option$d'(X0),X1) )
| ( 'none$a' != X1 ) )
& ( ( 'none$a' = X1 )
| ( 'none$' != 'fun_app$an'('map_option$d'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f216]) ).
tff(f216,axiom,
! [X0: 'B_c_fun$',X1: 'B_option$'] :
( ( 'none$' = 'fun_app$an'('map_option$d'(X0),X1) )
<=> ( 'none$a' = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom214) ).
tff(f5542,plain,
spl249_381,
inference(avatar_split_clause,[],[f2488,f5540]) ).
tff(f5540,plain,
( spl249_381
<=> ! [X0: 'C_c_fun$',X1: 'C_option$'] :
( ( 'none$' = X1 )
| ( 'none$' != 'fun_app$u'('map_option$c'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_381])]) ).
tff(f2488,plain,
! [X0: 'C_c_fun$',X1: 'C_option$'] :
( ( 'none$' = X1 )
| ( 'none$' != 'fun_app$u'('map_option$c'(X0),X1) ) ),
inference(cnf_transformation,[],[f1503]) ).
tff(f1503,plain,
! [X0: 'C_c_fun$',X1: 'C_option$'] :
( ( ( 'none$' = 'fun_app$u'('map_option$c'(X0),X1) )
| ( 'none$' != X1 ) )
& ( ( 'none$' = X1 )
| ( 'none$' != 'fun_app$u'('map_option$c'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f206]) ).
tff(f206,axiom,
! [X0: 'C_c_fun$',X1: 'C_option$'] :
( ( 'none$' = 'fun_app$u'('map_option$c'(X0),X1) )
<=> ( 'none$' = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom204) ).
tff(f5538,plain,
spl249_380,
inference(avatar_split_clause,[],[f2479,f5536]) ).
tff(f5536,plain,
( spl249_380
<=> ! [X0: 'A_c_fun$',X1: 'A_option$'] :
( ( 'none$b' = X1 )
| ( 'none$' != 'fun_app$bh'('map_option$f'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_380])]) ).
tff(f2479,plain,
! [X0: 'A_c_fun$',X1: 'A_option$'] :
( ( 'none$b' = X1 )
| ( 'none$' != 'fun_app$bh'('map_option$f'(X0),X1) ) ),
inference(cnf_transformation,[],[f1498]) ).
tff(f1498,plain,
! [X0: 'A_c_fun$',X1: 'A_option$'] :
( ( ( 'none$' = 'fun_app$bh'('map_option$f'(X0),X1) )
| ( 'none$b' != X1 ) )
& ( ( 'none$b' = X1 )
| ( 'none$' != 'fun_app$bh'('map_option$f'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f201]) ).
tff(f201,axiom,
! [X0: 'A_c_fun$',X1: 'A_option$'] :
( ( 'none$' = 'fun_app$bh'('map_option$f'(X0),X1) )
<=> ( 'none$b' = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom199) ).
tff(f5534,plain,
spl249_379,
inference(avatar_split_clause,[],[f2473,f5532]) ).
tff(f5532,plain,
( spl249_379
<=> ! [X0: 'A_a_fun$',X1: 'A_option$'] :
( ( 'none$b' = X1 )
| ( 'none$b' != 'fun_app$be'('map_option$a'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_379])]) ).
tff(f2473,plain,
! [X0: 'A_a_fun$',X1: 'A_option$'] :
( ( 'none$b' = X1 )
| ( 'none$b' != 'fun_app$be'('map_option$a'(X0),X1) ) ),
inference(cnf_transformation,[],[f1495]) ).
tff(f1495,plain,
! [X0: 'A_a_fun$',X1: 'A_option$'] :
( ( ( 'none$b' = 'fun_app$be'('map_option$a'(X0),X1) )
| ( 'none$b' != X1 ) )
& ( ( 'none$b' = X1 )
| ( 'none$b' != 'fun_app$be'('map_option$a'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f205]) ).
tff(f205,axiom,
! [X0: 'A_a_fun$',X1: 'A_option$'] :
( ( 'none$b' = 'fun_app$be'('map_option$a'(X0),X1) )
<=> ( 'none$b' = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom203) ).
tff(f5530,plain,
spl249_378,
inference(avatar_split_clause,[],[f2467,f5528]) ).
tff(f5528,plain,
( spl249_378
<=> ! [X0: 'B_a_fun$',X1: 'B_option$'] :
( ( 'none$a' = X1 )
| ( 'none$b' != 'fun_app$bj'('map_option$h'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_378])]) ).
tff(f2467,plain,
! [X0: 'B_a_fun$',X1: 'B_option$'] :
( ( 'none$a' = X1 )
| ( 'none$b' != 'fun_app$bj'('map_option$h'(X0),X1) ) ),
inference(cnf_transformation,[],[f1492]) ).
tff(f1492,plain,
! [X0: 'B_a_fun$',X1: 'B_option$'] :
( ( ( 'none$b' = 'fun_app$bj'('map_option$h'(X0),X1) )
| ( 'none$a' != X1 ) )
& ( ( 'none$a' = X1 )
| ( 'none$b' != 'fun_app$bj'('map_option$h'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f212]) ).
tff(f212,axiom,
! [X0: 'B_a_fun$',X1: 'B_option$'] :
( ( 'none$b' = 'fun_app$bj'('map_option$h'(X0),X1) )
<=> ( 'none$a' = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom210) ).
tff(f5526,plain,
spl249_377,
inference(avatar_split_clause,[],[f2461,f5524]) ).
tff(f5524,plain,
( spl249_377
<=> ! [X0: 'C_a_fun$',X1: 'C_option$'] :
( ( 'none$' = X1 )
| ( 'none$b' != 'fun_app$bi'('map_option$g'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_377])]) ).
tff(f2461,plain,
! [X0: 'C_a_fun$',X1: 'C_option$'] :
( ( 'none$' = X1 )
| ( 'none$b' != 'fun_app$bi'('map_option$g'(X0),X1) ) ),
inference(cnf_transformation,[],[f1489]) ).
tff(f1489,plain,
! [X0: 'C_a_fun$',X1: 'C_option$'] :
( ( ( 'none$b' = 'fun_app$bi'('map_option$g'(X0),X1) )
| ( 'none$' != X1 ) )
& ( ( 'none$' = X1 )
| ( 'none$b' != 'fun_app$bi'('map_option$g'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f202]) ).
tff(f202,axiom,
! [X0: 'C_a_fun$',X1: 'C_option$'] :
( ( 'none$b' = 'fun_app$bi'('map_option$g'(X0),X1) )
<=> ( 'none$' = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom200) ).
tff(f5522,plain,
( spl249_376
| ~ spl249_20
| ~ spl249_302 ),
inference(avatar_split_clause,[],[f5295,f5012,f3692,f5520]) ).
tff(f5520,plain,
( spl249_376
<=> ! [X0: 'B$'] : ( tltrue = def_2('uug$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_376])]) ).
tff(f5295,plain,
( ! [X0: 'B$'] : ( tltrue = def_2('uug$',X0) )
| ~ spl249_20
| ~ spl249_302 ),
inference(resolution,[],[f5013,f3693]) ).
tff(f5518,plain,
spl249_375,
inference(avatar_split_clause,[],[f2385,f5516]) ).
tff(f5516,plain,
( spl249_375
<=> ! [X0: 'B$',X1: 'B_option_set$'] :
( 'member$c'(X0,'these$a'(X1))
| ~ 'member$a'('fun_app$g'('some$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_375])]) ).
tff(f2385,plain,
! [X0: 'B$',X1: 'B_option_set$'] :
( 'member$c'(X0,'these$a'(X1))
| ~ 'member$a'('fun_app$g'('some$',X0),X1) ),
inference(cnf_transformation,[],[f1445]) ).
tff(f1445,plain,
! [X0: 'B$',X1: 'B_option_set$'] :
( ( 'member$c'(X0,'these$a'(X1))
| ~ 'member$a'('fun_app$g'('some$',X0),X1) )
& ( 'member$a'('fun_app$g'('some$',X0),X1)
| ~ 'member$c'(X0,'these$a'(X1)) ) ),
inference(nnf_transformation,[],[f701]) ).
tff(f701,axiom,
! [X0: 'B$',X1: 'B_option_set$'] :
( 'member$c'(X0,'these$a'(X1))
<=> 'member$a'('fun_app$g'('some$',X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom699) ).
tff(f5514,plain,
spl249_374,
inference(avatar_split_clause,[],[f2384,f5512]) ).
tff(f5512,plain,
( spl249_374
<=> ! [X0: 'B$',X1: 'B_option_set$'] :
( 'member$a'('fun_app$g'('some$',X0),X1)
| ~ 'member$c'(X0,'these$a'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_374])]) ).
tff(f2384,plain,
! [X0: 'B$',X1: 'B_option_set$'] :
( 'member$a'('fun_app$g'('some$',X0),X1)
| ~ 'member$c'(X0,'these$a'(X1)) ),
inference(cnf_transformation,[],[f1445]) ).
tff(f5510,plain,
spl249_373,
inference(avatar_split_clause,[],[f2379,f5508]) ).
tff(f5508,plain,
( spl249_373
<=> ! [X0: 'C$',X1: 'C_option_set$'] :
( 'member$b'(X0,'these$'(X1))
| ~ 'member$'('fun_app$j'('some$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_373])]) ).
tff(f2379,plain,
! [X0: 'C$',X1: 'C_option_set$'] :
( 'member$b'(X0,'these$'(X1))
| ~ 'member$'('fun_app$j'('some$a',X0),X1) ),
inference(cnf_transformation,[],[f1442]) ).
tff(f1442,plain,
! [X0: 'C$',X1: 'C_option_set$'] :
( ( 'member$b'(X0,'these$'(X1))
| ~ 'member$'('fun_app$j'('some$a',X0),X1) )
& ( 'member$'('fun_app$j'('some$a',X0),X1)
| ~ 'member$b'(X0,'these$'(X1)) ) ),
inference(nnf_transformation,[],[f700]) ).
tff(f700,axiom,
! [X0: 'C$',X1: 'C_option_set$'] :
( 'member$b'(X0,'these$'(X1))
<=> 'member$'('fun_app$j'('some$a',X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom698) ).
tff(f5506,plain,
spl249_372,
inference(avatar_split_clause,[],[f2378,f5504]) ).
tff(f5504,plain,
( spl249_372
<=> ! [X0: 'C$',X1: 'C_option_set$'] :
( 'member$'('fun_app$j'('some$a',X0),X1)
| ~ 'member$b'(X0,'these$'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_372])]) ).
tff(f2378,plain,
! [X0: 'C$',X1: 'C_option_set$'] :
( 'member$'('fun_app$j'('some$a',X0),X1)
| ~ 'member$b'(X0,'these$'(X1)) ),
inference(cnf_transformation,[],[f1442]) ).
tff(f5502,plain,
spl249_371,
inference(avatar_split_clause,[],[f2316,f5500]) ).
tff(f5500,plain,
( spl249_371
<=> ! [X0: 'B$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',X0) = X1 )
| ~ 'member$c'(X0,'set_option$d'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_371])]) ).
tff(f2316,plain,
! [X0: 'B$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',X0) = X1 )
| ~ 'member$c'(X0,'set_option$d'(X1)) ),
inference(cnf_transformation,[],[f936]) ).
tff(f936,plain,
! [X0: 'B$',X1: 'B_option$'] :
( ( 'fun_app$g'('some$',X0) = X1 )
| ~ 'member$c'(X0,'set_option$d'(X1)) ),
inference(ennf_transformation,[],[f819]) ).
tff(f819,plain,
! [X0: 'B$',X1: 'B_option$'] :
~ ( ( 'fun_app$g'('some$',X0) != X1 )
& 'member$c'(X0,'set_option$d'(X1)) ),
inference(flattening,[],[f818]) ).
tff(f818,plain,
! [X0: 'B$',X1: 'B_option$'] :
~ ( ( ~ 'fun_app$g'('some$',X0) = X1 )
& 'member$c'(X0,'set_option$d'(X1)) ),
inference(true_and_false_elimination,[],[f441]) ).
tff(f441,axiom,
! [X0: 'B$',X1: 'B_option$'] :
( ( ( ( 'fun_app$g'('some$',X0) = X1 )
=> $false )
& 'member$c'(X0,'set_option$d'(X1)) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom439) ).
tff(f5498,plain,
spl249_370,
inference(avatar_split_clause,[],[f2315,f5496]) ).
tff(f5496,plain,
( spl249_370
<=> ! [X0: 'C$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',X0) = X1 )
| ~ 'member$b'(X0,'set_option$c'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_370])]) ).
tff(f2315,plain,
! [X0: 'C$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',X0) = X1 )
| ~ 'member$b'(X0,'set_option$c'(X1)) ),
inference(cnf_transformation,[],[f935]) ).
tff(f935,plain,
! [X0: 'C$',X1: 'C_option$'] :
( ( 'fun_app$j'('some$a',X0) = X1 )
| ~ 'member$b'(X0,'set_option$c'(X1)) ),
inference(ennf_transformation,[],[f817]) ).
tff(f817,plain,
! [X0: 'C$',X1: 'C_option$'] :
~ ( ( 'fun_app$j'('some$a',X0) != X1 )
& 'member$b'(X0,'set_option$c'(X1)) ),
inference(flattening,[],[f816]) ).
tff(f816,plain,
! [X0: 'C$',X1: 'C_option$'] :
~ ( ( ~ 'fun_app$j'('some$a',X0) = X1 )
& 'member$b'(X0,'set_option$c'(X1)) ),
inference(true_and_false_elimination,[],[f440]) ).
tff(f440,axiom,
! [X0: 'C$',X1: 'C_option$'] :
( ( ( ( 'fun_app$j'('some$a',X0) = X1 )
=> $false )
& 'member$b'(X0,'set_option$c'(X1)) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom438) ).
tff(f5494,plain,
spl249_369,
inference(avatar_split_clause,[],[f2314,f5492]) ).
tff(f5492,plain,
( spl249_369
<=> ! [X0: 'A$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',X0) = X1 )
| ~ 'member$d'(X0,'set_option$b'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_369])]) ).
tff(f2314,plain,
! [X0: 'A$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',X0) = X1 )
| ~ 'member$d'(X0,'set_option$b'(X1)) ),
inference(cnf_transformation,[],[f934]) ).
tff(f934,plain,
! [X0: 'A$',X1: 'A_option$'] :
( ( 'fun_app$q'('some$b',X0) = X1 )
| ~ 'member$d'(X0,'set_option$b'(X1)) ),
inference(ennf_transformation,[],[f815]) ).
tff(f815,plain,
! [X0: 'A$',X1: 'A_option$'] :
~ ( ( 'fun_app$q'('some$b',X0) != X1 )
& 'member$d'(X0,'set_option$b'(X1)) ),
inference(flattening,[],[f814]) ).
tff(f814,plain,
! [X0: 'A$',X1: 'A_option$'] :
~ ( ( ~ 'fun_app$q'('some$b',X0) = X1 )
& 'member$d'(X0,'set_option$b'(X1)) ),
inference(true_and_false_elimination,[],[f439]) ).
tff(f439,axiom,
! [X0: 'A$',X1: 'A_option$'] :
( ( ( ( 'fun_app$q'('some$b',X0) = X1 )
=> $false )
& 'member$d'(X0,'set_option$b'(X1)) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom437) ).
tff(f5490,plain,
spl249_368,
inference(avatar_split_clause,[],[f2303,f5488]) ).
tff(f2303,plain,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ( 'setter$a'('register_from_getter_setter$'(X0,X1)) = X1 )
| ~ 'valid_getter_setter$a'(X0,X1) ),
inference(cnf_transformation,[],[f918]) ).
tff(f918,plain,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ( 'setter$a'('register_from_getter_setter$'(X0,X1)) = X1 )
| ~ 'valid_getter_setter$a'(X0,X1) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,axiom,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( 'valid_getter_setter$a'(X0,X1)
=> ( 'setter$a'('register_from_getter_setter$'(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom167) ).
tff(f5486,plain,
spl249_367,
inference(avatar_split_clause,[],[f2302,f5484]) ).
tff(f2302,plain,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ( 'getter$a'('register_from_getter_setter$'(X0,X1)) = X0 )
| ~ 'valid_getter_setter$a'(X0,X1) ),
inference(cnf_transformation,[],[f917]) ).
tff(f917,plain,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( ( 'getter$a'('register_from_getter_setter$'(X0,X1)) = X0 )
| ~ 'valid_getter_setter$a'(X0,X1) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,axiom,
! [X0: 'B_a_fun$',X1: 'A_b_b_fun_fun$'] :
( 'valid_getter_setter$a'(X0,X1)
=> ( 'getter$a'('register_from_getter_setter$'(X0,X1)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom164) ).
tff(f5482,plain,
spl249_366,
inference(avatar_split_clause,[],[f2301,f5480]) ).
tff(f5480,plain,
( spl249_366
<=> ! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ( 'setter$'('register_from_getter_setter$a'(X0,X1)) = X1 )
| ~ 'valid_getter_setter$'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_366])]) ).
tff(f2301,plain,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ( 'setter$'('register_from_getter_setter$a'(X0,X1)) = X1 )
| ~ 'valid_getter_setter$'(X0,X1) ),
inference(cnf_transformation,[],[f916]) ).
tff(f916,plain,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ( 'setter$'('register_from_getter_setter$a'(X0,X1)) = X1 )
| ~ 'valid_getter_setter$'(X0,X1) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,axiom,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( 'valid_getter_setter$'(X0,X1)
=> ( 'setter$'('register_from_getter_setter$a'(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom166) ).
tff(f5478,plain,
( spl249_365
| ~ spl249_20
| ~ spl249_299 ),
inference(avatar_split_clause,[],[f5287,f4999,f3692,f5476]) ).
tff(f5476,plain,
( spl249_365
<=> ! [X0: 'B$'] : ( tltrue = def_5('uug$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_365])]) ).
tff(f5287,plain,
( ! [X0: 'B$'] : ( tltrue = def_5('uug$',X0) )
| ~ spl249_20
| ~ spl249_299 ),
inference(resolution,[],[f5000,f3693]) ).
tff(f5474,plain,
spl249_364,
inference(avatar_split_clause,[],[f2300,f5472]) ).
tff(f5472,plain,
( spl249_364
<=> ! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ( 'getter$'('register_from_getter_setter$a'(X0,X1)) = X0 )
| ~ 'valid_getter_setter$'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_364])]) ).
tff(f2300,plain,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ( 'getter$'('register_from_getter_setter$a'(X0,X1)) = X0 )
| ~ 'valid_getter_setter$'(X0,X1) ),
inference(cnf_transformation,[],[f915]) ).
tff(f915,plain,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( ( 'getter$'('register_from_getter_setter$a'(X0,X1)) = X0 )
| ~ 'valid_getter_setter$'(X0,X1) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,axiom,
! [X0: 'C_b_fun$',X1: 'B_c_c_fun_fun$'] :
( 'valid_getter_setter$'(X0,X1)
=> ( 'getter$'('register_from_getter_setter$a'(X0,X1)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom163) ).
tff(f5470,plain,
spl249_363,
inference(avatar_split_clause,[],[f2232,f5468]) ).
tff(f5468,plain,
( spl249_363
<=> ! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C$'] : ( 'fun_app$m'('getter$'(X0),X1) = 'the$d'('uvr$'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_363])]) ).
tff(f2232,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C$'] : ( 'fun_app$m'('getter$'(X0),X1) = 'the$d'('uvr$'(X0,X1)) ),
inference(cnf_transformation,[],[f319]) ).
tff(f319,axiom,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C$'] : ( 'fun_app$m'('getter$'(X0),X1) = 'the$d'('uvr$'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom317) ).
tff(f5466,plain,
spl249_362,
inference(avatar_split_clause,[],[f2231,f5464]) ).
tff(f5464,plain,
( spl249_362
<=> ! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B$'] : ( 'fun_app$ao'('getter$a'(X0),X1) = 'the$c'('uvq$'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_362])]) ).
tff(f2231,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B$'] : ( 'fun_app$ao'('getter$a'(X0),X1) = 'the$c'('uvq$'(X0,X1)) ),
inference(cnf_transformation,[],[f318]) ).
tff(f318,axiom,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B$'] : ( 'fun_app$ao'('getter$a'(X0),X1) = 'the$c'('uvq$'(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom316) ).
tff(f5462,plain,
spl249_361,
inference(avatar_split_clause,[],[f2210,f5460]) ).
tff(f5460,plain,
( spl249_361
<=> ! [X2: 'B$',X0: 'B_option_bool_fun$'] :
( 'fun_app$a'(X0,sK109(X0))
| ~ 'fun_app$a'(X0,'fun_app$g'('some$',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_361])]) ).
tff(f2210,plain,
! [X2: 'B$',X0: 'B_option_bool_fun$'] :
( 'fun_app$a'(X0,sK109(X0))
| ~ 'fun_app$a'(X0,'fun_app$g'('some$',X2)) ),
inference(cnf_transformation,[],[f1382]) ).
tff(f5458,plain,
spl249_360,
inference(avatar_split_clause,[],[f2207,f5456]) ).
tff(f5456,plain,
( spl249_360
<=> ! [X2: 'C$',X0: 'C_option_bool_fun$'] :
( 'fun_app$'(X0,sK107(X0))
| ~ 'fun_app$'(X0,'fun_app$j'('some$a',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_360])]) ).
tff(f2207,plain,
! [X2: 'C$',X0: 'C_option_bool_fun$'] :
( 'fun_app$'(X0,sK107(X0))
| ~ 'fun_app$'(X0,'fun_app$j'('some$a',X2)) ),
inference(cnf_transformation,[],[f1376]) ).
tff(f5454,plain,
spl249_359,
inference(avatar_split_clause,[],[f2204,f5452]) ).
tff(f5452,plain,
( spl249_359
<=> ! [X2: 'A$',X0: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X0,sK105(X0))
| ~ 'fun_app$aw'(X0,'fun_app$q'('some$b',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_359])]) ).
tff(f2204,plain,
! [X2: 'A$',X0: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X0,sK105(X0))
| ~ 'fun_app$aw'(X0,'fun_app$q'('some$b',X2)) ),
inference(cnf_transformation,[],[f1370]) ).
tff(f5450,plain,
spl249_358,
inference(avatar_split_clause,[],[f2196,f5448]) ).
tff(f5448,plain,
( spl249_358
<=> ! [X0: 'B_option$'] :
( ( 'none$a' = X0 )
| ( 'fun_app$g'('some$',sK102(X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_358])]) ).
tff(f2196,plain,
! [X0: 'B_option$'] :
( ( 'none$a' = X0 )
| ( 'fun_app$g'('some$',sK102(X0)) = X0 ) ),
inference(cnf_transformation,[],[f1356]) ).
tff(f1356,plain,
! [X0: 'B_option$'] :
( ( ! [X1: 'B$'] : ( 'fun_app$g'('some$',X1) != X0 )
| ( 'none$a' != X0 ) )
& ( ( 'none$a' = X0 )
| ( 'fun_app$g'('some$',sK102(X0)) = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK102])],[f1354,f1355]) ).
tff(f1355,plain,
! [X0: 'B_option$'] :
( ? [X2: 'B$'] : ( 'fun_app$g'('some$',X2) = X0 )
=> ( 'fun_app$g'('some$',sK102(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f1354,plain,
! [X0: 'B_option$'] :
( ( ! [X1: 'B$'] : ( 'fun_app$g'('some$',X1) != X0 )
| ( 'none$a' != X0 ) )
& ( ( 'none$a' = X0 )
| ? [X2: 'B$'] : ( 'fun_app$g'('some$',X2) = X0 ) ) ),
inference(rectify,[],[f1353]) ).
tff(f1353,plain,
! [X0: 'B_option$'] :
( ( ! [X1: 'B$'] : ( 'fun_app$g'('some$',X1) != X0 )
| ( 'none$a' != X0 ) )
& ( ( 'none$a' = X0 )
| ? [X1: 'B$'] : ( 'fun_app$g'('some$',X1) = X0 ) ) ),
inference(nnf_transformation,[],[f85]) ).
tff(f85,axiom,
! [X0: 'B_option$'] :
( ! [X1: 'B$'] : ( 'fun_app$g'('some$',X1) != X0 )
<=> ( 'none$a' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom83) ).
tff(f5446,plain,
spl249_357,
inference(avatar_split_clause,[],[f2194,f5444]) ).
tff(f5444,plain,
( spl249_357
<=> ! [X0: 'C_option$'] :
( ( 'none$' = X0 )
| ( 'fun_app$j'('some$a',sK101(X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_357])]) ).
tff(f2194,plain,
! [X0: 'C_option$'] :
( ( 'none$' = X0 )
| ( 'fun_app$j'('some$a',sK101(X0)) = X0 ) ),
inference(cnf_transformation,[],[f1352]) ).
tff(f1352,plain,
! [X0: 'C_option$'] :
( ( ! [X1: 'C$'] : ( 'fun_app$j'('some$a',X1) != X0 )
| ( 'none$' != X0 ) )
& ( ( 'none$' = X0 )
| ( 'fun_app$j'('some$a',sK101(X0)) = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK101])],[f1350,f1351]) ).
tff(f1351,plain,
! [X0: 'C_option$'] :
( ? [X2: 'C$'] : ( 'fun_app$j'('some$a',X2) = X0 )
=> ( 'fun_app$j'('some$a',sK101(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f1350,plain,
! [X0: 'C_option$'] :
( ( ! [X1: 'C$'] : ( 'fun_app$j'('some$a',X1) != X0 )
| ( 'none$' != X0 ) )
& ( ( 'none$' = X0 )
| ? [X2: 'C$'] : ( 'fun_app$j'('some$a',X2) = X0 ) ) ),
inference(rectify,[],[f1349]) ).
tff(f1349,plain,
! [X0: 'C_option$'] :
( ( ! [X1: 'C$'] : ( 'fun_app$j'('some$a',X1) != X0 )
| ( 'none$' != X0 ) )
& ( ( 'none$' = X0 )
| ? [X1: 'C$'] : ( 'fun_app$j'('some$a',X1) = X0 ) ) ),
inference(nnf_transformation,[],[f84]) ).
tff(f84,axiom,
! [X0: 'C_option$'] :
( ! [X1: 'C$'] : ( 'fun_app$j'('some$a',X1) != X0 )
<=> ( 'none$' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom82) ).
tff(f5442,plain,
spl249_356,
inference(avatar_split_clause,[],[f2192,f5440]) ).
tff(f5440,plain,
( spl249_356
<=> ! [X0: 'A_option$'] :
( ( 'none$b' = X0 )
| ( 'fun_app$q'('some$b',sK100(X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_356])]) ).
tff(f2192,plain,
! [X0: 'A_option$'] :
( ( 'none$b' = X0 )
| ( 'fun_app$q'('some$b',sK100(X0)) = X0 ) ),
inference(cnf_transformation,[],[f1348]) ).
tff(f1348,plain,
! [X0: 'A_option$'] :
( ( ! [X1: 'A$'] : ( 'fun_app$q'('some$b',X1) != X0 )
| ( 'none$b' != X0 ) )
& ( ( 'none$b' = X0 )
| ( 'fun_app$q'('some$b',sK100(X0)) = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK100])],[f1346,f1347]) ).
tff(f1347,plain,
! [X0: 'A_option$'] :
( ? [X2: 'A$'] : ( 'fun_app$q'('some$b',X2) = X0 )
=> ( 'fun_app$q'('some$b',sK100(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f1346,plain,
! [X0: 'A_option$'] :
( ( ! [X1: 'A$'] : ( 'fun_app$q'('some$b',X1) != X0 )
| ( 'none$b' != X0 ) )
& ( ( 'none$b' = X0 )
| ? [X2: 'A$'] : ( 'fun_app$q'('some$b',X2) = X0 ) ) ),
inference(rectify,[],[f1345]) ).
tff(f1345,plain,
! [X0: 'A_option$'] :
( ( ! [X1: 'A$'] : ( 'fun_app$q'('some$b',X1) != X0 )
| ( 'none$b' != X0 ) )
& ( ( 'none$b' = X0 )
| ? [X1: 'A$'] : ( 'fun_app$q'('some$b',X1) = X0 ) ) ),
inference(nnf_transformation,[],[f83]) ).
tff(f83,axiom,
! [X0: 'A_option$'] :
( ! [X1: 'A$'] : ( 'fun_app$q'('some$b',X1) != X0 )
<=> ( 'none$b' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom81) ).
tff(f5438,plain,
spl249_355,
inference(avatar_split_clause,[],[f2190,f5436]) ).
tff(f5436,plain,
( spl249_355
<=> ! [X0: 'B_option_bool_fun$',X3: 'B$'] :
( 'fun_app$a'(X0,'fun_app$g'('some$',X3))
| ~ 'fun_app$a'(X0,sK99(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_355])]) ).
tff(f2190,plain,
! [X3: 'B$',X0: 'B_option_bool_fun$'] :
( 'fun_app$a'(X0,'fun_app$g'('some$',X3))
| ~ 'fun_app$a'(X0,sK99(X0)) ),
inference(cnf_transformation,[],[f1344]) ).
tff(f5434,plain,
( spl249_354
| ~ spl249_18
| ~ spl249_297 ),
inference(avatar_split_clause,[],[f5279,f4991,f3684,f5432]) ).
tff(f5432,plain,
( spl249_354
<=> ! [X0: 'C$'] : ( tltrue = def_1('uuf$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_354])]) ).
tff(f5279,plain,
( ! [X0: 'C$'] : ( tltrue = def_1('uuf$',X0) )
| ~ spl249_18
| ~ spl249_297 ),
inference(resolution,[],[f4992,f3685]) ).
tff(f5430,plain,
spl249_353,
inference(avatar_split_clause,[],[f2187,f5428]) ).
tff(f5428,plain,
( spl249_353
<=> ! [X0: 'C_option_bool_fun$',X3: 'C$'] :
( 'fun_app$'(X0,'fun_app$j'('some$a',X3))
| ~ 'fun_app$'(X0,sK97(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_353])]) ).
tff(f2187,plain,
! [X3: 'C$',X0: 'C_option_bool_fun$'] :
( 'fun_app$'(X0,'fun_app$j'('some$a',X3))
| ~ 'fun_app$'(X0,sK97(X0)) ),
inference(cnf_transformation,[],[f1338]) ).
tff(f5426,plain,
spl249_352,
inference(avatar_split_clause,[],[f2184,f5424]) ).
tff(f5424,plain,
( spl249_352
<=> ! [X0: 'A_option_bool_fun$',X3: 'A$'] :
( 'fun_app$aw'(X0,'fun_app$q'('some$b',X3))
| ~ 'fun_app$aw'(X0,sK95(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_352])]) ).
tff(f2184,plain,
! [X3: 'A$',X0: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X0,'fun_app$q'('some$b',X3))
| ~ 'fun_app$aw'(X0,sK95(X0)) ),
inference(cnf_transformation,[],[f1332]) ).
tff(f5422,plain,
spl249_351,
inference(avatar_split_clause,[],[f2100,f5420]) ).
tff(f5420,plain,
( spl249_351
<=> ! [X0: 'B_option$'] :
( ( 'fun_app$g'('some$',sK81(X0)) = X0 )
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_351])]) ).
tff(f2100,plain,
! [X0: 'B_option$'] :
( ( 'fun_app$g'('some$',sK81(X0)) = X0 )
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f1255]) ).
tff(f1255,plain,
! [X0: 'B_option$'] :
( ( ( 'none$a' != X0 )
| ! [X1: 'B$'] : ( 'fun_app$g'('some$',X1) != X0 ) )
& ( ( 'fun_app$g'('some$',sK81(X0)) = X0 )
| ( 'none$a' = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK81])],[f1253,f1254]) ).
tff(f1254,plain,
! [X0: 'B_option$'] :
( ? [X2: 'B$'] : ( 'fun_app$g'('some$',X2) = X0 )
=> ( 'fun_app$g'('some$',sK81(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f1253,plain,
! [X0: 'B_option$'] :
( ( ( 'none$a' != X0 )
| ! [X1: 'B$'] : ( 'fun_app$g'('some$',X1) != X0 ) )
& ( ? [X2: 'B$'] : ( 'fun_app$g'('some$',X2) = X0 )
| ( 'none$a' = X0 ) ) ),
inference(rectify,[],[f1252]) ).
tff(f1252,plain,
! [X0: 'B_option$'] :
( ( ( 'none$a' != X0 )
| ! [X1: 'B$'] : ( 'fun_app$g'('some$',X1) != X0 ) )
& ( ? [X1: 'B$'] : ( 'fun_app$g'('some$',X1) = X0 )
| ( 'none$a' = X0 ) ) ),
inference(nnf_transformation,[],[f82]) ).
tff(f82,axiom,
! [X0: 'B_option$'] :
( ( 'none$a' != X0 )
<=> ? [X1: 'B$'] : ( 'fun_app$g'('some$',X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom80) ).
tff(f5418,plain,
spl249_350,
inference(avatar_split_clause,[],[f2096,f5416]) ).
tff(f5416,plain,
( spl249_350
<=> ! [X0: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK80(X0)) = X0 )
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_350])]) ).
tff(f2096,plain,
! [X0: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK80(X0)) = X0 )
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f1250]) ).
tff(f1250,plain,
! [X0: 'C_option$'] :
( ( ( 'none$' != X0 )
| ! [X1: 'C$'] : ( 'fun_app$j'('some$a',X1) != X0 ) )
& ( ( 'fun_app$j'('some$a',sK80(X0)) = X0 )
| ( 'none$' = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK80])],[f1248,f1249]) ).
tff(f1249,plain,
! [X0: 'C_option$'] :
( ? [X2: 'C$'] : ( 'fun_app$j'('some$a',X2) = X0 )
=> ( 'fun_app$j'('some$a',sK80(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f1248,plain,
! [X0: 'C_option$'] :
( ( ( 'none$' != X0 )
| ! [X1: 'C$'] : ( 'fun_app$j'('some$a',X1) != X0 ) )
& ( ? [X2: 'C$'] : ( 'fun_app$j'('some$a',X2) = X0 )
| ( 'none$' = X0 ) ) ),
inference(rectify,[],[f1247]) ).
tff(f1247,plain,
! [X0: 'C_option$'] :
( ( ( 'none$' != X0 )
| ! [X1: 'C$'] : ( 'fun_app$j'('some$a',X1) != X0 ) )
& ( ? [X1: 'C$'] : ( 'fun_app$j'('some$a',X1) = X0 )
| ( 'none$' = X0 ) ) ),
inference(nnf_transformation,[],[f81]) ).
tff(f81,axiom,
! [X0: 'C_option$'] :
( ( 'none$' != X0 )
<=> ? [X1: 'C$'] : ( 'fun_app$j'('some$a',X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom79) ).
tff(f5414,plain,
spl249_349,
inference(avatar_split_clause,[],[f2092,f5412]) ).
tff(f5412,plain,
( spl249_349
<=> ! [X0: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK79(X0)) = X0 )
| ( 'none$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_349])]) ).
tff(f2092,plain,
! [X0: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK79(X0)) = X0 )
| ( 'none$b' = X0 ) ),
inference(cnf_transformation,[],[f1245]) ).
tff(f1245,plain,
! [X0: 'A_option$'] :
( ( ( 'none$b' != X0 )
| ! [X1: 'A$'] : ( 'fun_app$q'('some$b',X1) != X0 ) )
& ( ( 'fun_app$q'('some$b',sK79(X0)) = X0 )
| ( 'none$b' = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79])],[f1243,f1244]) ).
tff(f1244,plain,
! [X0: 'A_option$'] :
( ? [X2: 'A$'] : ( 'fun_app$q'('some$b',X2) = X0 )
=> ( 'fun_app$q'('some$b',sK79(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f1243,plain,
! [X0: 'A_option$'] :
( ( ( 'none$b' != X0 )
| ! [X1: 'A$'] : ( 'fun_app$q'('some$b',X1) != X0 ) )
& ( ? [X2: 'A$'] : ( 'fun_app$q'('some$b',X2) = X0 )
| ( 'none$b' = X0 ) ) ),
inference(rectify,[],[f1242]) ).
tff(f1242,plain,
! [X0: 'A_option$'] :
( ( ( 'none$b' != X0 )
| ! [X1: 'A$'] : ( 'fun_app$q'('some$b',X1) != X0 ) )
& ( ? [X1: 'A$'] : ( 'fun_app$q'('some$b',X1) = X0 )
| ( 'none$b' = X0 ) ) ),
inference(nnf_transformation,[],[f80]) ).
tff(f80,axiom,
! [X0: 'A_option$'] :
( ( 'none$b' != X0 )
<=> ? [X1: 'A$'] : ( 'fun_app$q'('some$b',X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom78) ).
tff(f5410,plain,
spl249_348,
inference(avatar_split_clause,[],[f2081,f5408]) ).
tff(f2081,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( 'register_from_getter_setter$'(sK65(X0),sK66(X0)) = X0 )
| ~ 'register$'(X0) ),
inference(cnf_transformation,[],[f1225]) ).
tff(f1225,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( 'register$'(X0)
| ! [X1: 'B_a_fun$',X2: 'A_b_b_fun_fun$'] :
( ~ 'valid_getter_setter$a'(X1,X2)
| ( 'register_from_getter_setter$'(X1,X2) != X0 ) ) )
& ( ( 'valid_getter_setter$a'(sK65(X0),sK66(X0))
& ( 'register_from_getter_setter$'(sK65(X0),sK66(X0)) = X0 ) )
| ~ 'register$'(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65,sK66])],[f1223,f1224]) ).
tff(f1224,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ? [X3: 'B_a_fun$',X4: 'A_b_b_fun_fun$'] :
( 'valid_getter_setter$a'(X3,X4)
& ( 'register_from_getter_setter$'(X3,X4) = X0 ) )
=> ( 'valid_getter_setter$a'(sK65(X0),sK66(X0))
& ( 'register_from_getter_setter$'(sK65(X0),sK66(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1223,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( 'register$'(X0)
| ! [X1: 'B_a_fun$',X2: 'A_b_b_fun_fun$'] :
( ~ 'valid_getter_setter$a'(X1,X2)
| ( 'register_from_getter_setter$'(X1,X2) != X0 ) ) )
& ( ? [X3: 'B_a_fun$',X4: 'A_b_b_fun_fun$'] :
( 'valid_getter_setter$a'(X3,X4)
& ( 'register_from_getter_setter$'(X3,X4) = X0 ) )
| ~ 'register$'(X0) ) ),
inference(rectify,[],[f1222]) ).
tff(f1222,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( 'register$'(X0)
| ! [X1: 'B_a_fun$',X2: 'A_b_b_fun_fun$'] :
( ~ 'valid_getter_setter$a'(X1,X2)
| ( 'register_from_getter_setter$'(X1,X2) != X0 ) ) )
& ( ? [X1: 'B_a_fun$',X2: 'A_b_b_fun_fun$'] :
( 'valid_getter_setter$a'(X1,X2)
& ( 'register_from_getter_setter$'(X1,X2) = X0 ) )
| ~ 'register$'(X0) ) ),
inference(nnf_transformation,[],[f139]) ).
tff(f139,axiom,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( 'register$'(X0)
<=> ? [X1: 'B_a_fun$',X2: 'A_b_b_fun_fun$'] :
( 'valid_getter_setter$a'(X1,X2)
& ( 'register_from_getter_setter$'(X1,X2) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom137) ).
tff(f5406,plain,
spl249_347,
inference(avatar_split_clause,[],[f2078,f5404]) ).
tff(f2078,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( 'register_from_getter_setter$a'(sK63(X0),sK64(X0)) = X0 )
| ~ 'register$a'(X0) ),
inference(cnf_transformation,[],[f1221]) ).
tff(f1221,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( 'register$a'(X0)
| ! [X1: 'C_b_fun$',X2: 'B_c_c_fun_fun$'] :
( ~ 'valid_getter_setter$'(X1,X2)
| ( 'register_from_getter_setter$a'(X1,X2) != X0 ) ) )
& ( ( 'valid_getter_setter$'(sK63(X0),sK64(X0))
& ( 'register_from_getter_setter$a'(sK63(X0),sK64(X0)) = X0 ) )
| ~ 'register$a'(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64])],[f1219,f1220]) ).
tff(f1220,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ? [X3: 'C_b_fun$',X4: 'B_c_c_fun_fun$'] :
( 'valid_getter_setter$'(X3,X4)
& ( 'register_from_getter_setter$a'(X3,X4) = X0 ) )
=> ( 'valid_getter_setter$'(sK63(X0),sK64(X0))
& ( 'register_from_getter_setter$a'(sK63(X0),sK64(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1219,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( 'register$a'(X0)
| ! [X1: 'C_b_fun$',X2: 'B_c_c_fun_fun$'] :
( ~ 'valid_getter_setter$'(X1,X2)
| ( 'register_from_getter_setter$a'(X1,X2) != X0 ) ) )
& ( ? [X3: 'C_b_fun$',X4: 'B_c_c_fun_fun$'] :
( 'valid_getter_setter$'(X3,X4)
& ( 'register_from_getter_setter$a'(X3,X4) = X0 ) )
| ~ 'register$a'(X0) ) ),
inference(rectify,[],[f1218]) ).
tff(f1218,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( 'register$a'(X0)
| ! [X1: 'C_b_fun$',X2: 'B_c_c_fun_fun$'] :
( ~ 'valid_getter_setter$'(X1,X2)
| ( 'register_from_getter_setter$a'(X1,X2) != X0 ) ) )
& ( ? [X1: 'C_b_fun$',X2: 'B_c_c_fun_fun$'] :
( 'valid_getter_setter$'(X1,X2)
& ( 'register_from_getter_setter$a'(X1,X2) = X0 ) )
| ~ 'register$a'(X0) ) ),
inference(nnf_transformation,[],[f138]) ).
tff(f138,axiom,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( 'register$a'(X0)
<=> ? [X1: 'C_b_fun$',X2: 'B_c_c_fun_fun$'] :
( 'valid_getter_setter$'(X1,X2)
& ( 'register_from_getter_setter$a'(X1,X2) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom136) ).
tff(f5402,plain,
spl249_346,
inference(avatar_split_clause,[],[f2075,f5400]) ).
tff(f2075,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ( 'register_from_getter_setter$b'(sK61(X0),sK62(X0)) = X0 )
| ~ 'register$h'(X0) ),
inference(cnf_transformation,[],[f1217]) ).
tff(f1217,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ( 'register$h'(X0)
| ! [X1: 'B_b_fun$',X2: 'B_b_b_fun_fun$'] :
( ~ 'valid_getter_setter$b'(X1,X2)
| ( 'register_from_getter_setter$b'(X1,X2) != X0 ) ) )
& ( ( 'valid_getter_setter$b'(sK61(X0),sK62(X0))
& ( 'register_from_getter_setter$b'(sK61(X0),sK62(X0)) = X0 ) )
| ~ 'register$h'(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61,sK62])],[f1215,f1216]) ).
tff(f1216,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ? [X3: 'B_b_fun$',X4: 'B_b_b_fun_fun$'] :
( 'valid_getter_setter$b'(X3,X4)
& ( 'register_from_getter_setter$b'(X3,X4) = X0 ) )
=> ( 'valid_getter_setter$b'(sK61(X0),sK62(X0))
& ( 'register_from_getter_setter$b'(sK61(X0),sK62(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1215,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ( 'register$h'(X0)
| ! [X1: 'B_b_fun$',X2: 'B_b_b_fun_fun$'] :
( ~ 'valid_getter_setter$b'(X1,X2)
| ( 'register_from_getter_setter$b'(X1,X2) != X0 ) ) )
& ( ? [X3: 'B_b_fun$',X4: 'B_b_b_fun_fun$'] :
( 'valid_getter_setter$b'(X3,X4)
& ( 'register_from_getter_setter$b'(X3,X4) = X0 ) )
| ~ 'register$h'(X0) ) ),
inference(rectify,[],[f1214]) ).
tff(f1214,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ( 'register$h'(X0)
| ! [X1: 'B_b_fun$',X2: 'B_b_b_fun_fun$'] :
( ~ 'valid_getter_setter$b'(X1,X2)
| ( 'register_from_getter_setter$b'(X1,X2) != X0 ) ) )
& ( ? [X1: 'B_b_fun$',X2: 'B_b_b_fun_fun$'] :
( 'valid_getter_setter$b'(X1,X2)
& ( 'register_from_getter_setter$b'(X1,X2) = X0 ) )
| ~ 'register$h'(X0) ) ),
inference(nnf_transformation,[],[f135]) ).
tff(f135,axiom,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( 'register$h'(X0)
<=> ? [X1: 'B_b_fun$',X2: 'B_b_b_fun_fun$'] :
( 'valid_getter_setter$b'(X1,X2)
& ( 'register_from_getter_setter$b'(X1,X2) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom133) ).
tff(f5398,plain,
spl249_345,
inference(avatar_split_clause,[],[f2072,f5396]) ).
tff(f2072,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ( 'register_from_getter_setter$d'(sK59(X0),sK60(X0)) = X0 )
| ~ 'register$f'(X0) ),
inference(cnf_transformation,[],[f1213]) ).
tff(f1213,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ( 'register$f'(X0)
| ! [X1: 'C_c_fun$',X2: 'C_c_c_fun_fun$'] :
( ~ 'valid_getter_setter$d'(X1,X2)
| ( 'register_from_getter_setter$d'(X1,X2) != X0 ) ) )
& ( ( 'valid_getter_setter$d'(sK59(X0),sK60(X0))
& ( 'register_from_getter_setter$d'(sK59(X0),sK60(X0)) = X0 ) )
| ~ 'register$f'(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59,sK60])],[f1211,f1212]) ).
tff(f1212,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ? [X3: 'C_c_fun$',X4: 'C_c_c_fun_fun$'] :
( 'valid_getter_setter$d'(X3,X4)
& ( 'register_from_getter_setter$d'(X3,X4) = X0 ) )
=> ( 'valid_getter_setter$d'(sK59(X0),sK60(X0))
& ( 'register_from_getter_setter$d'(sK59(X0),sK60(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1211,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ( 'register$f'(X0)
| ! [X1: 'C_c_fun$',X2: 'C_c_c_fun_fun$'] :
( ~ 'valid_getter_setter$d'(X1,X2)
| ( 'register_from_getter_setter$d'(X1,X2) != X0 ) ) )
& ( ? [X3: 'C_c_fun$',X4: 'C_c_c_fun_fun$'] :
( 'valid_getter_setter$d'(X3,X4)
& ( 'register_from_getter_setter$d'(X3,X4) = X0 ) )
| ~ 'register$f'(X0) ) ),
inference(rectify,[],[f1210]) ).
tff(f1210,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ( 'register$f'(X0)
| ! [X1: 'C_c_fun$',X2: 'C_c_c_fun_fun$'] :
( ~ 'valid_getter_setter$d'(X1,X2)
| ( 'register_from_getter_setter$d'(X1,X2) != X0 ) ) )
& ( ? [X1: 'C_c_fun$',X2: 'C_c_c_fun_fun$'] :
( 'valid_getter_setter$d'(X1,X2)
& ( 'register_from_getter_setter$d'(X1,X2) = X0 ) )
| ~ 'register$f'(X0) ) ),
inference(nnf_transformation,[],[f137]) ).
tff(f137,axiom,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( 'register$f'(X0)
<=> ? [X1: 'C_c_fun$',X2: 'C_c_c_fun_fun$'] :
( 'valid_getter_setter$d'(X1,X2)
& ( 'register_from_getter_setter$d'(X1,X2) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom135) ).
tff(f5394,plain,
spl249_344,
inference(avatar_split_clause,[],[f2065,f5392]) ).
tff(f5392,plain,
( spl249_344
<=> ! [X0: 'B_option$'] :
( ( 'fun_app$g'('some$',sK50(X0)) = X0 )
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_344])]) ).
tff(f2065,plain,
! [X0: 'B_option$'] :
( ( 'fun_app$g'('some$',sK50(X0)) = X0 )
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f1196]) ).
tff(f1196,plain,
! [X0: 'B_option$'] :
( ( 'fun_app$g'('some$',sK50(X0)) = X0 )
| ( 'none$a' = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50])],[f888,f1195]) ).
tff(f1195,plain,
! [X0: 'B_option$'] :
( ? [X1: 'B$'] : ( 'fun_app$g'('some$',X1) = X0 )
=> ( 'fun_app$g'('some$',sK50(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f888,plain,
! [X0: 'B_option$'] :
( ? [X1: 'B$'] : ( 'fun_app$g'('some$',X1) = X0 )
| ( 'none$a' = X0 ) ),
inference(ennf_transformation,[],[f768]) ).
tff(f768,plain,
! [X0: 'B_option$'] :
~ ( ! [X1: 'B$'] : ( 'fun_app$g'('some$',X1) != X0 )
& ( 'none$a' != X0 ) ),
inference(flattening,[],[f767]) ).
tff(f767,plain,
! [X0: 'B_option$'] :
~ ( ! [X1: 'B$'] :
( ~ 'fun_app$g'('some$',X1) = X0 )
& ( ~ 'none$a' = X0 ) ),
inference(true_and_false_elimination,[],[f120]) ).
tff(f120,axiom,
! [X0: 'B_option$'] :
( ( ! [X1: 'B$'] :
( ( 'fun_app$g'('some$',X1) = X0 )
=> $false )
& ( ( 'none$a' = X0 )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom118) ).
tff(f5388,plain,
spl249_343,
inference(avatar_split_clause,[],[f2062,f5386]) ).
tff(f5386,plain,
( spl249_343
<=> ! [X0: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK49(X0)) = X0 )
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_343])]) ).
tff(f2062,plain,
! [X0: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK49(X0)) = X0 )
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f1194]) ).
tff(f1194,plain,
! [X0: 'C_option$'] :
( ( 'fun_app$j'('some$a',sK49(X0)) = X0 )
| ( 'none$' = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49])],[f885,f1193]) ).
tff(f1193,plain,
! [X0: 'C_option$'] :
( ? [X1: 'C$'] : ( 'fun_app$j'('some$a',X1) = X0 )
=> ( 'fun_app$j'('some$a',sK49(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f885,plain,
! [X0: 'C_option$'] :
( ? [X1: 'C$'] : ( 'fun_app$j'('some$a',X1) = X0 )
| ( 'none$' = X0 ) ),
inference(ennf_transformation,[],[f762]) ).
tff(f762,plain,
! [X0: 'C_option$'] :
~ ( ! [X1: 'C$'] : ( 'fun_app$j'('some$a',X1) != X0 )
& ( 'none$' != X0 ) ),
inference(flattening,[],[f761]) ).
tff(f761,plain,
! [X0: 'C_option$'] :
~ ( ! [X1: 'C$'] :
( ~ 'fun_app$j'('some$a',X1) = X0 )
& ( ~ 'none$' = X0 ) ),
inference(true_and_false_elimination,[],[f119]) ).
tff(f119,axiom,
! [X0: 'C_option$'] :
( ( ! [X1: 'C$'] :
( ( 'fun_app$j'('some$a',X1) = X0 )
=> $false )
& ( ( 'none$' = X0 )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom117) ).
tff(f5384,plain,
spl249_342,
inference(avatar_split_clause,[],[f2059,f5382]) ).
tff(f5382,plain,
( spl249_342
<=> ! [X0: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK48(X0)) = X0 )
| ( 'none$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_342])]) ).
tff(f2059,plain,
! [X0: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK48(X0)) = X0 )
| ( 'none$b' = X0 ) ),
inference(cnf_transformation,[],[f1192]) ).
tff(f1192,plain,
! [X0: 'A_option$'] :
( ( 'fun_app$q'('some$b',sK48(X0)) = X0 )
| ( 'none$b' = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48])],[f882,f1191]) ).
tff(f1191,plain,
! [X0: 'A_option$'] :
( ? [X1: 'A$'] : ( 'fun_app$q'('some$b',X1) = X0 )
=> ( 'fun_app$q'('some$b',sK48(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f882,plain,
! [X0: 'A_option$'] :
( ? [X1: 'A$'] : ( 'fun_app$q'('some$b',X1) = X0 )
| ( 'none$b' = X0 ) ),
inference(ennf_transformation,[],[f756]) ).
tff(f756,plain,
! [X0: 'A_option$'] :
~ ( ! [X1: 'A$'] : ( 'fun_app$q'('some$b',X1) != X0 )
& ( 'none$b' != X0 ) ),
inference(flattening,[],[f755]) ).
tff(f755,plain,
! [X0: 'A_option$'] :
~ ( ! [X1: 'A$'] :
( ~ 'fun_app$q'('some$b',X1) = X0 )
& ( ~ 'none$b' = X0 ) ),
inference(true_and_false_elimination,[],[f118]) ).
tff(f118,axiom,
! [X0: 'A_option$'] :
( ( ! [X1: 'A$'] :
( ( 'fun_app$q'('some$b',X1) = X0 )
=> $false )
& ( ( 'none$b' = X0 )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom116) ).
tff(f5380,plain,
spl249_341,
inference(avatar_split_clause,[],[f2051,f5378]) ).
tff(f5378,plain,
( spl249_341
<=> ! [X0: 'B_option$'] :
( 'member$c'('fun_app$al'('the$',X0),'set_option$d'(X0))
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_341])]) ).
tff(f2051,plain,
! [X0: 'B_option$'] :
( 'member$c'('fun_app$al'('the$',X0),'set_option$d'(X0))
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f878]) ).
tff(f878,plain,
! [X0: 'B_option$'] :
( 'member$c'('fun_app$al'('the$',X0),'set_option$d'(X0))
| ( 'none$a' = X0 ) ),
inference(ennf_transformation,[],[f336]) ).
tff(f336,axiom,
! [X0: 'B_option$'] :
( ( 'none$a' != X0 )
=> 'member$c'('fun_app$al'('the$',X0),'set_option$d'(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom334) ).
tff(f5376,plain,
spl249_340,
inference(avatar_split_clause,[],[f2049,f5374]) ).
tff(f5374,plain,
( spl249_340
<=> ! [X0: 'C_option$'] :
( 'member$b'('fun_app$ak'('the$a',X0),'set_option$c'(X0))
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_340])]) ).
tff(f2049,plain,
! [X0: 'C_option$'] :
( 'member$b'('fun_app$ak'('the$a',X0),'set_option$c'(X0))
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f876]) ).
tff(f876,plain,
! [X0: 'C_option$'] :
( 'member$b'('fun_app$ak'('the$a',X0),'set_option$c'(X0))
| ( 'none$' = X0 ) ),
inference(ennf_transformation,[],[f335]) ).
tff(f335,axiom,
! [X0: 'C_option$'] :
( ( 'none$' != X0 )
=> 'member$b'('fun_app$ak'('the$a',X0),'set_option$c'(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom333) ).
tff(f5372,plain,
spl249_339,
inference(avatar_split_clause,[],[f2047,f5370]) ).
tff(f5370,plain,
( spl249_339
<=> ! [X0: 'A_option$'] :
( 'member$d'('fun_app$bf'('the$b',X0),'set_option$b'(X0))
| ( 'none$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_339])]) ).
tff(f2047,plain,
! [X0: 'A_option$'] :
( 'member$d'('fun_app$bf'('the$b',X0),'set_option$b'(X0))
| ( 'none$b' = X0 ) ),
inference(cnf_transformation,[],[f874]) ).
tff(f874,plain,
! [X0: 'A_option$'] :
( 'member$d'('fun_app$bf'('the$b',X0),'set_option$b'(X0))
| ( 'none$b' = X0 ) ),
inference(ennf_transformation,[],[f334]) ).
tff(f334,axiom,
! [X0: 'A_option$'] :
( ( 'none$b' != X0 )
=> 'member$d'('fun_app$bf'('the$b',X0),'set_option$b'(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom332) ).
tff(f5368,plain,
spl249_338,
inference(avatar_split_clause,[],[f2035,f5366]) ).
tff(f5366,plain,
( spl249_338
<=> ! [X0: 'B_option$'] : ( 'fun_app$al'('the$',X0) = 'fun_app$al'('case_option$j'('undefined$a','uvm$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_338])]) ).
tff(f2035,plain,
! [X0: 'B_option$'] : ( 'fun_app$al'('the$',X0) = 'fun_app$al'('case_option$j'('undefined$a','uvm$'),X0) ),
inference(cnf_transformation,[],[f330]) ).
tff(f330,axiom,
! [X0: 'B_option$'] : ( 'fun_app$al'('the$',X0) = 'fun_app$al'('case_option$j'('undefined$a','uvm$'),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom328) ).
tff(f5364,plain,
spl249_337,
inference(avatar_split_clause,[],[f2034,f5362]) ).
tff(f5362,plain,
( spl249_337
<=> ! [X0: 'C_option$'] : ( 'fun_app$ak'('the$a',X0) = 'fun_app$ak'('case_option$k'('undefined$b','uvs$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_337])]) ).
tff(f2034,plain,
! [X0: 'C_option$'] : ( 'fun_app$ak'('the$a',X0) = 'fun_app$ak'('case_option$k'('undefined$b','uvs$'),X0) ),
inference(cnf_transformation,[],[f331]) ).
tff(f331,axiom,
! [X0: 'C_option$'] : ( 'fun_app$ak'('the$a',X0) = 'fun_app$ak'('case_option$k'('undefined$b','uvs$'),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom329) ).
tff(f5360,plain,
( spl249_336
| ~ spl249_18
| ~ spl249_295 ),
inference(avatar_split_clause,[],[f5266,f4983,f3684,f5358]) ).
tff(f5358,plain,
( spl249_336
<=> ! [X0: 'C$'] : ( tltrue = def_4('uuf$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_336])]) ).
tff(f5266,plain,
( ! [X0: 'C$'] : ( tltrue = def_4('uuf$',X0) )
| ~ spl249_18
| ~ spl249_295 ),
inference(resolution,[],[f4984,f3685]) ).
tff(f5355,plain,
( spl249_335
| ~ spl249_10
| ~ spl249_293 ),
inference(avatar_split_clause,[],[f5263,f4975,f3650,f5352]) ).
tff(f5352,plain,
( spl249_335
<=> ( tltrue = def_14('is_none$','none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_335])]) ).
tff(f5263,plain,
( ( tltrue = def_14('is_none$','none$a') )
| ~ spl249_10
| ~ spl249_293 ),
inference(resolution,[],[f4976,f3652]) ).
tff(f3652,plain,
( 'fun_app$a'('is_none$','none$a')
| ~ spl249_10 ),
inference(avatar_component_clause,[],[f3650]) ).
tff(f5326,plain,
( spl249_334
| ~ spl249_9
| ~ spl249_291 ),
inference(avatar_split_clause,[],[f5252,f4967,f3645,f5323]) ).
tff(f5323,plain,
( spl249_334
<=> ( tltrue = def_10('is_none$a','none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_334])]) ).
tff(f5252,plain,
( ( tltrue = def_10('is_none$a','none$') )
| ~ spl249_9
| ~ spl249_291 ),
inference(resolution,[],[f4968,f3647]) ).
tff(f3647,plain,
( 'fun_app$'('is_none$a','none$')
| ~ spl249_9 ),
inference(avatar_component_clause,[],[f3645]) ).
tff(f5278,plain,
( spl249_333
| ~ spl249_9
| ~ spl249_288 ),
inference(avatar_split_clause,[],[f5241,f4954,f3645,f5275]) ).
tff(f5275,plain,
( spl249_333
<=> ( tltrue = def_15('is_none$a','none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_333])]) ).
tff(f5241,plain,
( ( tltrue = def_15('is_none$a','none$') )
| ~ spl249_9
| ~ spl249_288 ),
inference(resolution,[],[f4955,f3647]) ).
tff(f5230,plain,
( spl249_332
| ~ spl249_58
| ~ spl249_133 ),
inference(avatar_split_clause,[],[f4241,f4181,f3864,f5228]) ).
tff(f5228,plain,
( spl249_332
<=> ! [X0: tlbool,X1: 'C_bool_fun$'] :
( sP20('none$',X1,X0)
| ( tlfalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_332])]) ).
tff(f3864,plain,
( spl249_58
<=> ! [X1: 'C_bool_fun$'] : sP20('none$',X1,tltrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_58])]) ).
tff(f4241,plain,
( ! [X0: tlbool,X1: 'C_bool_fun$'] :
( sP20('none$',X1,X0)
| ( tlfalse = X0 ) )
| ~ spl249_58
| ~ spl249_133 ),
inference(superposition,[],[f3865,f4182]) ).
tff(f3865,plain,
( ! [X1: 'C_bool_fun$'] : sP20('none$',X1,tltrue)
| ~ spl249_58 ),
inference(avatar_component_clause,[],[f3864]) ).
tff(f5131,plain,
spl249_331,
inference(avatar_split_clause,[],[f3563,f5129]) ).
tff(f5129,plain,
( spl249_331
<=> ! [X2: 'B_option_bool_fun$',X1: 'B_b_option_fun$',X3: 'B_option$'] :
( 'fun_app$a'(X2,X3)
| ~ sP43('none$a',X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_331])]) ).
tff(f3563,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'(X2,X3)
| ~ sP43('none$a',X1,X2,X3) ),
inference(equality_resolution,[],[f3219]) ).
tff(f3219,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'(X2,X3)
| ( 'none$a' != X0 )
| ~ sP43(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1912]) ).
tff(f5127,plain,
spl249_330,
inference(avatar_split_clause,[],[f3562,f5125]) ).
tff(f5125,plain,
( spl249_330
<=> ! [X2: 'B_option_bool_fun$',X1: 'B_b_option_fun$',X3: 'B_option$'] :
( 'fun_app$a'(X2,X3)
| ~ sP42('none$a',X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_330])]) ).
tff(f3562,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'(X2,X3)
| ~ sP42('none$a',X1,X2,X3) ),
inference(equality_resolution,[],[f3211]) ).
tff(f3211,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'B_option$',X1: 'B_b_option_fun$'] :
( 'fun_app$a'(X2,X3)
| ( 'none$a' != X0 )
| ~ sP42(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1908]) ).
tff(f5123,plain,
spl249_329,
inference(avatar_split_clause,[],[f3561,f5121]) ).
tff(f5121,plain,
( spl249_329
<=> ! [X2: 'B_option_bool_fun$',X1: 'A_b_option_fun$',X3: 'B_option$'] :
( 'fun_app$a'(X2,X3)
| ~ sP41('none$b',X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_329])]) ).
tff(f3561,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'(X2,X3)
| ~ sP41('none$b',X1,X2,X3) ),
inference(equality_resolution,[],[f3201]) ).
tff(f3201,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'(X2,X3)
| ( 'none$b' != X0 )
| ~ sP41(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1903]) ).
tff(f5119,plain,
spl249_328,
inference(avatar_split_clause,[],[f3560,f5117]) ).
tff(f5117,plain,
( spl249_328
<=> ! [X2: 'B_option_bool_fun$',X1: 'A_b_option_fun$',X3: 'B_option$'] :
( 'fun_app$a'(X2,X3)
| ~ sP40('none$b',X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_328])]) ).
tff(f3560,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'(X2,X3)
| ~ sP40('none$b',X1,X2,X3) ),
inference(equality_resolution,[],[f3193]) ).
tff(f3193,plain,
! [X2: 'B_option_bool_fun$',X3: 'B_option$',X0: 'A_option$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'(X2,X3)
| ( 'none$b' != X0 )
| ~ sP40(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1899]) ).
tff(f5115,plain,
spl249_327,
inference(avatar_split_clause,[],[f3559,f5113]) ).
tff(f5113,plain,
( spl249_327
<=> ! [X2: 'C_option_bool_fun$',X1: 'B_c_option_fun$',X3: 'C_option$'] :
( 'fun_app$'(X2,X3)
| ~ sP39('none$a',X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_327])]) ).
tff(f3559,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X2,X3)
| ~ sP39('none$a',X1,X2,X3) ),
inference(equality_resolution,[],[f3185]) ).
tff(f3185,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X2,X3)
| ( 'none$a' != X0 )
| ~ sP39(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1895]) ).
tff(f5111,plain,
spl249_326,
inference(avatar_split_clause,[],[f3558,f5109]) ).
tff(f5109,plain,
( spl249_326
<=> ! [X2: 'C_option_bool_fun$',X1: 'B_c_option_fun$',X3: 'C_option$'] :
( 'fun_app$'(X2,X3)
| ~ sP38('none$a',X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_326])]) ).
tff(f3558,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X2,X3)
| ~ sP38('none$a',X1,X2,X3) ),
inference(equality_resolution,[],[f3177]) ).
tff(f3177,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'(X2,X3)
| ( 'none$a' != X0 )
| ~ sP38(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1891]) ).
tff(f5107,plain,
spl249_325,
inference(avatar_split_clause,[],[f3557,f5105]) ).
tff(f5105,plain,
( spl249_325
<=> ! [X2: 'C_option_bool_fun$',X1: 'C_c_option_fun$',X3: 'C_option$'] :
( 'fun_app$'(X2,X3)
| ~ sP37('none$',X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_325])]) ).
tff(f3557,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X1: 'C_c_option_fun$'] :
( 'fun_app$'(X2,X3)
| ~ sP37('none$',X1,X2,X3) ),
inference(equality_resolution,[],[f3167]) ).
tff(f3167,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( 'fun_app$'(X2,X3)
| ( 'none$' != X0 )
| ~ sP37(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1886]) ).
tff(f5103,plain,
spl249_324,
inference(avatar_split_clause,[],[f3556,f5101]) ).
tff(f5101,plain,
( spl249_324
<=> ! [X2: 'C_option_bool_fun$',X1: 'C_c_option_fun$',X3: 'C_option$'] :
( 'fun_app$'(X2,X3)
| ~ sP36('none$',X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_324])]) ).
tff(f3556,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X1: 'C_c_option_fun$'] :
( 'fun_app$'(X2,X3)
| ~ sP36('none$',X1,X2,X3) ),
inference(equality_resolution,[],[f3159]) ).
tff(f3159,plain,
! [X2: 'C_option_bool_fun$',X3: 'C_option$',X0: 'C_option$',X1: 'C_c_option_fun$'] :
( 'fun_app$'(X2,X3)
| ( 'none$' != X0 )
| ~ sP36(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1882]) ).
tff(f5099,plain,
spl249_323,
inference(avatar_split_clause,[],[f3555,f5097]) ).
tff(f5097,plain,
( spl249_323
<=> ! [X2: 'Bool_bool_fun$',X1: 'B_bool_fun$',X3: tlbool] :
( 'fun_app$ag'(X2,X3)
| ~ sP35('none$a',X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_323])]) ).
tff(f3555,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$ag'(X2,X3)
| ~ sP35('none$a',X1,X2,X3) ),
inference(equality_resolution,[],[f3149]) ).
tff(f3149,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( 'fun_app$ag'(X2,X3)
| ( 'none$a' != X0 )
| ~ sP35(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1877]) ).
tff(f5095,plain,
spl249_322,
inference(avatar_split_clause,[],[f3554,f5093]) ).
tff(f5093,plain,
( spl249_322
<=> ! [X2: 'Bool_bool_fun$',X1: 'C_bool_fun$',X3: tlbool] :
( 'fun_app$ag'(X2,X3)
| ~ sP34('none$',X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_322])]) ).
tff(f3554,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$ag'(X2,X3)
| ~ sP34('none$',X1,X2,X3) ),
inference(equality_resolution,[],[f3141]) ).
tff(f3141,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( 'fun_app$ag'(X2,X3)
| ( 'none$' != X0 )
| ~ sP34(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1873]) ).
tff(f5091,plain,
spl249_321,
inference(avatar_split_clause,[],[f3553,f5089]) ).
tff(f5089,plain,
( spl249_321
<=> ! [X2: 'Bool_bool_fun$',X1: 'B_bool_fun$',X3: tlbool] :
( 'fun_app$ag'(X2,X3)
| ~ sP33('none$a',X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_321])]) ).
tff(f3553,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$ag'(X2,X3)
| ~ sP33('none$a',X1,X2,X3) ),
inference(equality_resolution,[],[f3133]) ).
tff(f3133,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( 'fun_app$ag'(X2,X3)
| ( 'none$a' != X0 )
| ~ sP33(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1869]) ).
tff(f5087,plain,
spl249_320,
inference(avatar_split_clause,[],[f3552,f5085]) ).
tff(f5085,plain,
( spl249_320
<=> ! [X2: 'Bool_bool_fun$',X1: 'C_bool_fun$',X3: tlbool] :
( 'fun_app$ag'(X2,X3)
| ~ sP32('none$',X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_320])]) ).
tff(f3552,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$ag'(X2,X3)
| ~ sP32('none$',X1,X2,X3) ),
inference(equality_resolution,[],[f3125]) ).
tff(f3125,plain,
! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( 'fun_app$ag'(X2,X3)
| ( 'none$' != X0 )
| ~ sP32(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f1865]) ).
tff(f5083,plain,
spl249_319,
inference(avatar_split_clause,[],[f3243,f5081]) ).
tff(f5081,plain,
( spl249_319
<=> ! [X0: 'C_option$',X1: 'B$'] : ( 'bind$b'('fun_app$g'('some$',X1),'uwi$'(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_319])]) ).
tff(f3243,plain,
! [X0: 'C_option$',X1: 'B$'] : ( 'bind$b'('fun_app$g'('some$',X1),'uwi$'(X0)) = X0 ),
inference(definition_unfolding,[],[f2216,f2234]) ).
tff(f2216,plain,
! [X0: 'C_option$',X1: 'B$'] : ( 'fun_app$n'('uwi$'(X0),X1) = X0 ),
inference(cnf_transformation,[],[f52]) ).
tff(f52,axiom,
! [X0: 'C_option$',X1: 'B$'] : ( 'fun_app$n'('uwi$'(X0),X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom51) ).
tff(f5079,plain,
spl249_318,
inference(avatar_split_clause,[],[f2548,f5077]) ).
tff(f5077,plain,
( spl249_318
<=> ! [X2: 'B$',X0: 'B$',X1: 'B_b_option_fun$'] : ( 'fun_app$h'('comp$m'('uwj$'(X0),X1),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_318])]) ).
tff(f2548,plain,
! [X2: 'B$',X0: 'B$',X1: 'B_b_option_fun$'] : ( 'fun_app$h'('comp$m'('uwj$'(X0),X1),X2) = X0 ),
inference(cnf_transformation,[],[f647]) ).
tff(f647,axiom,
! [X0: 'B$',X1: 'B_b_option_fun$',X2: 'B$'] : ( 'fun_app$h'('comp$m'('uwj$'(X0),X1),X2) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom645) ).
tff(f5075,plain,
spl249_317,
inference(avatar_split_clause,[],[f2546,f5073]) ).
tff(f5073,plain,
( spl249_317
<=> ! [X2: 'C$',X0: 'C$',X1: 'C_c_option_fun$'] : ( 'fun_app$k'('comp$n'('uwk$'(X0),X1),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_317])]) ).
tff(f2546,plain,
! [X2: 'C$',X0: 'C$',X1: 'C_c_option_fun$'] : ( 'fun_app$k'('comp$n'('uwk$'(X0),X1),X2) = X0 ),
inference(cnf_transformation,[],[f648]) ).
tff(f648,axiom,
! [X0: 'C$',X1: 'C_c_option_fun$',X2: 'C$'] : ( 'fun_app$k'('comp$n'('uwk$'(X0),X1),X2) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom646) ).
tff(f5071,plain,
spl249_316,
inference(avatar_split_clause,[],[f2545,f5069]) ).
tff(f5069,plain,
( spl249_316
<=> ! [X2: 'A$',X0: 'B_option$',X1: 'A_a_fun$'] : ( 'fun_app$f'('comp$g'('uwh$'(X0),X1),X2) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_316])]) ).
tff(f2545,plain,
! [X2: 'A$',X0: 'B_option$',X1: 'A_a_fun$'] : ( 'fun_app$f'('comp$g'('uwh$'(X0),X1),X2) = X0 ),
inference(cnf_transformation,[],[f645]) ).
tff(f645,axiom,
! [X0: 'B_option$',X1: 'A_a_fun$',X2: 'A$'] : ( 'fun_app$f'('comp$g'('uwh$'(X0),X1),X2) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom643) ).
tff(f5067,plain,
spl249_315,
inference(avatar_split_clause,[],[f2456,f5065]) ).
tff(f5065,plain,
( spl249_315
<=> ! [X0: tlbool,X1: 'B_bool_fun$'] :
( ( tltrue = X0 )
| ~ 'fun_app$a'('case_option$e'(X0,X1),'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_315])]) ).
tff(f2456,plain,
! [X0: tlbool,X1: 'B_bool_fun$'] :
( ( tltrue = X0 )
| ~ 'fun_app$a'('case_option$e'(X0,X1),'none$a') ),
inference(cnf_transformation,[],[f1486]) ).
tff(f1486,plain,
! [X0: tlbool,X1: 'B_bool_fun$'] :
( ( 'fun_app$a'('case_option$e'(X0,X1),'none$a')
| ( tltrue != X0 ) )
& ( ( tltrue = X0 )
| ~ 'fun_app$a'('case_option$e'(X0,X1),'none$a') ) ),
inference(nnf_transformation,[],[f106]) ).
tff(f106,axiom,
! [X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),'none$a')
<=> ( tltrue = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom104) ).
tff(f5063,plain,
spl249_314,
inference(avatar_split_clause,[],[f2454,f5061]) ).
tff(f5061,plain,
( spl249_314
<=> ! [X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| ~ 'fun_app$a'('fun_app$e'('uwr$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_314])]) ).
tff(f2454,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| ~ 'fun_app$a'('fun_app$e'('uwr$',X0),X1) ),
inference(cnf_transformation,[],[f1485]) ).
tff(f1485,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$a'('fun_app$e'('uwr$',X0),X1)
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ~ 'fun_app$a'('fun_app$e'('uwr$',X0),X1) ) ),
inference(nnf_transformation,[],[f10]) ).
tff(f10,axiom,
! [X0: 'B_option$',X1: 'B_option$'] :
( 'fun_app$a'('fun_app$e'('uwr$',X0),X1)
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).
tff(f5059,plain,
spl249_313,
inference(avatar_split_clause,[],[f2452,f5057]) ).
tff(f5057,plain,
( spl249_313
<=> ! [X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| ~ 'fun_app$a'('fun_app$e'('uwn$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_313])]) ).
tff(f2452,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( ( X0 = X1 )
| ~ 'fun_app$a'('fun_app$e'('uwn$',X0),X1) ),
inference(cnf_transformation,[],[f1484]) ).
tff(f1484,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( ( 'fun_app$a'('fun_app$e'('uwn$',X0),X1)
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ~ 'fun_app$a'('fun_app$e'('uwn$',X0),X1) ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f6,axiom,
! [X0: 'B_option$',X1: 'B_option$'] :
( 'fun_app$a'('fun_app$e'('uwn$',X0),X1)
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5) ).
tff(f5055,plain,
( spl249_312
| ~ spl249_3
| ~ spl249_160 ),
inference(avatar_split_clause,[],[f4676,f4309,f3615,f5052]) ).
tff(f5052,plain,
( spl249_312
<=> ( 'some$' = 'fun_app$ad'('id$f','some$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_312])]) ).
tff(f4309,plain,
( spl249_160
<=> ! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ( 'some$' = 'fun_app$ad'(X0,'some$') )
| ~ 'register$h'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_160])]) ).
tff(f4676,plain,
( ( 'some$' = 'fun_app$ad'('id$f','some$') )
| ~ spl249_3
| ~ spl249_160 ),
inference(resolution,[],[f4310,f3617]) ).
tff(f4310,plain,
( ! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ~ 'register$h'(X0)
| ( 'some$' = 'fun_app$ad'(X0,'some$') ) )
| ~ spl249_160 ),
inference(avatar_component_clause,[],[f4309]) ).
tff(f5050,plain,
spl249_311,
inference(avatar_split_clause,[],[f2450,f5048]) ).
tff(f2450,plain,
! [X0: 'C_option$',X1: 'C_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$a'(X0,X1))
| ~ 'fun_app$'('is_none$a',X0) ),
inference(cnf_transformation,[],[f1483]) ).
tff(f5046,plain,
spl249_310,
inference(avatar_split_clause,[],[f2447,f5044]) ).
tff(f2447,plain,
! [X0: 'A_option$',X1: 'A_b_option_fun$'] :
( 'fun_app$a'('is_none$','bind$e'(X0,X1))
| ~ 'fun_app$aw'('is_none$b',X0) ),
inference(cnf_transformation,[],[f1481]) ).
tff(f5042,plain,
spl249_309,
inference(avatar_split_clause,[],[f2444,f5040]) ).
tff(f5040,plain,
( spl249_309
<=> ! [X0: tlbool,X1: 'C_bool_fun$'] :
( ( tltrue = X0 )
| ~ 'fun_app$'('case_option$f'(X0,X1),'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_309])]) ).
tff(f2444,plain,
! [X0: tlbool,X1: 'C_bool_fun$'] :
( ( tltrue = X0 )
| ~ 'fun_app$'('case_option$f'(X0,X1),'none$') ),
inference(cnf_transformation,[],[f1479]) ).
tff(f1479,plain,
! [X0: tlbool,X1: 'C_bool_fun$'] :
( ( 'fun_app$'('case_option$f'(X0,X1),'none$')
| ( tltrue != X0 ) )
& ( ( tltrue = X0 )
| ~ 'fun_app$'('case_option$f'(X0,X1),'none$') ) ),
inference(nnf_transformation,[],[f107]) ).
tff(f107,axiom,
! [X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),'none$')
<=> ( tltrue = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom105) ).
tff(f5038,plain,
spl249_308,
inference(avatar_split_clause,[],[f2442,f5036]) ).
tff(f5036,plain,
( spl249_308
<=> ! [X0: 'C_option$',X1: 'C_option$'] :
( ( X0 = X1 )
| ~ 'fun_app$'('fun_app$d'('uws$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_308])]) ).
tff(f2442,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( ( X0 = X1 )
| ~ 'fun_app$'('fun_app$d'('uws$',X0),X1) ),
inference(cnf_transformation,[],[f1478]) ).
tff(f1478,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$'('fun_app$d'('uws$',X0),X1)
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ~ 'fun_app$'('fun_app$d'('uws$',X0),X1) ) ),
inference(nnf_transformation,[],[f9]) ).
tff(f9,axiom,
! [X0: 'C_option$',X1: 'C_option$'] :
( 'fun_app$'('fun_app$d'('uws$',X0),X1)
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8) ).
tff(f5034,plain,
spl249_307,
inference(avatar_split_clause,[],[f2440,f5032]) ).
tff(f5032,plain,
( spl249_307
<=> ! [X0: 'C_option$',X1: 'C_option$'] :
( ( X0 = X1 )
| ~ 'fun_app$'('fun_app$d'('uwo$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_307])]) ).
tff(f2440,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( ( X0 = X1 )
| ~ 'fun_app$'('fun_app$d'('uwo$',X0),X1) ),
inference(cnf_transformation,[],[f1477]) ).
tff(f1477,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( ( 'fun_app$'('fun_app$d'('uwo$',X0),X1)
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ~ 'fun_app$'('fun_app$d'('uwo$',X0),X1) ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f5,axiom,
! [X0: 'C_option$',X1: 'C_option$'] :
( 'fun_app$'('fun_app$d'('uwo$',X0),X1)
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4) ).
tff(f5030,plain,
spl249_306,
inference(avatar_split_clause,[],[f2438,f5028]) ).
tff(f2438,plain,
! [X0: 'B_option$',X1: 'B_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$b'(X0,X1))
| ~ 'fun_app$a'('is_none$',X0) ),
inference(cnf_transformation,[],[f1476]) ).
tff(f5026,plain,
spl249_305,
inference(avatar_split_clause,[],[f2435,f5024]) ).
tff(f2435,plain,
! [X0: 'A_option$',X1: 'A_c_option_fun$'] :
( 'fun_app$'('is_none$a','bind$d'(X0,X1))
| ~ 'fun_app$aw'('is_none$b',X0) ),
inference(cnf_transformation,[],[f1474]) ).
tff(f5022,plain,
spl249_304,
inference(avatar_split_clause,[],[f2433,f5020]) ).
tff(f2433,plain,
! [X0: 'B_bool_fun$',X1: 'B$'] :
( ( tltrue = def_3(X0,X1) )
| ~ 'fun_app$c'(X0,X1) ),
inference(cnf_transformation,[],[f1472]) ).
tff(f1472,plain,
! [X0: 'B_bool_fun$',X1: 'B$'] :
( ( ( tltrue = def_3(X0,X1) )
| ~ 'fun_app$c'(X0,X1) )
& ( 'fun_app$c'(X0,X1)
| ( tltrue != def_3(X0,X1) ) ) ),
inference(nnf_transformation,[],[f830]) ).
tff(f830,plain,
! [X0: 'B_bool_fun$',X1: 'B$'] :
( ( tltrue = def_3(X0,X1) )
<=> 'fun_app$c'(X0,X1) ),
inference(rectify,[],[f714]) ).
tff(f714,axiom,
! [X1: 'B_bool_fun$',X2: 'B$'] :
( ( def_3(X1,X2) = tltrue )
<=> 'fun_app$c'(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_713) ).
tff(f5018,plain,
spl249_303,
inference(avatar_split_clause,[],[f2432,f5016]) ).
tff(f5016,plain,
( spl249_303
<=> ! [X0: 'B_bool_fun$',X1: 'B$'] :
( 'fun_app$c'(X0,X1)
| ( tltrue != def_3(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_303])]) ).
tff(f2432,plain,
! [X0: 'B_bool_fun$',X1: 'B$'] :
( 'fun_app$c'(X0,X1)
| ( tltrue != def_3(X0,X1) ) ),
inference(cnf_transformation,[],[f1472]) ).
tff(f5014,plain,
spl249_302,
inference(avatar_split_clause,[],[f2431,f5012]) ).
tff(f2431,plain,
! [X0: 'B_bool_fun$',X1: 'B$'] :
( ( tltrue = def_2(X0,X1) )
| ~ 'fun_app$c'(X0,X1) ),
inference(cnf_transformation,[],[f1471]) ).
tff(f1471,plain,
! [X0: 'B_bool_fun$',X1: 'B$'] :
( ( ( tltrue = def_2(X0,X1) )
| ~ 'fun_app$c'(X0,X1) )
& ( 'fun_app$c'(X0,X1)
| ( tltrue != def_2(X0,X1) ) ) ),
inference(nnf_transformation,[],[f829]) ).
tff(f829,plain,
! [X0: 'B_bool_fun$',X1: 'B$'] :
( ( tltrue = def_2(X0,X1) )
<=> 'fun_app$c'(X0,X1) ),
inference(rectify,[],[f713]) ).
tff(f713,axiom,
! [X1: 'B_bool_fun$',X2: 'B$'] :
( ( def_2(X1,X2) = tltrue )
<=> 'fun_app$c'(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_712) ).
tff(f5010,plain,
( spl249_301
| ~ spl249_5
| ~ spl249_159 ),
inference(avatar_split_clause,[],[f4675,f4305,f3625,f5007]) ).
tff(f5007,plain,
( spl249_301
<=> ( 'some$' = 'fun_app$au'('f$','some$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_301])]) ).
tff(f4305,plain,
( spl249_159
<=> ! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( 'some$' = 'fun_app$au'(X0,'some$b') )
| ~ 'register$'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_159])]) ).
tff(f4675,plain,
( ( 'some$' = 'fun_app$au'('f$','some$b') )
| ~ spl249_5
| ~ spl249_159 ),
inference(resolution,[],[f4306,f3627]) ).
tff(f4306,plain,
( ! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ~ 'register$'(X0)
| ( 'some$' = 'fun_app$au'(X0,'some$b') ) )
| ~ spl249_159 ),
inference(avatar_component_clause,[],[f4305]) ).
tff(f5005,plain,
spl249_300,
inference(avatar_split_clause,[],[f2430,f5003]) ).
tff(f5003,plain,
( spl249_300
<=> ! [X0: 'B_bool_fun$',X1: 'B$'] :
( 'fun_app$c'(X0,X1)
| ( tltrue != def_2(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_300])]) ).
tff(f2430,plain,
! [X0: 'B_bool_fun$',X1: 'B$'] :
( 'fun_app$c'(X0,X1)
| ( tltrue != def_2(X0,X1) ) ),
inference(cnf_transformation,[],[f1471]) ).
tff(f5001,plain,
spl249_299,
inference(avatar_split_clause,[],[f2429,f4999]) ).
tff(f2429,plain,
! [X0: 'B_bool_fun$',X1: 'B$'] :
( ( tltrue = def_5(X0,X1) )
| ~ 'fun_app$c'(X0,X1) ),
inference(cnf_transformation,[],[f1470]) ).
tff(f1470,plain,
! [X0: 'B_bool_fun$',X1: 'B$'] :
( ( ( tltrue = def_5(X0,X1) )
| ~ 'fun_app$c'(X0,X1) )
& ( 'fun_app$c'(X0,X1)
| ( tltrue != def_5(X0,X1) ) ) ),
inference(nnf_transformation,[],[f828]) ).
tff(f828,plain,
! [X0: 'B_bool_fun$',X1: 'B$'] :
( ( tltrue = def_5(X0,X1) )
<=> 'fun_app$c'(X0,X1) ),
inference(rectify,[],[f716]) ).
tff(f716,axiom,
! [X1: 'B_bool_fun$',X2: 'B$'] :
( ( def_5(X1,X2) = tltrue )
<=> 'fun_app$c'(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_715) ).
tff(f4997,plain,
spl249_298,
inference(avatar_split_clause,[],[f2428,f4995]) ).
tff(f4995,plain,
( spl249_298
<=> ! [X0: 'B_bool_fun$',X1: 'B$'] :
( 'fun_app$c'(X0,X1)
| ( tltrue != def_5(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_298])]) ).
tff(f2428,plain,
! [X0: 'B_bool_fun$',X1: 'B$'] :
( 'fun_app$c'(X0,X1)
| ( tltrue != def_5(X0,X1) ) ),
inference(cnf_transformation,[],[f1470]) ).
tff(f4993,plain,
spl249_297,
inference(avatar_split_clause,[],[f2427,f4991]) ).
tff(f2427,plain,
! [X0: 'C_bool_fun$',X1: 'C$'] :
( ( tltrue = def_1(X0,X1) )
| ~ 'fun_app$b'(X0,X1) ),
inference(cnf_transformation,[],[f1469]) ).
tff(f1469,plain,
! [X0: 'C_bool_fun$',X1: 'C$'] :
( ( ( tltrue = def_1(X0,X1) )
| ~ 'fun_app$b'(X0,X1) )
& ( 'fun_app$b'(X0,X1)
| ( tltrue != def_1(X0,X1) ) ) ),
inference(nnf_transformation,[],[f827]) ).
tff(f827,plain,
! [X0: 'C_bool_fun$',X1: 'C$'] :
( ( tltrue = def_1(X0,X1) )
<=> 'fun_app$b'(X0,X1) ),
inference(rectify,[],[f712]) ).
tff(f712,axiom,
! [X1: 'C_bool_fun$',X2: 'C$'] :
( ( def_1(X1,X2) = tltrue )
<=> 'fun_app$b'(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_711) ).
tff(f4989,plain,
spl249_296,
inference(avatar_split_clause,[],[f2426,f4987]) ).
tff(f4987,plain,
( spl249_296
<=> ! [X0: 'C_bool_fun$',X1: 'C$'] :
( 'fun_app$b'(X0,X1)
| ( tltrue != def_1(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_296])]) ).
tff(f2426,plain,
! [X0: 'C_bool_fun$',X1: 'C$'] :
( 'fun_app$b'(X0,X1)
| ( tltrue != def_1(X0,X1) ) ),
inference(cnf_transformation,[],[f1469]) ).
tff(f4985,plain,
spl249_295,
inference(avatar_split_clause,[],[f2425,f4983]) ).
tff(f2425,plain,
! [X0: 'C_bool_fun$',X1: 'C$'] :
( ( tltrue = def_4(X0,X1) )
| ~ 'fun_app$b'(X0,X1) ),
inference(cnf_transformation,[],[f1468]) ).
tff(f1468,plain,
! [X0: 'C_bool_fun$',X1: 'C$'] :
( ( ( tltrue = def_4(X0,X1) )
| ~ 'fun_app$b'(X0,X1) )
& ( 'fun_app$b'(X0,X1)
| ( tltrue != def_4(X0,X1) ) ) ),
inference(nnf_transformation,[],[f826]) ).
tff(f826,plain,
! [X0: 'C_bool_fun$',X1: 'C$'] :
( ( tltrue = def_4(X0,X1) )
<=> 'fun_app$b'(X0,X1) ),
inference(rectify,[],[f715]) ).
tff(f715,axiom,
! [X1: 'C_bool_fun$',X2: 'C$'] :
( ( def_4(X1,X2) = tltrue )
<=> 'fun_app$b'(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_714) ).
tff(f4981,plain,
spl249_294,
inference(avatar_split_clause,[],[f2424,f4979]) ).
tff(f4979,plain,
( spl249_294
<=> ! [X0: 'C_bool_fun$',X1: 'C$'] :
( 'fun_app$b'(X0,X1)
| ( tltrue != def_4(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_294])]) ).
tff(f2424,plain,
! [X0: 'C_bool_fun$',X1: 'C$'] :
( 'fun_app$b'(X0,X1)
| ( tltrue != def_4(X0,X1) ) ),
inference(cnf_transformation,[],[f1468]) ).
tff(f4977,plain,
spl249_293,
inference(avatar_split_clause,[],[f2397,f4975]) ).
tff(f2397,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( tltrue = def_14(X0,X1) )
| ~ 'fun_app$a'(X0,X1) ),
inference(cnf_transformation,[],[f1451]) ).
tff(f1451,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( ( tltrue = def_14(X0,X1) )
| ~ 'fun_app$a'(X0,X1) )
& ( 'fun_app$a'(X0,X1)
| ( tltrue != def_14(X0,X1) ) ) ),
inference(nnf_transformation,[],[f725]) ).
tff(f725,axiom,
! [X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( ( tltrue = def_14(X0,X1) )
<=> 'fun_app$a'(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_724) ).
tff(f4973,plain,
spl249_292,
inference(avatar_split_clause,[],[f2396,f4971]) ).
tff(f4971,plain,
( spl249_292
<=> ! [X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,X1)
| ( tltrue != def_14(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_292])]) ).
tff(f2396,plain,
! [X0: 'B_option_bool_fun$',X1: 'B_option$'] :
( 'fun_app$a'(X0,X1)
| ( tltrue != def_14(X0,X1) ) ),
inference(cnf_transformation,[],[f1451]) ).
tff(f4969,plain,
spl249_291,
inference(avatar_split_clause,[],[f2395,f4967]) ).
tff(f2395,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( tltrue = def_10(X0,X1) )
| ~ 'fun_app$'(X0,X1) ),
inference(cnf_transformation,[],[f1450]) ).
tff(f1450,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( ( tltrue = def_10(X0,X1) )
| ~ 'fun_app$'(X0,X1) )
& ( 'fun_app$'(X0,X1)
| ( tltrue != def_10(X0,X1) ) ) ),
inference(nnf_transformation,[],[f721]) ).
tff(f721,axiom,
! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( tltrue = def_10(X0,X1) )
<=> 'fun_app$'(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_720) ).
tff(f4965,plain,
( spl249_290
| ~ spl249_4
| ~ spl249_158 ),
inference(avatar_split_clause,[],[f4674,f4301,f3620,f4962]) ).
tff(f4962,plain,
( spl249_290
<=> ( 'some$a' = 'fun_app$am'('g$','some$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_290])]) ).
tff(f4301,plain,
( spl249_158
<=> ! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( 'some$a' = 'fun_app$am'(X0,'some$') )
| ~ 'register$a'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_158])]) ).
tff(f4674,plain,
( ( 'some$a' = 'fun_app$am'('g$','some$') )
| ~ spl249_4
| ~ spl249_158 ),
inference(resolution,[],[f4302,f3622]) ).
tff(f4302,plain,
( ! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ~ 'register$a'(X0)
| ( 'some$a' = 'fun_app$am'(X0,'some$') ) )
| ~ spl249_158 ),
inference(avatar_component_clause,[],[f4301]) ).
tff(f4960,plain,
spl249_289,
inference(avatar_split_clause,[],[f2394,f4958]) ).
tff(f4958,plain,
( spl249_289
<=> ! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,X1)
| ( tltrue != def_10(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_289])]) ).
tff(f2394,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,X1)
| ( tltrue != def_10(X0,X1) ) ),
inference(cnf_transformation,[],[f1450]) ).
tff(f4956,plain,
spl249_288,
inference(avatar_split_clause,[],[f2393,f4954]) ).
tff(f2393,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( tltrue = def_15(X0,X1) )
| ~ 'fun_app$'(X0,X1) ),
inference(cnf_transformation,[],[f1449]) ).
tff(f1449,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( ( tltrue = def_15(X0,X1) )
| ~ 'fun_app$'(X0,X1) )
& ( 'fun_app$'(X0,X1)
| ( tltrue != def_15(X0,X1) ) ) ),
inference(nnf_transformation,[],[f726]) ).
tff(f726,axiom,
! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( ( tltrue = def_15(X0,X1) )
<=> 'fun_app$'(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_725) ).
tff(f4952,plain,
spl249_287,
inference(avatar_split_clause,[],[f2392,f4950]) ).
tff(f4950,plain,
( spl249_287
<=> ! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,X1)
| ( tltrue != def_15(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_287])]) ).
tff(f2392,plain,
! [X0: 'C_option_bool_fun$',X1: 'C_option$'] :
( 'fun_app$'(X0,X1)
| ( tltrue != def_15(X0,X1) ) ),
inference(cnf_transformation,[],[f1449]) ).
tff(f4948,plain,
spl249_286,
inference(avatar_split_clause,[],[f2391,f4946]) ).
tff(f4946,plain,
( spl249_286
<=> ! [X0: 'Bool_bool_fun$',X1: tlbool] :
( ( tltrue = def_7(X0,X1) )
| ~ 'fun_app$ag'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_286])]) ).
tff(f2391,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool] :
( ( tltrue = def_7(X0,X1) )
| ~ 'fun_app$ag'(X0,X1) ),
inference(cnf_transformation,[],[f1448]) ).
tff(f1448,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool] :
( ( ( tltrue = def_7(X0,X1) )
| ~ 'fun_app$ag'(X0,X1) )
& ( 'fun_app$ag'(X0,X1)
| ( tltrue != def_7(X0,X1) ) ) ),
inference(nnf_transformation,[],[f718]) ).
tff(f718,axiom,
! [X0: 'Bool_bool_fun$',X1: tlbool] :
( ( tltrue = def_7(X0,X1) )
<=> 'fun_app$ag'(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_717) ).
tff(f4944,plain,
spl249_285,
inference(avatar_split_clause,[],[f2390,f4942]) ).
tff(f4942,plain,
( spl249_285
<=> ! [X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,X1)
| ( tltrue != def_7(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_285])]) ).
tff(f2390,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,X1)
| ( tltrue != def_7(X0,X1) ) ),
inference(cnf_transformation,[],[f1448]) ).
tff(f4940,plain,
spl249_284,
inference(avatar_split_clause,[],[f2389,f4938]) ).
tff(f4938,plain,
( spl249_284
<=> ! [X0: 'Bool_bool_fun$',X1: tlbool] :
( ( tltrue = def_9(X0,X1) )
| ~ 'fun_app$ag'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_284])]) ).
tff(f2389,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool] :
( ( tltrue = def_9(X0,X1) )
| ~ 'fun_app$ag'(X0,X1) ),
inference(cnf_transformation,[],[f1447]) ).
tff(f1447,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool] :
( ( ( tltrue = def_9(X0,X1) )
| ~ 'fun_app$ag'(X0,X1) )
& ( 'fun_app$ag'(X0,X1)
| ( tltrue != def_9(X0,X1) ) ) ),
inference(nnf_transformation,[],[f720]) ).
tff(f720,axiom,
! [X0: 'Bool_bool_fun$',X1: tlbool] :
( ( tltrue = def_9(X0,X1) )
<=> 'fun_app$ag'(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_719) ).
tff(f4936,plain,
spl249_283,
inference(avatar_split_clause,[],[f2388,f4934]) ).
tff(f4934,plain,
( spl249_283
<=> ! [X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,X1)
| ( tltrue != def_9(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_283])]) ).
tff(f2388,plain,
! [X0: 'Bool_bool_fun$',X1: tlbool] :
( 'fun_app$ag'(X0,X1)
| ( tltrue != def_9(X0,X1) ) ),
inference(cnf_transformation,[],[f1447]) ).
tff(f4932,plain,
spl249_282,
inference(avatar_split_clause,[],[f2313,f4930]) ).
tff(f4930,plain,
( spl249_282
<=> ! [X0: 'C_option$',X1: 'C_option_option$'] :
( ( 'some$d'(X0) = X1 )
| ~ 'member$'(X0,'set_option$a'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_282])]) ).
tff(f2313,plain,
! [X0: 'C_option$',X1: 'C_option_option$'] :
( ( 'some$d'(X0) = X1 )
| ~ 'member$'(X0,'set_option$a'(X1)) ),
inference(cnf_transformation,[],[f933]) ).
tff(f933,plain,
! [X0: 'C_option$',X1: 'C_option_option$'] :
( ( 'some$d'(X0) = X1 )
| ~ 'member$'(X0,'set_option$a'(X1)) ),
inference(ennf_transformation,[],[f813]) ).
tff(f813,plain,
! [X0: 'C_option$',X1: 'C_option_option$'] :
~ ( ( 'some$d'(X0) != X1 )
& 'member$'(X0,'set_option$a'(X1)) ),
inference(flattening,[],[f812]) ).
tff(f812,plain,
! [X0: 'C_option$',X1: 'C_option_option$'] :
~ ( ( ~ 'some$d'(X0) = X1 )
& 'member$'(X0,'set_option$a'(X1)) ),
inference(true_and_false_elimination,[],[f438]) ).
tff(f438,axiom,
! [X0: 'C_option$',X1: 'C_option_option$'] :
( ( ( ( 'some$d'(X0) = X1 )
=> $false )
& 'member$'(X0,'set_option$a'(X1)) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom436) ).
tff(f4928,plain,
spl249_281,
inference(avatar_split_clause,[],[f2312,f4926]) ).
tff(f4926,plain,
( spl249_281
<=> ! [X0: 'B_option$',X1: 'B_option_option$'] :
( ( 'some$c'(X0) = X1 )
| ~ 'member$a'(X0,'set_option$'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_281])]) ).
tff(f2312,plain,
! [X0: 'B_option$',X1: 'B_option_option$'] :
( ( 'some$c'(X0) = X1 )
| ~ 'member$a'(X0,'set_option$'(X1)) ),
inference(cnf_transformation,[],[f932]) ).
tff(f932,plain,
! [X0: 'B_option$',X1: 'B_option_option$'] :
( ( 'some$c'(X0) = X1 )
| ~ 'member$a'(X0,'set_option$'(X1)) ),
inference(ennf_transformation,[],[f811]) ).
tff(f811,plain,
! [X0: 'B_option$',X1: 'B_option_option$'] :
~ ( ( 'some$c'(X0) != X1 )
& 'member$a'(X0,'set_option$'(X1)) ),
inference(flattening,[],[f810]) ).
tff(f810,plain,
! [X0: 'B_option$',X1: 'B_option_option$'] :
~ ( ( ~ 'some$c'(X0) = X1 )
& 'member$a'(X0,'set_option$'(X1)) ),
inference(true_and_false_elimination,[],[f437]) ).
tff(f437,axiom,
! [X0: 'B_option$',X1: 'B_option_option$'] :
( ( ( ( 'some$c'(X0) = X1 )
=> $false )
& 'member$a'(X0,'set_option$'(X1)) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom435) ).
tff(f4924,plain,
spl249_280,
inference(avatar_split_clause,[],[f2309,f4922]) ).
tff(f4922,plain,
( spl249_280
<=> ! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B_b_option_fun_b_b_option_fun_fun$'] :
( 'preregister$c'('comp$al'(X1,X0))
| ~ 'preregister$'(X1)
| ~ 'preregister$c'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_280])]) ).
tff(f2309,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B_b_option_fun_b_b_option_fun_fun$'] :
( 'preregister$c'('comp$al'(X1,X0))
| ~ 'preregister$'(X1)
| ~ 'preregister$c'(X0) ),
inference(cnf_transformation,[],[f927]) ).
tff(f927,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B_b_option_fun_b_b_option_fun_fun$'] :
( 'preregister$c'('comp$al'(X1,X0))
| ~ 'preregister$'(X1)
| ~ 'preregister$c'(X0) ),
inference(flattening,[],[f926]) ).
tff(f926,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B_b_option_fun_b_b_option_fun_fun$'] :
( 'preregister$c'('comp$al'(X1,X0))
| ~ 'preregister$'(X1)
| ~ 'preregister$c'(X0) ),
inference(ennf_transformation,[],[f533]) ).
tff(f533,axiom,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ( 'preregister$'(X1)
& 'preregister$c'(X0) )
=> 'preregister$c'('comp$al'(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom531) ).
tff(f4920,plain,
( spl249_279
| ~ spl249_2
| ~ spl249_157 ),
inference(avatar_split_clause,[],[f4673,f4297,f3610,f4917]) ).
tff(f4917,plain,
( spl249_279
<=> ( 'some$a' = 'fun_app$aa'('id$g','some$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_279])]) ).
tff(f4297,plain,
( spl249_157
<=> ! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ( 'some$a' = 'fun_app$aa'(X0,'some$a') )
| ~ 'register$f'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_157])]) ).
tff(f4673,plain,
( ( 'some$a' = 'fun_app$aa'('id$g','some$a') )
| ~ spl249_2
| ~ spl249_157 ),
inference(resolution,[],[f4298,f3612]) ).
tff(f4298,plain,
( ! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ~ 'register$f'(X0)
| ( 'some$a' = 'fun_app$aa'(X0,'some$a') ) )
| ~ spl249_157 ),
inference(avatar_component_clause,[],[f4297]) ).
tff(f4915,plain,
spl249_278,
inference(avatar_split_clause,[],[f2308,f4913]) ).
tff(f4913,plain,
( spl249_278
<=> ! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C_c_option_fun_c_c_option_fun_fun$'] :
( 'preregister$b'('comp$an'(X1,X0))
| ~ 'preregister$a'(X1)
| ~ 'preregister$b'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_278])]) ).
tff(f2308,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C_c_option_fun_c_c_option_fun_fun$'] :
( 'preregister$b'('comp$an'(X1,X0))
| ~ 'preregister$a'(X1)
| ~ 'preregister$b'(X0) ),
inference(cnf_transformation,[],[f925]) ).
tff(f925,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C_c_option_fun_c_c_option_fun_fun$'] :
( 'preregister$b'('comp$an'(X1,X0))
| ~ 'preregister$a'(X1)
| ~ 'preregister$b'(X0) ),
inference(flattening,[],[f924]) ).
tff(f924,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C_c_option_fun_c_c_option_fun_fun$'] :
( 'preregister$b'('comp$an'(X1,X0))
| ~ 'preregister$a'(X1)
| ~ 'preregister$b'(X0) ),
inference(ennf_transformation,[],[f535]) ).
tff(f535,axiom,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ( 'preregister$a'(X1)
& 'preregister$b'(X0) )
=> 'preregister$b'('comp$an'(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom533) ).
tff(f4911,plain,
spl249_277,
inference(avatar_split_clause,[],[f2307,f4909]) ).
tff(f4909,plain,
( spl249_277
<=> ! [X0: 'B_b_option_fun_b_b_option_fun_fun$',X1: 'B_b_option_fun_c_c_option_fun_fun$'] :
( 'preregister$b'('comp$ak'(X1,X0))
| ~ 'preregister$b'(X1)
| ~ 'preregister$'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_277])]) ).
tff(f2307,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$',X1: 'B_b_option_fun_c_c_option_fun_fun$'] :
( 'preregister$b'('comp$ak'(X1,X0))
| ~ 'preregister$b'(X1)
| ~ 'preregister$'(X0) ),
inference(cnf_transformation,[],[f923]) ).
tff(f923,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$',X1: 'B_b_option_fun_c_c_option_fun_fun$'] :
( 'preregister$b'('comp$ak'(X1,X0))
| ~ 'preregister$b'(X1)
| ~ 'preregister$'(X0) ),
inference(flattening,[],[f922]) ).
tff(f922,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$',X1: 'B_b_option_fun_c_c_option_fun_fun$'] :
( 'preregister$b'('comp$ak'(X1,X0))
| ~ 'preregister$b'(X1)
| ~ 'preregister$'(X0) ),
inference(ennf_transformation,[],[f532]) ).
tff(f532,axiom,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$',X1: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( 'preregister$b'(X1)
& 'preregister$'(X0) )
=> 'preregister$b'('comp$ak'(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom530) ).
tff(f4907,plain,
spl249_276,
inference(avatar_split_clause,[],[f2161,f4905]) ).
tff(f4905,plain,
( spl249_276
<=> ! [X0: 'B_option_bool_fun$'] :
( ( 'bot$a' = 'collect$b'(X0) )
| 'fun_app$a'(X0,sK89(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_276])]) ).
tff(f2161,plain,
! [X0: 'B_option_bool_fun$'] :
( ( 'bot$a' = 'collect$b'(X0) )
| 'fun_app$a'(X0,sK89(X0)) ),
inference(cnf_transformation,[],[f1305]) ).
tff(f1305,plain,
! [X0: 'B_option_bool_fun$'] :
( ( ( 'bot$a' = 'collect$b'(X0) )
| 'fun_app$a'(X0,sK89(X0)) )
& ( ! [X2: 'B_option$'] : ~ 'fun_app$a'(X0,X2)
| ( 'bot$a' != 'collect$b'(X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK89])],[f1303,f1304]) ).
tff(f1304,plain,
! [X0: 'B_option_bool_fun$'] :
( ? [X1: 'B_option$'] : 'fun_app$a'(X0,X1)
=> 'fun_app$a'(X0,sK89(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1303,plain,
! [X0: 'B_option_bool_fun$'] :
( ( ( 'bot$a' = 'collect$b'(X0) )
| ? [X1: 'B_option$'] : 'fun_app$a'(X0,X1) )
& ( ! [X2: 'B_option$'] : ~ 'fun_app$a'(X0,X2)
| ( 'bot$a' != 'collect$b'(X0) ) ) ),
inference(rectify,[],[f1302]) ).
tff(f1302,plain,
! [X0: 'B_option_bool_fun$'] :
( ( ( 'bot$a' = 'collect$b'(X0) )
| ? [X1: 'B_option$'] : 'fun_app$a'(X0,X1) )
& ( ! [X1: 'B_option$'] : ~ 'fun_app$a'(X0,X1)
| ( 'bot$a' != 'collect$b'(X0) ) ) ),
inference(nnf_transformation,[],[f567]) ).
tff(f567,axiom,
! [X0: 'B_option_bool_fun$'] :
( ( 'bot$a' = 'collect$b'(X0) )
<=> ! [X1: 'B_option$'] : ~ 'fun_app$a'(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom565) ).
tff(f4903,plain,
spl249_275,
inference(avatar_split_clause,[],[f2159,f4901]) ).
tff(f4901,plain,
( spl249_275
<=> ! [X0: 'B_option_bool_fun$'] :
( ( 'bot$a' = 'collect$b'(X0) )
| 'fun_app$a'(X0,sK88(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_275])]) ).
tff(f2159,plain,
! [X0: 'B_option_bool_fun$'] :
( ( 'bot$a' = 'collect$b'(X0) )
| 'fun_app$a'(X0,sK88(X0)) ),
inference(cnf_transformation,[],[f1301]) ).
tff(f1301,plain,
! [X0: 'B_option_bool_fun$'] :
( ( ( 'bot$a' = 'collect$b'(X0) )
| 'fun_app$a'(X0,sK88(X0)) )
& ( ! [X2: 'B_option$'] : ~ 'fun_app$a'(X0,X2)
| ( 'bot$a' != 'collect$b'(X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK88])],[f1299,f1300]) ).
tff(f1300,plain,
! [X0: 'B_option_bool_fun$'] :
( ? [X1: 'B_option$'] : 'fun_app$a'(X0,X1)
=> 'fun_app$a'(X0,sK88(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1299,plain,
! [X0: 'B_option_bool_fun$'] :
( ( ( 'bot$a' = 'collect$b'(X0) )
| ? [X1: 'B_option$'] : 'fun_app$a'(X0,X1) )
& ( ! [X2: 'B_option$'] : ~ 'fun_app$a'(X0,X2)
| ( 'bot$a' != 'collect$b'(X0) ) ) ),
inference(rectify,[],[f1298]) ).
tff(f1298,plain,
! [X0: 'B_option_bool_fun$'] :
( ( ( 'bot$a' = 'collect$b'(X0) )
| ? [X1: 'B_option$'] : 'fun_app$a'(X0,X1) )
& ( ! [X1: 'B_option$'] : ~ 'fun_app$a'(X0,X1)
| ( 'bot$a' != 'collect$b'(X0) ) ) ),
inference(nnf_transformation,[],[f571]) ).
tff(f571,axiom,
! [X0: 'B_option_bool_fun$'] :
( ( 'bot$a' = 'collect$b'(X0) )
<=> ! [X1: 'B_option$'] : ~ 'fun_app$a'(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom569) ).
tff(f4899,plain,
spl249_274,
inference(avatar_split_clause,[],[f2157,f4897]) ).
tff(f4897,plain,
( spl249_274
<=> ! [X0: 'C_option_bool_fun$'] :
( ( 'bot$b' = 'collect$c'(X0) )
| 'fun_app$'(X0,sK87(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_274])]) ).
tff(f2157,plain,
! [X0: 'C_option_bool_fun$'] :
( ( 'bot$b' = 'collect$c'(X0) )
| 'fun_app$'(X0,sK87(X0)) ),
inference(cnf_transformation,[],[f1297]) ).
tff(f1297,plain,
! [X0: 'C_option_bool_fun$'] :
( ( ( 'bot$b' = 'collect$c'(X0) )
| 'fun_app$'(X0,sK87(X0)) )
& ( ! [X2: 'C_option$'] : ~ 'fun_app$'(X0,X2)
| ( 'bot$b' != 'collect$c'(X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK87])],[f1295,f1296]) ).
tff(f1296,plain,
! [X0: 'C_option_bool_fun$'] :
( ? [X1: 'C_option$'] : 'fun_app$'(X0,X1)
=> 'fun_app$'(X0,sK87(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1295,plain,
! [X0: 'C_option_bool_fun$'] :
( ( ( 'bot$b' = 'collect$c'(X0) )
| ? [X1: 'C_option$'] : 'fun_app$'(X0,X1) )
& ( ! [X2: 'C_option$'] : ~ 'fun_app$'(X0,X2)
| ( 'bot$b' != 'collect$c'(X0) ) ) ),
inference(rectify,[],[f1294]) ).
tff(f1294,plain,
! [X0: 'C_option_bool_fun$'] :
( ( ( 'bot$b' = 'collect$c'(X0) )
| ? [X1: 'C_option$'] : 'fun_app$'(X0,X1) )
& ( ! [X1: 'C_option$'] : ~ 'fun_app$'(X0,X1)
| ( 'bot$b' != 'collect$c'(X0) ) ) ),
inference(nnf_transformation,[],[f568]) ).
tff(f568,axiom,
! [X0: 'C_option_bool_fun$'] :
( ( 'bot$b' = 'collect$c'(X0) )
<=> ! [X1: 'C_option$'] : ~ 'fun_app$'(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom566) ).
tff(f4895,plain,
spl249_273,
inference(avatar_split_clause,[],[f2155,f4893]) ).
tff(f4893,plain,
( spl249_273
<=> ! [X0: 'C_option_bool_fun$'] :
( ( 'bot$b' = 'collect$c'(X0) )
| 'fun_app$'(X0,sK86(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_273])]) ).
tff(f2155,plain,
! [X0: 'C_option_bool_fun$'] :
( ( 'bot$b' = 'collect$c'(X0) )
| 'fun_app$'(X0,sK86(X0)) ),
inference(cnf_transformation,[],[f1293]) ).
tff(f1293,plain,
! [X0: 'C_option_bool_fun$'] :
( ( ( 'bot$b' = 'collect$c'(X0) )
| 'fun_app$'(X0,sK86(X0)) )
& ( ! [X2: 'C_option$'] : ~ 'fun_app$'(X0,X2)
| ( 'bot$b' != 'collect$c'(X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK86])],[f1291,f1292]) ).
tff(f1292,plain,
! [X0: 'C_option_bool_fun$'] :
( ? [X1: 'C_option$'] : 'fun_app$'(X0,X1)
=> 'fun_app$'(X0,sK86(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1291,plain,
! [X0: 'C_option_bool_fun$'] :
( ( ( 'bot$b' = 'collect$c'(X0) )
| ? [X1: 'C_option$'] : 'fun_app$'(X0,X1) )
& ( ! [X2: 'C_option$'] : ~ 'fun_app$'(X0,X2)
| ( 'bot$b' != 'collect$c'(X0) ) ) ),
inference(rectify,[],[f1290]) ).
tff(f1290,plain,
! [X0: 'C_option_bool_fun$'] :
( ( ( 'bot$b' = 'collect$c'(X0) )
| ? [X1: 'C_option$'] : 'fun_app$'(X0,X1) )
& ( ! [X1: 'C_option$'] : ~ 'fun_app$'(X0,X1)
| ( 'bot$b' != 'collect$c'(X0) ) ) ),
inference(nnf_transformation,[],[f572]) ).
tff(f572,axiom,
! [X0: 'C_option_bool_fun$'] :
( ( 'bot$b' = 'collect$c'(X0) )
<=> ! [X1: 'C_option$'] : ~ 'fun_app$'(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom570) ).
tff(f4891,plain,
spl249_272,
inference(avatar_split_clause,[],[f2153,f4889]) ).
tff(f4889,plain,
( spl249_272
<=> ! [X0: 'B_bool_fun$'] :
( ( 'bot$d' = 'collect$'(X0) )
| 'fun_app$c'(X0,sK85(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_272])]) ).
tff(f2153,plain,
! [X0: 'B_bool_fun$'] :
( ( 'bot$d' = 'collect$'(X0) )
| 'fun_app$c'(X0,sK85(X0)) ),
inference(cnf_transformation,[],[f1289]) ).
tff(f1289,plain,
! [X0: 'B_bool_fun$'] :
( ( ( 'bot$d' = 'collect$'(X0) )
| 'fun_app$c'(X0,sK85(X0)) )
& ( ! [X2: 'B$'] : ~ 'fun_app$c'(X0,X2)
| ( 'bot$d' != 'collect$'(X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85])],[f1287,f1288]) ).
tff(f1288,plain,
! [X0: 'B_bool_fun$'] :
( ? [X1: 'B$'] : 'fun_app$c'(X0,X1)
=> 'fun_app$c'(X0,sK85(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1287,plain,
! [X0: 'B_bool_fun$'] :
( ( ( 'bot$d' = 'collect$'(X0) )
| ? [X1: 'B$'] : 'fun_app$c'(X0,X1) )
& ( ! [X2: 'B$'] : ~ 'fun_app$c'(X0,X2)
| ( 'bot$d' != 'collect$'(X0) ) ) ),
inference(rectify,[],[f1286]) ).
tff(f1286,plain,
! [X0: 'B_bool_fun$'] :
( ( ( 'bot$d' = 'collect$'(X0) )
| ? [X1: 'B$'] : 'fun_app$c'(X0,X1) )
& ( ! [X1: 'B$'] : ~ 'fun_app$c'(X0,X1)
| ( 'bot$d' != 'collect$'(X0) ) ) ),
inference(nnf_transformation,[],[f565]) ).
tff(f565,axiom,
! [X0: 'B_bool_fun$'] :
( ( 'bot$d' = 'collect$'(X0) )
<=> ! [X1: 'B$'] : ~ 'fun_app$c'(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom563) ).
tff(f4887,plain,
spl249_271,
inference(avatar_split_clause,[],[f2151,f4885]) ).
tff(f2151,plain,
! [X0: 'B_bool_fun$'] :
( ( 'bot$d' = 'collect$'(X0) )
| 'fun_app$c'(X0,sK84(X0)) ),
inference(cnf_transformation,[],[f1285]) ).
tff(f1285,plain,
! [X0: 'B_bool_fun$'] :
( ( ( 'bot$d' = 'collect$'(X0) )
| 'fun_app$c'(X0,sK84(X0)) )
& ( ! [X2: 'B$'] : ~ 'fun_app$c'(X0,X2)
| ( 'bot$d' != 'collect$'(X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK84])],[f1283,f1284]) ).
tff(f1284,plain,
! [X0: 'B_bool_fun$'] :
( ? [X1: 'B$'] : 'fun_app$c'(X0,X1)
=> 'fun_app$c'(X0,sK84(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1283,plain,
! [X0: 'B_bool_fun$'] :
( ( ( 'bot$d' = 'collect$'(X0) )
| ? [X1: 'B$'] : 'fun_app$c'(X0,X1) )
& ( ! [X2: 'B$'] : ~ 'fun_app$c'(X0,X2)
| ( 'bot$d' != 'collect$'(X0) ) ) ),
inference(rectify,[],[f1282]) ).
tff(f1282,plain,
! [X0: 'B_bool_fun$'] :
( ( ( 'bot$d' = 'collect$'(X0) )
| ? [X1: 'B$'] : 'fun_app$c'(X0,X1) )
& ( ! [X1: 'B$'] : ~ 'fun_app$c'(X0,X1)
| ( 'bot$d' != 'collect$'(X0) ) ) ),
inference(nnf_transformation,[],[f569]) ).
tff(f569,axiom,
! [X0: 'B_bool_fun$'] :
( ( 'bot$d' = 'collect$'(X0) )
<=> ! [X1: 'B$'] : ~ 'fun_app$c'(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom567) ).
tff(f4883,plain,
spl249_270,
inference(avatar_split_clause,[],[f2149,f4881]) ).
tff(f4881,plain,
( spl249_270
<=> ! [X0: 'C_bool_fun$'] :
( ( 'bot$c' = 'collect$a'(X0) )
| 'fun_app$b'(X0,sK83(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_270])]) ).
tff(f2149,plain,
! [X0: 'C_bool_fun$'] :
( ( 'bot$c' = 'collect$a'(X0) )
| 'fun_app$b'(X0,sK83(X0)) ),
inference(cnf_transformation,[],[f1281]) ).
tff(f1281,plain,
! [X0: 'C_bool_fun$'] :
( ( ( 'bot$c' = 'collect$a'(X0) )
| 'fun_app$b'(X0,sK83(X0)) )
& ( ! [X2: 'C$'] : ~ 'fun_app$b'(X0,X2)
| ( 'bot$c' != 'collect$a'(X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK83])],[f1279,f1280]) ).
tff(f1280,plain,
! [X0: 'C_bool_fun$'] :
( ? [X1: 'C$'] : 'fun_app$b'(X0,X1)
=> 'fun_app$b'(X0,sK83(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1279,plain,
! [X0: 'C_bool_fun$'] :
( ( ( 'bot$c' = 'collect$a'(X0) )
| ? [X1: 'C$'] : 'fun_app$b'(X0,X1) )
& ( ! [X2: 'C$'] : ~ 'fun_app$b'(X0,X2)
| ( 'bot$c' != 'collect$a'(X0) ) ) ),
inference(rectify,[],[f1278]) ).
tff(f1278,plain,
! [X0: 'C_bool_fun$'] :
( ( ( 'bot$c' = 'collect$a'(X0) )
| ? [X1: 'C$'] : 'fun_app$b'(X0,X1) )
& ( ! [X1: 'C$'] : ~ 'fun_app$b'(X0,X1)
| ( 'bot$c' != 'collect$a'(X0) ) ) ),
inference(nnf_transformation,[],[f566]) ).
tff(f566,axiom,
! [X0: 'C_bool_fun$'] :
( ( 'bot$c' = 'collect$a'(X0) )
<=> ! [X1: 'C$'] : ~ 'fun_app$b'(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom564) ).
tff(f4879,plain,
spl249_269,
inference(avatar_split_clause,[],[f2147,f4877]) ).
tff(f4877,plain,
( spl249_269
<=> ! [X0: 'C_bool_fun$'] :
( ( 'bot$c' = 'collect$a'(X0) )
| 'fun_app$b'(X0,sK82(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_269])]) ).
tff(f2147,plain,
! [X0: 'C_bool_fun$'] :
( ( 'bot$c' = 'collect$a'(X0) )
| 'fun_app$b'(X0,sK82(X0)) ),
inference(cnf_transformation,[],[f1277]) ).
tff(f1277,plain,
! [X0: 'C_bool_fun$'] :
( ( ( 'bot$c' = 'collect$a'(X0) )
| 'fun_app$b'(X0,sK82(X0)) )
& ( ! [X2: 'C$'] : ~ 'fun_app$b'(X0,X2)
| ( 'bot$c' != 'collect$a'(X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK82])],[f1275,f1276]) ).
tff(f1276,plain,
! [X0: 'C_bool_fun$'] :
( ? [X1: 'C$'] : 'fun_app$b'(X0,X1)
=> 'fun_app$b'(X0,sK82(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1275,plain,
! [X0: 'C_bool_fun$'] :
( ( ( 'bot$c' = 'collect$a'(X0) )
| ? [X1: 'C$'] : 'fun_app$b'(X0,X1) )
& ( ! [X2: 'C$'] : ~ 'fun_app$b'(X0,X2)
| ( 'bot$c' != 'collect$a'(X0) ) ) ),
inference(rectify,[],[f1274]) ).
tff(f1274,plain,
! [X0: 'C_bool_fun$'] :
( ( ( 'bot$c' = 'collect$a'(X0) )
| ? [X1: 'C$'] : 'fun_app$b'(X0,X1) )
& ( ! [X1: 'C$'] : ~ 'fun_app$b'(X0,X1)
| ( 'bot$c' != 'collect$a'(X0) ) ) ),
inference(nnf_transformation,[],[f570]) ).
tff(f570,axiom,
! [X0: 'C_bool_fun$'] :
( ( 'bot$c' = 'collect$a'(X0) )
<=> ! [X1: 'C$'] : ~ 'fun_app$b'(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom568) ).
tff(f4875,plain,
spl249_268,
inference(avatar_split_clause,[],[f2107,f4873]) ).
tff(f2107,plain,
! [X0: 'B_option$'] :
( ( 'none$a' = X0 )
| ~ 'fun_app$a'('case_option$e'(tltrue,'uud$'),X0) ),
inference(cnf_transformation,[],[f1258]) ).
tff(f1258,plain,
! [X0: 'B_option$'] :
( ( ( 'none$a' = X0 )
| ~ 'fun_app$a'('case_option$e'(tltrue,'uud$'),X0) )
& ( 'fun_app$a'('case_option$e'(tltrue,'uud$'),X0)
| ( 'none$a' != X0 ) ) ),
inference(nnf_transformation,[],[f128]) ).
tff(f128,axiom,
! [X0: 'B_option$'] :
( ( 'none$a' = X0 )
<=> 'fun_app$a'('case_option$e'(tltrue,'uud$'),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom126) ).
tff(f4871,plain,
spl249_267,
inference(avatar_split_clause,[],[f2105,f4869]) ).
tff(f2105,plain,
! [X0: 'C_option$'] :
( ( 'none$' = X0 )
| ~ 'fun_app$'('case_option$f'(tltrue,'uuc$'),X0) ),
inference(cnf_transformation,[],[f1257]) ).
tff(f1257,plain,
! [X0: 'C_option$'] :
( ( ( 'none$' = X0 )
| ~ 'fun_app$'('case_option$f'(tltrue,'uuc$'),X0) )
& ( 'fun_app$'('case_option$f'(tltrue,'uuc$'),X0)
| ( 'none$' != X0 ) ) ),
inference(nnf_transformation,[],[f127]) ).
tff(f127,axiom,
! [X0: 'C_option$'] :
( ( 'none$' = X0 )
<=> 'fun_app$'('case_option$f'(tltrue,'uuc$'),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom125) ).
tff(f4867,plain,
spl249_266,
inference(avatar_split_clause,[],[f2103,f4865]) ).
tff(f4865,plain,
( spl249_266
<=> ! [X0: 'A_option$'] :
( ( 'none$b' = X0 )
| ~ 'fun_app$aw'('case_option$g'(tltrue,'uub$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_266])]) ).
tff(f2103,plain,
! [X0: 'A_option$'] :
( ( 'none$b' = X0 )
| ~ 'fun_app$aw'('case_option$g'(tltrue,'uub$'),X0) ),
inference(cnf_transformation,[],[f1256]) ).
tff(f1256,plain,
! [X0: 'A_option$'] :
( ( ( 'none$b' = X0 )
| ~ 'fun_app$aw'('case_option$g'(tltrue,'uub$'),X0) )
& ( 'fun_app$aw'('case_option$g'(tltrue,'uub$'),X0)
| ( 'none$b' != X0 ) ) ),
inference(nnf_transformation,[],[f126]) ).
tff(f126,axiom,
! [X0: 'A_option$'] :
( ( 'none$b' = X0 )
<=> 'fun_app$aw'('case_option$g'(tltrue,'uub$'),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom124) ).
tff(f4863,plain,
spl249_265,
inference(avatar_split_clause,[],[f2098,f4861]) ).
tff(f4861,plain,
( spl249_265
<=> ! [X0: 'B_option$'] :
( 'fun_app$a'('case_option$e'(tlfalse,'uug$'),X0)
| ( 'none$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_265])]) ).
tff(f2098,plain,
! [X0: 'B_option$'] :
( 'fun_app$a'('case_option$e'(tlfalse,'uug$'),X0)
| ( 'none$a' = X0 ) ),
inference(cnf_transformation,[],[f1251]) ).
tff(f1251,plain,
! [X0: 'B_option$'] :
( ( ( 'none$a' != X0 )
| ~ 'fun_app$a'('case_option$e'(tlfalse,'uug$'),X0) )
& ( 'fun_app$a'('case_option$e'(tlfalse,'uug$'),X0)
| ( 'none$a' = X0 ) ) ),
inference(nnf_transformation,[],[f131]) ).
tff(f131,axiom,
! [X0: 'B_option$'] :
( ( 'none$a' != X0 )
<=> 'fun_app$a'('case_option$e'(tlfalse,'uug$'),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom129) ).
tff(f4859,plain,
spl249_264,
inference(avatar_split_clause,[],[f2094,f4857]) ).
tff(f4857,plain,
( spl249_264
<=> ! [X0: 'C_option$'] :
( 'fun_app$'('case_option$f'(tlfalse,'uuf$'),X0)
| ( 'none$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_264])]) ).
tff(f2094,plain,
! [X0: 'C_option$'] :
( 'fun_app$'('case_option$f'(tlfalse,'uuf$'),X0)
| ( 'none$' = X0 ) ),
inference(cnf_transformation,[],[f1246]) ).
tff(f1246,plain,
! [X0: 'C_option$'] :
( ( ( 'none$' != X0 )
| ~ 'fun_app$'('case_option$f'(tlfalse,'uuf$'),X0) )
& ( 'fun_app$'('case_option$f'(tlfalse,'uuf$'),X0)
| ( 'none$' = X0 ) ) ),
inference(nnf_transformation,[],[f130]) ).
tff(f130,axiom,
! [X0: 'C_option$'] :
( ( 'none$' != X0 )
<=> 'fun_app$'('case_option$f'(tlfalse,'uuf$'),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom128) ).
tff(f4855,plain,
spl249_263,
inference(avatar_split_clause,[],[f2090,f4853]) ).
tff(f4853,plain,
( spl249_263
<=> ! [X0: 'A_option$'] :
( 'fun_app$aw'('case_option$g'(tlfalse,'uue$'),X0)
| ( 'none$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_263])]) ).
tff(f2090,plain,
! [X0: 'A_option$'] :
( 'fun_app$aw'('case_option$g'(tlfalse,'uue$'),X0)
| ( 'none$b' = X0 ) ),
inference(cnf_transformation,[],[f1241]) ).
tff(f1241,plain,
! [X0: 'A_option$'] :
( ( ( 'none$b' != X0 )
| ~ 'fun_app$aw'('case_option$g'(tlfalse,'uue$'),X0) )
& ( 'fun_app$aw'('case_option$g'(tlfalse,'uue$'),X0)
| ( 'none$b' = X0 ) ) ),
inference(nnf_transformation,[],[f129]) ).
tff(f129,axiom,
! [X0: 'A_option$'] :
( ( 'none$b' != X0 )
<=> 'fun_app$aw'('case_option$g'(tlfalse,'uue$'),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom127) ).
tff(f4851,plain,
spl249_262,
inference(avatar_split_clause,[],[f2046,f4849]) ).
tff(f4849,plain,
( spl249_262
<=> ! [X0: 'B_option_option$'] :
( 'member$a'('the$e'(X0),'set_option$'(X0))
| ( 'none$c' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_262])]) ).
tff(f2046,plain,
! [X0: 'B_option_option$'] :
( 'member$a'('the$e'(X0),'set_option$'(X0))
| ( 'none$c' = X0 ) ),
inference(cnf_transformation,[],[f873]) ).
tff(f873,plain,
! [X0: 'B_option_option$'] :
( 'member$a'('the$e'(X0),'set_option$'(X0))
| ( 'none$c' = X0 ) ),
inference(ennf_transformation,[],[f332]) ).
tff(f332,axiom,
! [X0: 'B_option_option$'] :
( ( 'none$c' != X0 )
=> 'member$a'('the$e'(X0),'set_option$'(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom330) ).
tff(f4847,plain,
spl249_261,
inference(avatar_split_clause,[],[f2045,f4845]) ).
tff(f4845,plain,
( spl249_261
<=> ! [X0: 'C_option_option$'] :
( 'member$'('the$f'(X0),'set_option$a'(X0))
| ( 'none$d' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_261])]) ).
tff(f2045,plain,
! [X0: 'C_option_option$'] :
( 'member$'('the$f'(X0),'set_option$a'(X0))
| ( 'none$d' = X0 ) ),
inference(cnf_transformation,[],[f872]) ).
tff(f872,plain,
! [X0: 'C_option_option$'] :
( 'member$'('the$f'(X0),'set_option$a'(X0))
| ( 'none$d' = X0 ) ),
inference(ennf_transformation,[],[f333]) ).
tff(f333,axiom,
! [X0: 'C_option_option$'] :
( ( 'none$d' != X0 )
=> 'member$'('the$f'(X0),'set_option$a'(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom331) ).
tff(f4843,plain,
spl249_260,
inference(avatar_split_clause,[],[f2033,f4841]) ).
tff(f4841,plain,
( spl249_260
<=> ! [X0: 'B$'] : ( 'set_option$d'('fun_app$g'('some$',X0)) = 'insert$'(X0,'bot$d') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_260])]) ).
tff(f4839,plain,
spl249_259,
inference(avatar_split_clause,[],[f2032,f4837]) ).
tff(f4837,plain,
( spl249_259
<=> ! [X0: 'C$'] : ( 'set_option$c'('fun_app$j'('some$a',X0)) = 'insert$a'(X0,'bot$c') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_259])]) ).
tff(f4835,plain,
( spl249_258
| ~ spl249_126
| ~ spl249_147
| ~ spl249_153 ),
inference(avatar_split_clause,[],[f4672,f4281,f4256,f4151,f4832]) ).
tff(f4832,plain,
( spl249_258
<=> ( 'top$c' = 'these$a'('top$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_258])]) ).
tff(f4151,plain,
( spl249_126
<=> ! [X0: 'B_set$'] : ( 'these$a'('image$a'('some$',X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_126])]) ).
tff(f4256,plain,
( spl249_147
<=> ( 'top$b' = 'insert$b'('none$a','image$a'('some$','top$c')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_147])]) ).
tff(f4281,plain,
( spl249_153
<=> ! [X0: 'B_option_set$'] : ( 'these$a'('insert$b'('none$a',X0)) = 'these$a'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_153])]) ).
tff(f4672,plain,
( ( 'top$c' = 'these$a'('top$b') )
| ~ spl249_126
| ~ spl249_147
| ~ spl249_153 ),
inference(forward_demodulation,[],[f4669,f4152]) ).
tff(f4152,plain,
( ! [X0: 'B_set$'] : ( 'these$a'('image$a'('some$',X0)) = X0 )
| ~ spl249_126 ),
inference(avatar_component_clause,[],[f4151]) ).
tff(f4669,plain,
( ( 'these$a'('image$a'('some$','top$c')) = 'these$a'('top$b') )
| ~ spl249_147
| ~ spl249_153 ),
inference(superposition,[],[f4282,f4258]) ).
tff(f4258,plain,
( ( 'top$b' = 'insert$b'('none$a','image$a'('some$','top$c')) )
| ~ spl249_147 ),
inference(avatar_component_clause,[],[f4256]) ).
tff(f4282,plain,
( ! [X0: 'B_option_set$'] : ( 'these$a'('insert$b'('none$a',X0)) = 'these$a'(X0) )
| ~ spl249_153 ),
inference(avatar_component_clause,[],[f4281]) ).
tff(f4830,plain,
spl249_257,
inference(avatar_split_clause,[],[f2031,f4828]) ).
tff(f4828,plain,
( spl249_257
<=> ! [X0: 'A_option$'] : ( 'fun_app$bf'('the$b',X0) = 'case_option$i'('undefined$','uvn$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_257])]) ).
tff(f2031,plain,
! [X0: 'A_option$'] : ( 'fun_app$bf'('the$b',X0) = 'case_option$i'('undefined$','uvn$',X0) ),
inference(cnf_transformation,[],[f329]) ).
tff(f329,axiom,
! [X0: 'A_option$'] : ( 'fun_app$bf'('the$b',X0) = 'case_option$i'('undefined$','uvn$',X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom327) ).
tff(f4826,plain,
spl249_256,
inference(avatar_split_clause,[],[f2030,f4824]) ).
tff(f4824,plain,
( spl249_256
<=> ! [X0: 'B_option$'] : ( 'insert$b'(X0,'bot$a') = 'collect$b'('fun_app$e'('uwn$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_256])]) ).
tff(f2030,plain,
! [X0: 'B_option$'] : ( 'insert$b'(X0,'bot$a') = 'collect$b'('fun_app$e'('uwn$',X0)) ),
inference(cnf_transformation,[],[f688]) ).
tff(f688,axiom,
! [X0: 'B_option$'] : ( 'insert$b'(X0,'bot$a') = 'collect$b'('fun_app$e'('uwn$',X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom686) ).
tff(f4822,plain,
spl249_255,
inference(avatar_split_clause,[],[f2029,f4820]) ).
tff(f4820,plain,
( spl249_255
<=> ! [X0: 'C_option$'] : ( 'insert$c'(X0,'bot$b') = 'collect$c'('fun_app$d'('uws$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_255])]) ).
tff(f2029,plain,
! [X0: 'C_option$'] : ( 'insert$c'(X0,'bot$b') = 'collect$c'('fun_app$d'('uws$',X0)) ),
inference(cnf_transformation,[],[f693]) ).
tff(f693,axiom,
! [X0: 'C_option$'] : ( 'insert$c'(X0,'bot$b') = 'collect$c'('fun_app$d'('uws$',X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom691) ).
tff(f4818,plain,
spl249_254,
inference(avatar_split_clause,[],[f2028,f4816]) ).
tff(f4816,plain,
( spl249_254
<=> ! [X0: 'C_option$'] : ( 'insert$c'(X0,'bot$b') = 'collect$c'('fun_app$d'('uwo$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_254])]) ).
tff(f2028,plain,
! [X0: 'C_option$'] : ( 'insert$c'(X0,'bot$b') = 'collect$c'('fun_app$d'('uwo$',X0)) ),
inference(cnf_transformation,[],[f689]) ).
tff(f689,axiom,
! [X0: 'C_option$'] : ( 'insert$c'(X0,'bot$b') = 'collect$c'('fun_app$d'('uwo$',X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom687) ).
tff(f4814,plain,
spl249_253,
inference(avatar_split_clause,[],[f2027,f4812]) ).
tff(f4812,plain,
( spl249_253
<=> ! [X0: 'B_option$'] : ( 'insert$b'(X0,'bot$a') = 'collect$b'('fun_app$e'('uwr$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_253])]) ).
tff(f2027,plain,
! [X0: 'B_option$'] : ( 'insert$b'(X0,'bot$a') = 'collect$b'('fun_app$e'('uwr$',X0)) ),
inference(cnf_transformation,[],[f692]) ).
tff(f692,axiom,
! [X0: 'B_option$'] : ( 'insert$b'(X0,'bot$a') = 'collect$b'('fun_app$e'('uwr$',X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom690) ).
tff(f4738,plain,
( spl249_252
| ~ spl249_40
| ~ spl249_172 ),
inference(avatar_split_clause,[],[f4703,f4357,f3782,f4736]) ).
tff(f3782,plain,
( spl249_40
<=> ( 'bot$a' = 'collect$b'('bot$g') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_40])]) ).
tff(f4703,plain,
( ! [X0: 'B_option$'] : ~ 'fun_app$a'('bot$g',X0)
| ~ spl249_40
| ~ spl249_172 ),
inference(trivial_inequality_removal,[],[f4701]) ).
tff(f4701,plain,
( ! [X0: 'B_option$'] :
( ( 'bot$a' != 'bot$a' )
| ~ 'fun_app$a'('bot$g',X0) )
| ~ spl249_40
| ~ spl249_172 ),
inference(superposition,[],[f4358,f3784]) ).
tff(f3784,plain,
( ( 'bot$a' = 'collect$b'('bot$g') )
| ~ spl249_40 ),
inference(avatar_component_clause,[],[f3782]) ).
tff(f4734,plain,
( spl249_251
| ~ spl249_39
| ~ spl249_171 ),
inference(avatar_split_clause,[],[f4698,f4353,f3777,f4732]) ).
tff(f3777,plain,
( spl249_39
<=> ( 'bot$b' = 'collect$c'('bot$h') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_39])]) ).
tff(f4698,plain,
( ! [X0: 'C_option$'] : ~ 'fun_app$'('bot$h',X0)
| ~ spl249_39
| ~ spl249_171 ),
inference(trivial_inequality_removal,[],[f4696]) ).
tff(f4696,plain,
( ! [X0: 'C_option$'] :
( ( 'bot$b' != 'bot$b' )
| ~ 'fun_app$'('bot$h',X0) )
| ~ spl249_39
| ~ spl249_171 ),
inference(superposition,[],[f4354,f3779]) ).
tff(f3779,plain,
( ( 'bot$b' = 'collect$c'('bot$h') )
| ~ spl249_39 ),
inference(avatar_component_clause,[],[f3777]) ).
tff(f4721,plain,
( spl249_250
| ~ spl249_32
| ~ spl249_170 ),
inference(avatar_split_clause,[],[f4694,f4349,f3742,f4719]) ).
tff(f4719,plain,
( spl249_250
<=> ! [X0: 'B$'] : ~ 'fun_app$c'('bot$e',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_250])]) ).
tff(f3742,plain,
( spl249_32
<=> ( 'bot$d' = 'collect$'('bot$e') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_32])]) ).
tff(f4694,plain,
( ! [X0: 'B$'] : ~ 'fun_app$c'('bot$e',X0)
| ~ spl249_32
| ~ spl249_170 ),
inference(trivial_inequality_removal,[],[f4688]) ).
tff(f4688,plain,
( ! [X0: 'B$'] :
( ( 'bot$d' != 'bot$d' )
| ~ 'fun_app$c'('bot$e',X0) )
| ~ spl249_32
| ~ spl249_170 ),
inference(superposition,[],[f4350,f3744]) ).
tff(f3744,plain,
( ( 'bot$d' = 'collect$'('bot$e') )
| ~ spl249_32 ),
inference(avatar_component_clause,[],[f3742]) ).
tff(f4708,plain,
( spl249_249
| ~ spl249_31
| ~ spl249_169 ),
inference(avatar_split_clause,[],[f4686,f4345,f3737,f4706]) ).
tff(f4706,plain,
( spl249_249
<=> ! [X0: 'C$'] : ~ 'fun_app$b'('bot$f',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_249])]) ).
tff(f3737,plain,
( spl249_31
<=> ( 'bot$c' = 'collect$a'('bot$f') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_31])]) ).
tff(f4686,plain,
( ! [X0: 'C$'] : ~ 'fun_app$b'('bot$f',X0)
| ~ spl249_31
| ~ spl249_169 ),
inference(trivial_inequality_removal,[],[f4684]) ).
tff(f4684,plain,
( ! [X0: 'C$'] :
( ( 'bot$c' != 'bot$c' )
| ~ 'fun_app$b'('bot$f',X0) )
| ~ spl249_31
| ~ spl249_169 ),
inference(superposition,[],[f4346,f3739]) ).
tff(f3739,plain,
( ( 'bot$c' = 'collect$a'('bot$f') )
| ~ spl249_31 ),
inference(avatar_component_clause,[],[f3737]) ).
tff(f4668,plain,
( spl249_248
| ~ spl249_125
| ~ spl249_146
| ~ spl249_152 ),
inference(avatar_split_clause,[],[f4663,f4277,f4251,f4147,f4665]) ).
tff(f4665,plain,
( spl249_248
<=> ( 'top$a' = 'these$'('top$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_248])]) ).
tff(f4147,plain,
( spl249_125
<=> ! [X0: 'C_set$'] : ( 'these$'('image$'('some$a',X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_125])]) ).
tff(f4251,plain,
( spl249_146
<=> ( 'top$' = 'insert$c'('none$','image$'('some$a','top$a')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_146])]) ).
tff(f4277,plain,
( spl249_152
<=> ! [X0: 'C_option_set$'] : ( 'these$'('insert$c'('none$',X0)) = 'these$'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_152])]) ).
tff(f4663,plain,
( ( 'top$a' = 'these$'('top$') )
| ~ spl249_125
| ~ spl249_146
| ~ spl249_152 ),
inference(forward_demodulation,[],[f4660,f4148]) ).
tff(f4148,plain,
( ! [X0: 'C_set$'] : ( 'these$'('image$'('some$a',X0)) = X0 )
| ~ spl249_125 ),
inference(avatar_component_clause,[],[f4147]) ).
tff(f4660,plain,
( ( 'these$'('image$'('some$a','top$a')) = 'these$'('top$') )
| ~ spl249_146
| ~ spl249_152 ),
inference(superposition,[],[f4278,f4253]) ).
tff(f4253,plain,
( ( 'top$' = 'insert$c'('none$','image$'('some$a','top$a')) )
| ~ spl249_146 ),
inference(avatar_component_clause,[],[f4251]) ).
tff(f4278,plain,
( ! [X0: 'C_option_set$'] : ( 'these$'('insert$c'('none$',X0)) = 'these$'(X0) )
| ~ spl249_152 ),
inference(avatar_component_clause,[],[f4277]) ).
tff(f4659,plain,
spl249_247,
inference(avatar_split_clause,[],[f3484,f4657]) ).
tff(f4657,plain,
( spl249_247
<=> ! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP31(X0,X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_247])]) ).
tff(f3484,plain,
! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP31(X0,X1,'none$a') ),
inference(equality_resolution,[],[f2967]) ).
tff(f2967,plain,
! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ( 'none$a' != X2 )
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f1729]) ).
tff(f4655,plain,
spl249_246,
inference(avatar_split_clause,[],[f3482,f4653]) ).
tff(f4653,plain,
( spl249_246
<=> ! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP30(X0,X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_246])]) ).
tff(f3482,plain,
! [X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP30(X0,X1,'none$a') ),
inference(equality_resolution,[],[f2959]) ).
tff(f2959,plain,
! [X2: 'B_option$',X0: 'B_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ( 'none$a' != X2 )
| ~ sP30(X0,X1,X2) ),
inference(cnf_transformation,[],[f1723]) ).
tff(f4651,plain,
spl249_245,
inference(avatar_split_clause,[],[f3480,f4649]) ).
tff(f4649,plain,
( spl249_245
<=> ! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP29(X0,X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_245])]) ).
tff(f3480,plain,
! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP29(X0,X1,'none$') ),
inference(equality_resolution,[],[f2951]) ).
tff(f2951,plain,
! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ( 'none$' != X2 )
| ~ sP29(X0,X1,X2) ),
inference(cnf_transformation,[],[f1717]) ).
tff(f4647,plain,
spl249_244,
inference(avatar_split_clause,[],[f3478,f4645]) ).
tff(f4645,plain,
( spl249_244
<=> ! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP28(X0,X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_244])]) ).
tff(f3478,plain,
! [X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP28(X0,X1,'none$') ),
inference(equality_resolution,[],[f2943]) ).
tff(f2943,plain,
! [X2: 'C_option$',X0: 'C_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ( 'none$' != X2 )
| ~ sP28(X0,X1,X2) ),
inference(cnf_transformation,[],[f1711]) ).
tff(f4643,plain,
spl249_243,
inference(avatar_split_clause,[],[f3476,f4641]) ).
tff(f4641,plain,
( spl249_243
<=> ! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ~ sP27(X0,X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_243])]) ).
tff(f3476,plain,
! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ~ sP27(X0,X1,'none$b') ),
inference(equality_resolution,[],[f2935]) ).
tff(f2935,plain,
! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ( 'none$b' != X2 )
| ~ sP27(X0,X1,X2) ),
inference(cnf_transformation,[],[f1705]) ).
tff(f4639,plain,
spl249_242,
inference(avatar_split_clause,[],[f3474,f4637]) ).
tff(f4637,plain,
( spl249_242
<=> ! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ~ sP26(X0,X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_242])]) ).
tff(f3474,plain,
! [X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ~ sP26(X0,X1,'none$b') ),
inference(equality_resolution,[],[f2927]) ).
tff(f2927,plain,
! [X2: 'A_option$',X0: 'A_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ( 'none$b' != X2 )
| ~ sP26(X0,X1,X2) ),
inference(cnf_transformation,[],[f1699]) ).
tff(f4635,plain,
spl249_241,
inference(avatar_split_clause,[],[f3472,f4633]) ).
tff(f4633,plain,
( spl249_241
<=> ! [X2: tlbool,X1: 'B_bool_fun$'] :
( ( tltrue = X2 )
| ~ sP25('none$a',X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_241])]) ).
tff(f3472,plain,
! [X2: tlbool,X1: 'B_bool_fun$'] :
( ( tltrue = X2 )
| ~ sP25('none$a',X1,X2) ),
inference(equality_resolution,[],[f2901]) ).
tff(f2901,plain,
! [X2: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( ( tltrue = X2 )
| ( 'none$a' != X0 )
| ~ sP25(X0,X1,X2) ),
inference(cnf_transformation,[],[f1684]) ).
tff(f4631,plain,
spl249_240,
inference(avatar_split_clause,[],[f3467,f4629]) ).
tff(f4629,plain,
( spl249_240
<=> ! [X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP24(X0,X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_240])]) ).
tff(f3467,plain,
! [X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP24(X0,X1,'none$') ),
inference(equality_resolution,[],[f2893]) ).
tff(f2893,plain,
! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ( 'none$' != X2 )
| ~ sP24(X0,X1,X2) ),
inference(cnf_transformation,[],[f1680]) ).
tff(f4627,plain,
spl249_239,
inference(avatar_split_clause,[],[f3465,f4625]) ).
tff(f4625,plain,
( spl249_239
<=> ! [X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP23(X0,X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_239])]) ).
tff(f3465,plain,
! [X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP23(X0,X1,'none$') ),
inference(equality_resolution,[],[f2885]) ).
tff(f2885,plain,
! [X2: 'C_option$',X0: 'C_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ( 'none$' != X2 )
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f1674]) ).
tff(f4623,plain,
spl249_238,
inference(avatar_split_clause,[],[f3463,f4621]) ).
tff(f4621,plain,
( spl249_238
<=> ! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP22(X0,X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_238])]) ).
tff(f3463,plain,
! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP22(X0,X1,'none$b') ),
inference(equality_resolution,[],[f2877]) ).
tff(f2877,plain,
! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ( 'none$b' != X2 )
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f1668]) ).
tff(f4619,plain,
spl249_237,
inference(avatar_split_clause,[],[f3461,f4617]) ).
tff(f4617,plain,
( spl249_237
<=> ! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP21(X0,X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_237])]) ).
tff(f3461,plain,
! [X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ~ sP21(X0,X1,'none$b') ),
inference(equality_resolution,[],[f2869]) ).
tff(f2869,plain,
! [X2: 'A_option$',X0: 'A_b_option_fun$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,'none$a')
| ( 'none$b' != X2 )
| ~ sP21(X0,X1,X2) ),
inference(cnf_transformation,[],[f1662]) ).
tff(f4615,plain,
spl249_236,
inference(avatar_split_clause,[],[f3459,f4613]) ).
tff(f4613,plain,
( spl249_236
<=> ! [X2: tlbool,X1: 'C_bool_fun$'] :
( ( tltrue = X2 )
| ~ sP20('none$',X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_236])]) ).
tff(f3459,plain,
! [X2: tlbool,X1: 'C_bool_fun$'] :
( ( tltrue = X2 )
| ~ sP20('none$',X1,X2) ),
inference(equality_resolution,[],[f2861]) ).
tff(f2861,plain,
! [X2: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( ( tltrue = X2 )
| ( 'none$' != X0 )
| ~ sP20(X0,X1,X2) ),
inference(cnf_transformation,[],[f1656]) ).
tff(f4611,plain,
spl249_235,
inference(avatar_split_clause,[],[f3454,f4609]) ).
tff(f4609,plain,
( spl249_235
<=> ! [X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP19(X0,X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_235])]) ).
tff(f3454,plain,
! [X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP19(X0,X1,'none$a') ),
inference(equality_resolution,[],[f2853]) ).
tff(f2853,plain,
! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ( 'none$a' != X2 )
| ~ sP19(X0,X1,X2) ),
inference(cnf_transformation,[],[f1652]) ).
tff(f4607,plain,
spl249_234,
inference(avatar_split_clause,[],[f3452,f4605]) ).
tff(f4605,plain,
( spl249_234
<=> ! [X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP18(X0,X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_234])]) ).
tff(f3452,plain,
! [X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP18(X0,X1,'none$a') ),
inference(equality_resolution,[],[f2845]) ).
tff(f2845,plain,
! [X2: 'B_option$',X0: 'B_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ( 'none$a' != X2 )
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f1646]) ).
tff(f4603,plain,
spl249_233,
inference(avatar_split_clause,[],[f3450,f4601]) ).
tff(f4601,plain,
( spl249_233
<=> ! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP17(X0,X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_233])]) ).
tff(f3450,plain,
! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP17(X0,X1,'none$b') ),
inference(equality_resolution,[],[f2837]) ).
tff(f2837,plain,
! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ( 'none$b' != X2 )
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f1640]) ).
tff(f4599,plain,
spl249_232,
inference(avatar_split_clause,[],[f3448,f4597]) ).
tff(f4597,plain,
( spl249_232
<=> ! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP16(X0,X1,'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_232])]) ).
tff(f3448,plain,
! [X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ~ sP16(X0,X1,'none$b') ),
inference(equality_resolution,[],[f2829]) ).
tff(f2829,plain,
! [X2: 'A_option$',X0: 'A_c_option_fun$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,'none$')
| ( 'none$b' != X2 )
| ~ sP16(X0,X1,X2) ),
inference(cnf_transformation,[],[f1634]) ).
tff(f4595,plain,
spl249_231,
inference(avatar_split_clause,[],[f3446,f4593]) ).
tff(f4593,plain,
( spl249_231
<=> ! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ~ sP15(X0,X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_231])]) ).
tff(f3446,plain,
! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ~ sP15(X0,X1,'none$a') ),
inference(equality_resolution,[],[f2821]) ).
tff(f2821,plain,
! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ( 'none$a' != X2 )
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f1628]) ).
tff(f4591,plain,
spl249_230,
inference(avatar_split_clause,[],[f3444,f4589]) ).
tff(f4589,plain,
( spl249_230
<=> ! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ~ sP14(X0,X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_230])]) ).
tff(f3444,plain,
! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ~ sP14(X0,X1,'none$') ),
inference(equality_resolution,[],[f2813]) ).
tff(f2813,plain,
! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ( 'none$' != X2 )
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f1622]) ).
tff(f4587,plain,
spl249_229,
inference(avatar_split_clause,[],[f3442,f4585]) ).
tff(f4585,plain,
( spl249_229
<=> ! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ~ sP13(X0,X1,'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_229])]) ).
tff(f3442,plain,
! [X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ~ sP13(X0,X1,'none$a') ),
inference(equality_resolution,[],[f2805]) ).
tff(f2805,plain,
! [X2: 'B_option$',X0: 'B_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ( 'none$a' != X2 )
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f1616]) ).
tff(f4583,plain,
spl249_228,
inference(avatar_split_clause,[],[f3440,f4581]) ).
tff(f4581,plain,
( spl249_228
<=> ! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ~ sP12(X0,X1,'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_228])]) ).
tff(f3440,plain,
! [X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ~ sP12(X0,X1,'none$') ),
inference(equality_resolution,[],[f2797]) ).
tff(f2797,plain,
! [X2: 'C_option$',X0: 'C_a_option_fun$',X1: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X1,'none$b')
| ( 'none$' != X2 )
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f1610]) ).
tff(f4579,plain,
spl249_227,
inference(avatar_split_clause,[],[f3308,f4577]) ).
tff(f3308,plain,
! [X2: 'A_b_b_fun_fun$',X1: 'B_a_fun$'] :
( 'register$'('register_from_getter_setter$'(X1,X2))
| ~ 'valid_getter_setter$a'(X1,X2) ),
inference(equality_resolution,[],[f2083]) ).
tff(f2083,plain,
! [X2: 'A_b_b_fun_fun$',X0: 'A_a_option_fun_b_b_option_fun_fun$',X1: 'B_a_fun$'] :
( 'register$'(X0)
| ~ 'valid_getter_setter$a'(X1,X2)
| ( 'register_from_getter_setter$'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1225]) ).
tff(f4575,plain,
spl249_226,
inference(avatar_split_clause,[],[f3307,f4573]) ).
tff(f3307,plain,
! [X2: 'B_c_c_fun_fun$',X1: 'C_b_fun$'] :
( 'register$a'('register_from_getter_setter$a'(X1,X2))
| ~ 'valid_getter_setter$'(X1,X2) ),
inference(equality_resolution,[],[f2080]) ).
tff(f2080,plain,
! [X2: 'B_c_c_fun_fun$',X0: 'B_b_option_fun_c_c_option_fun_fun$',X1: 'C_b_fun$'] :
( 'register$a'(X0)
| ~ 'valid_getter_setter$'(X1,X2)
| ( 'register_from_getter_setter$a'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1221]) ).
tff(f4571,plain,
spl249_225,
inference(avatar_split_clause,[],[f3306,f4569]) ).
tff(f3306,plain,
! [X2: 'B_b_b_fun_fun$',X1: 'B_b_fun$'] :
( 'register$h'('register_from_getter_setter$b'(X1,X2))
| ~ 'valid_getter_setter$b'(X1,X2) ),
inference(equality_resolution,[],[f2077]) ).
tff(f2077,plain,
! [X2: 'B_b_b_fun_fun$',X0: 'B_b_option_fun_b_b_option_fun_fun$',X1: 'B_b_fun$'] :
( 'register$h'(X0)
| ~ 'valid_getter_setter$b'(X1,X2)
| ( 'register_from_getter_setter$b'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1217]) ).
tff(f4567,plain,
spl249_224,
inference(avatar_split_clause,[],[f3305,f4565]) ).
tff(f3305,plain,
! [X2: 'C_c_c_fun_fun$',X1: 'C_c_fun$'] :
( 'register$f'('register_from_getter_setter$d'(X1,X2))
| ~ 'valid_getter_setter$d'(X1,X2) ),
inference(equality_resolution,[],[f2074]) ).
tff(f2074,plain,
! [X2: 'C_c_c_fun_fun$',X0: 'C_c_option_fun_c_c_option_fun_fun$',X1: 'C_c_fun$'] :
( 'register$f'(X0)
| ~ 'valid_getter_setter$d'(X1,X2)
| ( 'register_from_getter_setter$d'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f1213]) ).
tff(f4563,plain,
spl249_223,
inference(avatar_split_clause,[],[f2383,f4561]) ).
tff(f4561,plain,
( spl249_223
<=> ! [X0: 'B$',X1: 'B_bool_fun$'] :
( 'member$c'(X0,'collect$'(X1))
| ~ 'fun_app$c'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_223])]) ).
tff(f2383,plain,
! [X0: 'B$',X1: 'B_bool_fun$'] :
( 'member$c'(X0,'collect$'(X1))
| ~ 'fun_app$c'(X1,X0) ),
inference(cnf_transformation,[],[f1444]) ).
tff(f1444,plain,
! [X0: 'B$',X1: 'B_bool_fun$'] :
( ( 'member$c'(X0,'collect$'(X1))
| ~ 'fun_app$c'(X1,X0) )
& ( 'fun_app$c'(X1,X0)
| ~ 'member$c'(X0,'collect$'(X1)) ) ),
inference(nnf_transformation,[],[f250]) ).
tff(f250,axiom,
! [X0: 'B$',X1: 'B_bool_fun$'] :
( 'member$c'(X0,'collect$'(X1))
<=> 'fun_app$c'(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom248) ).
tff(f4559,plain,
spl249_222,
inference(avatar_split_clause,[],[f2382,f4557]) ).
tff(f4557,plain,
( spl249_222
<=> ! [X0: 'B$',X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,X0)
| ~ 'member$c'(X0,'collect$'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_222])]) ).
tff(f2382,plain,
! [X0: 'B$',X1: 'B_bool_fun$'] :
( 'fun_app$c'(X1,X0)
| ~ 'member$c'(X0,'collect$'(X1)) ),
inference(cnf_transformation,[],[f1444]) ).
tff(f4555,plain,
spl249_221,
inference(avatar_split_clause,[],[f2377,f4553]) ).
tff(f4553,plain,
( spl249_221
<=> ! [X0: 'C$',X1: 'C_bool_fun$'] :
( 'member$b'(X0,'collect$a'(X1))
| ~ 'fun_app$b'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_221])]) ).
tff(f2377,plain,
! [X0: 'C$',X1: 'C_bool_fun$'] :
( 'member$b'(X0,'collect$a'(X1))
| ~ 'fun_app$b'(X1,X0) ),
inference(cnf_transformation,[],[f1441]) ).
tff(f1441,plain,
! [X0: 'C$',X1: 'C_bool_fun$'] :
( ( 'member$b'(X0,'collect$a'(X1))
| ~ 'fun_app$b'(X1,X0) )
& ( 'fun_app$b'(X1,X0)
| ~ 'member$b'(X0,'collect$a'(X1)) ) ),
inference(nnf_transformation,[],[f251]) ).
tff(f251,axiom,
! [X0: 'C$',X1: 'C_bool_fun$'] :
( 'member$b'(X0,'collect$a'(X1))
<=> 'fun_app$b'(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom249) ).
tff(f4551,plain,
spl249_220,
inference(avatar_split_clause,[],[f2376,f4549]) ).
tff(f4549,plain,
( spl249_220
<=> ! [X0: 'C$',X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,X0)
| ~ 'member$b'(X0,'collect$a'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_220])]) ).
tff(f2376,plain,
! [X0: 'C$',X1: 'C_bool_fun$'] :
( 'fun_app$b'(X1,X0)
| ~ 'member$b'(X0,'collect$a'(X1)) ),
inference(cnf_transformation,[],[f1441]) ).
tff(f4547,plain,
spl249_219,
inference(avatar_split_clause,[],[f2373,f4545]) ).
tff(f4545,plain,
( spl249_219
<=> ! [X0: 'B_option_set$',X1: 'B_option$'] :
( 'fun_app$a'('uvk$'(X0),X1)
| ~ 'member$a'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_219])]) ).
tff(f2373,plain,
! [X0: 'B_option_set$',X1: 'B_option$'] :
( 'fun_app$a'('uvk$'(X0),X1)
| ~ 'member$a'(X1,X0) ),
inference(cnf_transformation,[],[f1439]) ).
tff(f1439,plain,
! [X0: 'B_option_set$',X1: 'B_option$'] :
( ( 'fun_app$a'('uvk$'(X0),X1)
| ~ 'member$a'(X1,X0) )
& ( 'member$a'(X1,X0)
| ~ 'fun_app$a'('uvk$'(X0),X1) ) ),
inference(nnf_transformation,[],[f2]) ).
tff(f2,axiom,
! [X0: 'B_option_set$',X1: 'B_option$'] :
( 'fun_app$a'('uvk$'(X0),X1)
<=> 'member$a'(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
tff(f4543,plain,
spl249_218,
inference(avatar_split_clause,[],[f2372,f4541]) ).
tff(f4541,plain,
( spl249_218
<=> ! [X0: 'B_option_set$',X1: 'B_option$'] :
( 'member$a'(X1,X0)
| ~ 'fun_app$a'('uvk$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_218])]) ).
tff(f2372,plain,
! [X0: 'B_option_set$',X1: 'B_option$'] :
( 'member$a'(X1,X0)
| ~ 'fun_app$a'('uvk$'(X0),X1) ),
inference(cnf_transformation,[],[f1439]) ).
tff(f4539,plain,
spl249_217,
inference(avatar_split_clause,[],[f2371,f4537]) ).
tff(f4537,plain,
( spl249_217
<=> ! [X0: 'C_option_set$',X1: 'C_option$'] :
( 'fun_app$'('uvl$'(X0),X1)
| ~ 'member$'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_217])]) ).
tff(f2371,plain,
! [X0: 'C_option_set$',X1: 'C_option$'] :
( 'fun_app$'('uvl$'(X0),X1)
| ~ 'member$'(X1,X0) ),
inference(cnf_transformation,[],[f1438]) ).
tff(f1438,plain,
! [X0: 'C_option_set$',X1: 'C_option$'] :
( ( 'fun_app$'('uvl$'(X0),X1)
| ~ 'member$'(X1,X0) )
& ( 'member$'(X1,X0)
| ~ 'fun_app$'('uvl$'(X0),X1) ) ),
inference(nnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: 'C_option_set$',X1: 'C_option$'] :
( 'fun_app$'('uvl$'(X0),X1)
<=> 'member$'(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom0) ).
tff(f4535,plain,
spl249_216,
inference(avatar_split_clause,[],[f2370,f4533]) ).
tff(f4533,plain,
( spl249_216
<=> ! [X0: 'C_option_set$',X1: 'C_option$'] :
( 'member$'(X1,X0)
| ~ 'fun_app$'('uvl$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_216])]) ).
tff(f2370,plain,
! [X0: 'C_option_set$',X1: 'C_option$'] :
( 'member$'(X1,X0)
| ~ 'fun_app$'('uvl$'(X0),X1) ),
inference(cnf_transformation,[],[f1438]) ).
tff(f4531,plain,
spl249_215,
inference(avatar_split_clause,[],[f2365,f4529]) ).
tff(f4529,plain,
( spl249_215
<=> ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'member$a'(X0,'collect$b'(X1))
| ~ 'fun_app$a'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_215])]) ).
tff(f2365,plain,
! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'member$a'(X0,'collect$b'(X1))
| ~ 'fun_app$a'(X1,X0) ),
inference(cnf_transformation,[],[f1435]) ).
tff(f1435,plain,
! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( ( 'member$a'(X0,'collect$b'(X1))
| ~ 'fun_app$a'(X1,X0) )
& ( 'fun_app$a'(X1,X0)
| ~ 'member$a'(X0,'collect$b'(X1)) ) ),
inference(nnf_transformation,[],[f252]) ).
tff(f252,axiom,
! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'member$a'(X0,'collect$b'(X1))
<=> 'fun_app$a'(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom250) ).
tff(f4527,plain,
spl249_214,
inference(avatar_split_clause,[],[f2364,f4525]) ).
tff(f4525,plain,
( spl249_214
<=> ! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,X0)
| ~ 'member$a'(X0,'collect$b'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_214])]) ).
tff(f2364,plain,
! [X0: 'B_option$',X1: 'B_option_bool_fun$'] :
( 'fun_app$a'(X1,X0)
| ~ 'member$a'(X0,'collect$b'(X1)) ),
inference(cnf_transformation,[],[f1435]) ).
tff(f4523,plain,
spl249_213,
inference(avatar_split_clause,[],[f2363,f4521]) ).
tff(f4521,plain,
( spl249_213
<=> ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'member$'(X0,'collect$c'(X1))
| ~ 'fun_app$'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_213])]) ).
tff(f2363,plain,
! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'member$'(X0,'collect$c'(X1))
| ~ 'fun_app$'(X1,X0) ),
inference(cnf_transformation,[],[f1434]) ).
tff(f1434,plain,
! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( ( 'member$'(X0,'collect$c'(X1))
| ~ 'fun_app$'(X1,X0) )
& ( 'fun_app$'(X1,X0)
| ~ 'member$'(X0,'collect$c'(X1)) ) ),
inference(nnf_transformation,[],[f253]) ).
tff(f253,axiom,
! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'member$'(X0,'collect$c'(X1))
<=> 'fun_app$'(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom251) ).
tff(f4519,plain,
spl249_212,
inference(avatar_split_clause,[],[f2362,f4517]) ).
tff(f4517,plain,
( spl249_212
<=> ! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,X0)
| ~ 'member$'(X0,'collect$c'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_212])]) ).
tff(f2362,plain,
! [X0: 'C_option$',X1: 'C_option_bool_fun$'] :
( 'fun_app$'(X1,X0)
| ~ 'member$'(X0,'collect$c'(X1)) ),
inference(cnf_transformation,[],[f1434]) ).
tff(f4515,plain,
spl249_211,
inference(avatar_split_clause,[],[f2361,f4513]) ).
tff(f4513,plain,
( spl249_211
<=> ! [X0: 'B_set$',X1: 'B$'] :
( 'fun_app$c'('uvi$'(X0),X1)
| ~ 'member$c'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_211])]) ).
tff(f2361,plain,
! [X0: 'B_set$',X1: 'B$'] :
( 'fun_app$c'('uvi$'(X0),X1)
| ~ 'member$c'(X1,X0) ),
inference(cnf_transformation,[],[f1433]) ).
tff(f1433,plain,
! [X0: 'B_set$',X1: 'B$'] :
( ( 'fun_app$c'('uvi$'(X0),X1)
| ~ 'member$c'(X1,X0) )
& ( 'member$c'(X1,X0)
| ~ 'fun_app$c'('uvi$'(X0),X1) ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f4,axiom,
! [X0: 'B_set$',X1: 'B$'] :
( 'fun_app$c'('uvi$'(X0),X1)
<=> 'member$c'(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).
tff(f4511,plain,
spl249_210,
inference(avatar_split_clause,[],[f2360,f4509]) ).
tff(f4509,plain,
( spl249_210
<=> ! [X0: 'B_set$',X1: 'B$'] :
( 'member$c'(X1,X0)
| ~ 'fun_app$c'('uvi$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_210])]) ).
tff(f2360,plain,
! [X0: 'B_set$',X1: 'B$'] :
( 'member$c'(X1,X0)
| ~ 'fun_app$c'('uvi$'(X0),X1) ),
inference(cnf_transformation,[],[f1433]) ).
tff(f4507,plain,
spl249_209,
inference(avatar_split_clause,[],[f2358,f4505]) ).
tff(f4505,plain,
( spl249_209
<=> ! [X0: 'B$',X1: 'B$'] :
( ( X0 = X1 )
| ~ 'fun_app$c'('uwl$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_209])]) ).
tff(f2358,plain,
! [X0: 'B$',X1: 'B$'] :
( ( X0 = X1 )
| ~ 'fun_app$c'('uwl$'(X0),X1) ),
inference(cnf_transformation,[],[f1432]) ).
tff(f1432,plain,
! [X0: 'B$',X1: 'B$'] :
( ( 'fun_app$c'('uwl$'(X0),X1)
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ~ 'fun_app$c'('uwl$'(X0),X1) ) ),
inference(nnf_transformation,[],[f8]) ).
tff(f8,axiom,
! [X0: 'B$',X1: 'B$'] :
( 'fun_app$c'('uwl$'(X0),X1)
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom7) ).
tff(f4503,plain,
spl249_208,
inference(avatar_split_clause,[],[f2356,f4501]) ).
tff(f4501,plain,
( spl249_208
<=> ! [X0: 'B$',X1: 'B$'] :
( ( X0 = X1 )
| ~ 'fun_app$c'('uwp$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_208])]) ).
tff(f2356,plain,
! [X0: 'B$',X1: 'B$'] :
( ( X0 = X1 )
| ~ 'fun_app$c'('uwp$'(X0),X1) ),
inference(cnf_transformation,[],[f1431]) ).
tff(f1431,plain,
! [X0: 'B$',X1: 'B$'] :
( ( 'fun_app$c'('uwp$'(X0),X1)
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ~ 'fun_app$c'('uwp$'(X0),X1) ) ),
inference(nnf_transformation,[],[f12]) ).
tff(f12,axiom,
! [X0: 'B$',X1: 'B$'] :
( 'fun_app$c'('uwp$'(X0),X1)
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom11) ).
tff(f4499,plain,
spl249_207,
inference(avatar_split_clause,[],[f2355,f4497]) ).
tff(f4497,plain,
( spl249_207
<=> ! [X0: 'C_set$',X1: 'C$'] :
( 'fun_app$b'('uvj$'(X0),X1)
| ~ 'member$b'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_207])]) ).
tff(f2355,plain,
! [X0: 'C_set$',X1: 'C$'] :
( 'fun_app$b'('uvj$'(X0),X1)
| ~ 'member$b'(X1,X0) ),
inference(cnf_transformation,[],[f1430]) ).
tff(f1430,plain,
! [X0: 'C_set$',X1: 'C$'] :
( ( 'fun_app$b'('uvj$'(X0),X1)
| ~ 'member$b'(X1,X0) )
& ( 'member$b'(X1,X0)
| ~ 'fun_app$b'('uvj$'(X0),X1) ) ),
inference(nnf_transformation,[],[f3]) ).
tff(f3,axiom,
! [X0: 'C_set$',X1: 'C$'] :
( 'fun_app$b'('uvj$'(X0),X1)
<=> 'member$b'(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
tff(f4495,plain,
spl249_206,
inference(avatar_split_clause,[],[f2354,f4493]) ).
tff(f4493,plain,
( spl249_206
<=> ! [X0: 'C_set$',X1: 'C$'] :
( 'member$b'(X1,X0)
| ~ 'fun_app$b'('uvj$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_206])]) ).
tff(f2354,plain,
! [X0: 'C_set$',X1: 'C$'] :
( 'member$b'(X1,X0)
| ~ 'fun_app$b'('uvj$'(X0),X1) ),
inference(cnf_transformation,[],[f1430]) ).
tff(f4491,plain,
spl249_205,
inference(avatar_split_clause,[],[f2352,f4489]) ).
tff(f4489,plain,
( spl249_205
<=> ! [X0: 'C$',X1: 'C$'] :
( ( X0 = X1 )
| ~ 'fun_app$b'('uwm$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_205])]) ).
tff(f2352,plain,
! [X0: 'C$',X1: 'C$'] :
( ( X0 = X1 )
| ~ 'fun_app$b'('uwm$'(X0),X1) ),
inference(cnf_transformation,[],[f1429]) ).
tff(f1429,plain,
! [X0: 'C$',X1: 'C$'] :
( ( 'fun_app$b'('uwm$'(X0),X1)
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ~ 'fun_app$b'('uwm$'(X0),X1) ) ),
inference(nnf_transformation,[],[f7]) ).
tff(f7,axiom,
! [X0: 'C$',X1: 'C$'] :
( 'fun_app$b'('uwm$'(X0),X1)
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6) ).
tff(f4487,plain,
spl249_204,
inference(avatar_split_clause,[],[f2350,f4485]) ).
tff(f4485,plain,
( spl249_204
<=> ! [X0: 'C$',X1: 'C$'] :
( ( X0 = X1 )
| ~ 'fun_app$b'('uwq$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_204])]) ).
tff(f2350,plain,
! [X0: 'C$',X1: 'C$'] :
( ( X0 = X1 )
| ~ 'fun_app$b'('uwq$'(X0),X1) ),
inference(cnf_transformation,[],[f1428]) ).
tff(f1428,plain,
! [X0: 'C$',X1: 'C$'] :
( ( 'fun_app$b'('uwq$'(X0),X1)
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ~ 'fun_app$b'('uwq$'(X0),X1) ) ),
inference(nnf_transformation,[],[f11]) ).
tff(f11,axiom,
! [X0: 'C$',X1: 'C$'] :
( 'fun_app$b'('uwq$'(X0),X1)
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).
tff(f4483,plain,
spl249_203,
inference(avatar_split_clause,[],[f2230,f4481]) ).
tff(f4481,plain,
( spl249_203
<=> ! [X0: 'B_b_b_fun_fun$',X1: 'B_option$'] : ( 'fun_app$s'('combine_options$b'(X0,X1),'none$a') = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_203])]) ).
tff(f2230,plain,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$'] : ( 'fun_app$s'('combine_options$b'(X0,X1),'none$a') = X1 ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,axiom,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$'] : ( 'fun_app$s'('combine_options$b'(X0,X1),'none$a') = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom237) ).
tff(f4479,plain,
spl249_202,
inference(avatar_split_clause,[],[f2229,f4477]) ).
tff(f2229,plain,
! [X0: 'B_option$',X1: 'B_b_option_fun$'] : ( 'fun_app$s'('case_option$'(X0,X1),'none$a') = X0 ),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
! [X0: 'B_option$',X1: 'B_b_option_fun$'] : ( 'fun_app$s'('case_option$'(X0,X1),'none$a') = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom106) ).
tff(f4475,plain,
spl249_201,
inference(avatar_split_clause,[],[f2228,f4473]) ).
tff(f2228,plain,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$'] : ( 'fun_app$s'('combine_options$b'(X0,'none$a'),X1) = X1 ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,axiom,
! [X0: 'B_b_b_fun_fun$',X1: 'B_option$'] : ( 'fun_app$s'('combine_options$b'(X0,'none$a'),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom240) ).
tff(f4471,plain,
spl249_200,
inference(avatar_split_clause,[],[f2227,f4469]) ).
tff(f4469,plain,
( spl249_200
<=> ! [X0: 'C_option$',X1: 'B_c_option_fun$'] : ( 'fun_app$an'('case_option$c'(X0,X1),'none$a') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_200])]) ).
tff(f2227,plain,
! [X0: 'C_option$',X1: 'B_c_option_fun$'] : ( 'fun_app$an'('case_option$c'(X0,X1),'none$a') = X0 ),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
! [X0: 'C_option$',X1: 'B_c_option_fun$'] : ( 'fun_app$an'('case_option$c'(X0,X1),'none$a') = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom108) ).
tff(f4467,plain,
spl249_199,
inference(avatar_split_clause,[],[f2226,f4465]) ).
tff(f4465,plain,
( spl249_199
<=> ! [X0: 'C_c_c_fun_fun$',X1: 'C_option$'] : ( 'fun_app$u'('combine_options$a'(X0,X1),'none$') = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_199])]) ).
tff(f2226,plain,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$'] : ( 'fun_app$u'('combine_options$a'(X0,X1),'none$') = X1 ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,axiom,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$'] : ( 'fun_app$u'('combine_options$a'(X0,X1),'none$') = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom236) ).
tff(f4463,plain,
spl249_198,
inference(avatar_split_clause,[],[f2225,f4461]) ).
tff(f4461,plain,
( spl249_198
<=> ! [X0: 'C_option$',X1: 'C_c_option_fun$'] : ( 'fun_app$u'('case_option$a'(X0,X1),'none$') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_198])]) ).
tff(f2225,plain,
! [X0: 'C_option$',X1: 'C_c_option_fun$'] : ( 'fun_app$u'('case_option$a'(X0,X1),'none$') = X0 ),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
! [X0: 'C_option$',X1: 'C_c_option_fun$'] : ( 'fun_app$u'('case_option$a'(X0,X1),'none$') = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom107) ).
tff(f4459,plain,
spl249_197,
inference(avatar_split_clause,[],[f2224,f4457]) ).
tff(f4457,plain,
( spl249_197
<=> ! [X0: 'B$',X1: 'B$'] : ( 'fun_app$h'('fun_app$ai'('uvp$',X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_197])]) ).
tff(f2224,plain,
! [X0: 'B$',X1: 'B$'] : ( 'fun_app$h'('fun_app$ai'('uvp$',X0),X1) = X0 ),
inference(cnf_transformation,[],[f56]) ).
tff(f56,axiom,
! [X0: 'B$',X1: 'B$'] : ( 'fun_app$h'('fun_app$ai'('uvp$',X0),X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom55) ).
tff(f4455,plain,
spl249_196,
inference(avatar_split_clause,[],[f2223,f4453]) ).
tff(f2223,plain,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$'] : ( 'fun_app$u'('combine_options$a'(X0,'none$'),X1) = X1 ),
inference(cnf_transformation,[],[f241]) ).
tff(f241,axiom,
! [X0: 'C_c_c_fun_fun$',X1: 'C_option$'] : ( 'fun_app$u'('combine_options$a'(X0,'none$'),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom239) ).
tff(f4451,plain,
spl249_195,
inference(avatar_split_clause,[],[f2222,f4449]) ).
tff(f4449,plain,
( spl249_195
<=> ! [X0: 'B_option$',X1: 'A_b_option_fun$'] : ( 'fun_app$av'('case_option$d'(X0,X1),'none$b') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_195])]) ).
tff(f2222,plain,
! [X0: 'B_option$',X1: 'A_b_option_fun$'] : ( 'fun_app$av'('case_option$d'(X0,X1),'none$b') = X0 ),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
! [X0: 'B_option$',X1: 'A_b_option_fun$'] : ( 'fun_app$av'('case_option$d'(X0,X1),'none$b') = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom109) ).
tff(f4447,plain,
spl249_194,
inference(avatar_split_clause,[],[f2221,f4445]) ).
tff(f4445,plain,
( spl249_194
<=> ! [X0: 'A_a_a_fun_fun$',X1: 'A_option$'] : ( 'fun_app$be'('combine_options$'(X0,X1),'none$b') = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_194])]) ).
tff(f2221,plain,
! [X0: 'A_a_a_fun_fun$',X1: 'A_option$'] : ( 'fun_app$be'('combine_options$'(X0,X1),'none$b') = X1 ),
inference(cnf_transformation,[],[f237]) ).
tff(f237,axiom,
! [X0: 'A_a_a_fun_fun$',X1: 'A_option$'] : ( 'fun_app$be'('combine_options$'(X0,X1),'none$b') = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom235) ).
tff(f4443,plain,
spl249_193,
inference(avatar_split_clause,[],[f2220,f4441]) ).
tff(f4441,plain,
( spl249_193
<=> ! [X0: 'A_a_a_fun_fun$',X1: 'A_option$'] : ( 'fun_app$be'('combine_options$'(X0,'none$b'),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_193])]) ).
tff(f2220,plain,
! [X0: 'A_a_a_fun_fun$',X1: 'A_option$'] : ( 'fun_app$be'('combine_options$'(X0,'none$b'),X1) = X1 ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,axiom,
! [X0: 'A_a_a_fun_fun$',X1: 'A_option$'] : ( 'fun_app$be'('combine_options$'(X0,'none$b'),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom238) ).
tff(f4439,plain,
spl249_192,
inference(avatar_split_clause,[],[f2219,f4437]) ).
tff(f4437,plain,
( spl249_192
<=> ! [X0: 'A$',X1: 'A$'] : ( 'fun_app$r'('fun_app$aj'('uvo$',X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_192])]) ).
tff(f2219,plain,
! [X0: 'A$',X1: 'A$'] : ( 'fun_app$r'('fun_app$aj'('uvo$',X0),X1) = X0 ),
inference(cnf_transformation,[],[f57]) ).
tff(f57,axiom,
! [X0: 'A$',X1: 'A$'] : ( 'fun_app$r'('fun_app$aj'('uvo$',X0),X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom56) ).
tff(f4435,plain,
spl249_191,
inference(avatar_split_clause,[],[f2214,f4433]) ).
tff(f4433,plain,
( spl249_191
<=> ! [X0: 'B_set$'] :
( 'member$c'(sK112(X0),X0)
| ( 'bot$d' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_191])]) ).
tff(f2214,plain,
! [X0: 'B_set$'] :
( 'member$c'(sK112(X0),X0)
| ( 'bot$d' = X0 ) ),
inference(cnf_transformation,[],[f1390]) ).
tff(f1390,plain,
! [X0: 'B_set$'] :
( ( 'member$c'(sK112(X0),X0)
| ( 'bot$d' = X0 ) )
& ( ( 'bot$d' != X0 )
| ! [X2: 'B$'] : ~ 'member$c'(X2,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK112])],[f1388,f1389]) ).
tff(f1389,plain,
! [X0: 'B_set$'] :
( ? [X1: 'B$'] : 'member$c'(X1,X0)
=> 'member$c'(sK112(X0),X0) ),
introduced(choice_axiom,[]) ).
tff(f1388,plain,
! [X0: 'B_set$'] :
( ( ? [X1: 'B$'] : 'member$c'(X1,X0)
| ( 'bot$d' = X0 ) )
& ( ( 'bot$d' != X0 )
| ! [X2: 'B$'] : ~ 'member$c'(X2,X0) ) ),
inference(rectify,[],[f1387]) ).
tff(f1387,plain,
! [X0: 'B_set$'] :
( ( ? [X1: 'B$'] : 'member$c'(X1,X0)
| ( 'bot$d' = X0 ) )
& ( ( 'bot$d' != X0 )
| ! [X1: 'B$'] : ~ 'member$c'(X1,X0) ) ),
inference(nnf_transformation,[],[f597]) ).
tff(f597,axiom,
! [X0: 'B_set$'] :
( ? [X1: 'B$'] : 'member$c'(X1,X0)
<=> ( 'bot$d' != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom595) ).
tff(f4431,plain,
spl249_190,
inference(avatar_split_clause,[],[f2212,f4429]) ).
tff(f4429,plain,
( spl249_190
<=> ! [X0: 'C_set$'] :
( 'member$b'(sK111(X0),X0)
| ( 'bot$c' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_190])]) ).
tff(f2212,plain,
! [X0: 'C_set$'] :
( 'member$b'(sK111(X0),X0)
| ( 'bot$c' = X0 ) ),
inference(cnf_transformation,[],[f1386]) ).
tff(f1386,plain,
! [X0: 'C_set$'] :
( ( 'member$b'(sK111(X0),X0)
| ( 'bot$c' = X0 ) )
& ( ( 'bot$c' != X0 )
| ! [X2: 'C$'] : ~ 'member$b'(X2,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK111])],[f1384,f1385]) ).
tff(f1385,plain,
! [X0: 'C_set$'] :
( ? [X1: 'C$'] : 'member$b'(X1,X0)
=> 'member$b'(sK111(X0),X0) ),
introduced(choice_axiom,[]) ).
tff(f1384,plain,
! [X0: 'C_set$'] :
( ( ? [X1: 'C$'] : 'member$b'(X1,X0)
| ( 'bot$c' = X0 ) )
& ( ( 'bot$c' != X0 )
| ! [X2: 'C$'] : ~ 'member$b'(X2,X0) ) ),
inference(rectify,[],[f1383]) ).
tff(f1383,plain,
! [X0: 'C_set$'] :
( ( ? [X1: 'C$'] : 'member$b'(X1,X0)
| ( 'bot$c' = X0 ) )
& ( ( 'bot$c' != X0 )
| ! [X1: 'C$'] : ~ 'member$b'(X1,X0) ) ),
inference(nnf_transformation,[],[f598]) ).
tff(f598,axiom,
! [X0: 'C_set$'] :
( ? [X1: 'C$'] : 'member$b'(X1,X0)
<=> ( 'bot$c' != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom596) ).
tff(f4427,plain,
spl249_189,
inference(avatar_split_clause,[],[f2209,f4425]) ).
tff(f2209,plain,
! [X0: 'B_option_bool_fun$'] :
( 'fun_app$a'(X0,sK109(X0))
| ~ 'fun_app$a'(X0,'none$a') ),
inference(cnf_transformation,[],[f1382]) ).
tff(f4423,plain,
spl249_188,
inference(avatar_split_clause,[],[f2206,f4421]) ).
tff(f2206,plain,
! [X0: 'C_option_bool_fun$'] :
( 'fun_app$'(X0,sK107(X0))
| ~ 'fun_app$'(X0,'none$') ),
inference(cnf_transformation,[],[f1376]) ).
tff(f4419,plain,
spl249_187,
inference(avatar_split_clause,[],[f2203,f4417]) ).
tff(f2203,plain,
! [X0: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X0,sK105(X0))
| ~ 'fun_app$aw'(X0,'none$b') ),
inference(cnf_transformation,[],[f1370]) ).
tff(f4415,plain,
spl249_186,
inference(avatar_split_clause,[],[f2201,f4413]) ).
tff(f4413,plain,
( spl249_186
<=> ! [X0: 'C_option_set$'] :
( 'member$'(sK104(X0),X0)
| ( 'bot$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_186])]) ).
tff(f2201,plain,
! [X0: 'C_option_set$'] :
( 'member$'(sK104(X0),X0)
| ( 'bot$b' = X0 ) ),
inference(cnf_transformation,[],[f1364]) ).
tff(f1364,plain,
! [X0: 'C_option_set$'] :
( ( 'member$'(sK104(X0),X0)
| ( 'bot$b' = X0 ) )
& ( ( 'bot$b' != X0 )
| ! [X2: 'C_option$'] : ~ 'member$'(X2,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK104])],[f1362,f1363]) ).
tff(f1363,plain,
! [X0: 'C_option_set$'] :
( ? [X1: 'C_option$'] : 'member$'(X1,X0)
=> 'member$'(sK104(X0),X0) ),
introduced(choice_axiom,[]) ).
tff(f1362,plain,
! [X0: 'C_option_set$'] :
( ( ? [X1: 'C_option$'] : 'member$'(X1,X0)
| ( 'bot$b' = X0 ) )
& ( ( 'bot$b' != X0 )
| ! [X2: 'C_option$'] : ~ 'member$'(X2,X0) ) ),
inference(rectify,[],[f1361]) ).
tff(f1361,plain,
! [X0: 'C_option_set$'] :
( ( ? [X1: 'C_option$'] : 'member$'(X1,X0)
| ( 'bot$b' = X0 ) )
& ( ( 'bot$b' != X0 )
| ! [X1: 'C_option$'] : ~ 'member$'(X1,X0) ) ),
inference(nnf_transformation,[],[f600]) ).
tff(f600,axiom,
! [X0: 'C_option_set$'] :
( ? [X1: 'C_option$'] : 'member$'(X1,X0)
<=> ( 'bot$b' != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom598) ).
tff(f4411,plain,
spl249_185,
inference(avatar_split_clause,[],[f2199,f4409]) ).
tff(f4409,plain,
( spl249_185
<=> ! [X0: 'B_option_set$'] :
( 'member$a'(sK103(X0),X0)
| ( 'bot$a' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_185])]) ).
tff(f2199,plain,
! [X0: 'B_option_set$'] :
( 'member$a'(sK103(X0),X0)
| ( 'bot$a' = X0 ) ),
inference(cnf_transformation,[],[f1360]) ).
tff(f1360,plain,
! [X0: 'B_option_set$'] :
( ( 'member$a'(sK103(X0),X0)
| ( 'bot$a' = X0 ) )
& ( ( 'bot$a' != X0 )
| ! [X2: 'B_option$'] : ~ 'member$a'(X2,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK103])],[f1358,f1359]) ).
tff(f1359,plain,
! [X0: 'B_option_set$'] :
( ? [X1: 'B_option$'] : 'member$a'(X1,X0)
=> 'member$a'(sK103(X0),X0) ),
introduced(choice_axiom,[]) ).
tff(f1358,plain,
! [X0: 'B_option_set$'] :
( ( ? [X1: 'B_option$'] : 'member$a'(X1,X0)
| ( 'bot$a' = X0 ) )
& ( ( 'bot$a' != X0 )
| ! [X2: 'B_option$'] : ~ 'member$a'(X2,X0) ) ),
inference(rectify,[],[f1357]) ).
tff(f1357,plain,
! [X0: 'B_option_set$'] :
( ( ? [X1: 'B_option$'] : 'member$a'(X1,X0)
| ( 'bot$a' = X0 ) )
& ( ( 'bot$a' != X0 )
| ! [X1: 'B_option$'] : ~ 'member$a'(X1,X0) ) ),
inference(nnf_transformation,[],[f599]) ).
tff(f599,axiom,
! [X0: 'B_option_set$'] :
( ? [X1: 'B_option$'] : 'member$a'(X1,X0)
<=> ( 'bot$a' != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom597) ).
tff(f4407,plain,
spl249_184,
inference(avatar_split_clause,[],[f2189,f4405]) ).
tff(f4405,plain,
( spl249_184
<=> ! [X0: 'B_option_bool_fun$'] :
( 'fun_app$a'(X0,'none$a')
| ~ 'fun_app$a'(X0,sK99(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_184])]) ).
tff(f2189,plain,
! [X0: 'B_option_bool_fun$'] :
( 'fun_app$a'(X0,'none$a')
| ~ 'fun_app$a'(X0,sK99(X0)) ),
inference(cnf_transformation,[],[f1344]) ).
tff(f4403,plain,
spl249_183,
inference(avatar_split_clause,[],[f2186,f4401]) ).
tff(f4401,plain,
( spl249_183
<=> ! [X0: 'C_option_bool_fun$'] :
( 'fun_app$'(X0,'none$')
| ~ 'fun_app$'(X0,sK97(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_183])]) ).
tff(f2186,plain,
! [X0: 'C_option_bool_fun$'] :
( 'fun_app$'(X0,'none$')
| ~ 'fun_app$'(X0,sK97(X0)) ),
inference(cnf_transformation,[],[f1338]) ).
tff(f4399,plain,
spl249_182,
inference(avatar_split_clause,[],[f2183,f4397]) ).
tff(f4397,plain,
( spl249_182
<=> ! [X0: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X0,'none$b')
| ~ 'fun_app$aw'(X0,sK95(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_182])]) ).
tff(f2183,plain,
! [X0: 'A_option_bool_fun$'] :
( 'fun_app$aw'(X0,'none$b')
| ~ 'fun_app$aw'(X0,sK95(X0)) ),
inference(cnf_transformation,[],[f1332]) ).
tff(f4395,plain,
spl249_181,
inference(avatar_split_clause,[],[f2181,f4393]) ).
tff(f4393,plain,
( spl249_181
<=> ! [X0: 'B_set$'] :
( ( 'bot$d' = X0 )
| 'member$c'(sK93(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_181])]) ).
tff(f2181,plain,
! [X0: 'B_set$'] :
( ( 'bot$d' = X0 )
| 'member$c'(sK93(X0),X0) ),
inference(cnf_transformation,[],[f1326]) ).
tff(f1326,plain,
! [X0: 'B_set$'] :
( ( ! [X1: 'B$'] : ~ 'member$c'(X1,X0)
| ( 'bot$d' != X0 ) )
& ( ( 'bot$d' = X0 )
| 'member$c'(sK93(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK93])],[f1324,f1325]) ).
tff(f1325,plain,
! [X0: 'B_set$'] :
( ? [X2: 'B$'] : 'member$c'(X2,X0)
=> 'member$c'(sK93(X0),X0) ),
introduced(choice_axiom,[]) ).
tff(f1324,plain,
! [X0: 'B_set$'] :
( ( ! [X1: 'B$'] : ~ 'member$c'(X1,X0)
| ( 'bot$d' != X0 ) )
& ( ( 'bot$d' = X0 )
| ? [X2: 'B$'] : 'member$c'(X2,X0) ) ),
inference(rectify,[],[f1323]) ).
tff(f1323,plain,
! [X0: 'B_set$'] :
( ( ! [X1: 'B$'] : ~ 'member$c'(X1,X0)
| ( 'bot$d' != X0 ) )
& ( ( 'bot$d' = X0 )
| ? [X1: 'B$'] : 'member$c'(X1,X0) ) ),
inference(nnf_transformation,[],[f573]) ).
tff(f573,axiom,
! [X0: 'B_set$'] :
( ! [X1: 'B$'] : ~ 'member$c'(X1,X0)
<=> ( 'bot$d' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom571) ).
tff(f4391,plain,
spl249_180,
inference(avatar_split_clause,[],[f2179,f4389]) ).
tff(f4389,plain,
( spl249_180
<=> ! [X0: 'C_set$'] :
( ( 'bot$c' = X0 )
| 'member$b'(sK92(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_180])]) ).
tff(f2179,plain,
! [X0: 'C_set$'] :
( ( 'bot$c' = X0 )
| 'member$b'(sK92(X0),X0) ),
inference(cnf_transformation,[],[f1322]) ).
tff(f1322,plain,
! [X0: 'C_set$'] :
( ( ! [X1: 'C$'] : ~ 'member$b'(X1,X0)
| ( 'bot$c' != X0 ) )
& ( ( 'bot$c' = X0 )
| 'member$b'(sK92(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK92])],[f1320,f1321]) ).
tff(f1321,plain,
! [X0: 'C_set$'] :
( ? [X2: 'C$'] : 'member$b'(X2,X0)
=> 'member$b'(sK92(X0),X0) ),
introduced(choice_axiom,[]) ).
tff(f1320,plain,
! [X0: 'C_set$'] :
( ( ! [X1: 'C$'] : ~ 'member$b'(X1,X0)
| ( 'bot$c' != X0 ) )
& ( ( 'bot$c' = X0 )
| ? [X2: 'C$'] : 'member$b'(X2,X0) ) ),
inference(rectify,[],[f1319]) ).
tff(f1319,plain,
! [X0: 'C_set$'] :
( ( ! [X1: 'C$'] : ~ 'member$b'(X1,X0)
| ( 'bot$c' != X0 ) )
& ( ( 'bot$c' = X0 )
| ? [X1: 'C$'] : 'member$b'(X1,X0) ) ),
inference(nnf_transformation,[],[f574]) ).
tff(f574,axiom,
! [X0: 'C_set$'] :
( ! [X1: 'C$'] : ~ 'member$b'(X1,X0)
<=> ( 'bot$c' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom572) ).
tff(f4387,plain,
spl249_179,
inference(avatar_split_clause,[],[f2177,f4385]) ).
tff(f4385,plain,
( spl249_179
<=> ! [X0: 'C_option_set$'] :
( ( 'bot$b' = X0 )
| 'member$'(sK91(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_179])]) ).
tff(f2177,plain,
! [X0: 'C_option_set$'] :
( ( 'bot$b' = X0 )
| 'member$'(sK91(X0),X0) ),
inference(cnf_transformation,[],[f1318]) ).
tff(f1318,plain,
! [X0: 'C_option_set$'] :
( ( ! [X1: 'C_option$'] : ~ 'member$'(X1,X0)
| ( 'bot$b' != X0 ) )
& ( ( 'bot$b' = X0 )
| 'member$'(sK91(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK91])],[f1316,f1317]) ).
tff(f1317,plain,
! [X0: 'C_option_set$'] :
( ? [X2: 'C_option$'] : 'member$'(X2,X0)
=> 'member$'(sK91(X0),X0) ),
introduced(choice_axiom,[]) ).
tff(f1316,plain,
! [X0: 'C_option_set$'] :
( ( ! [X1: 'C_option$'] : ~ 'member$'(X1,X0)
| ( 'bot$b' != X0 ) )
& ( ( 'bot$b' = X0 )
| ? [X2: 'C_option$'] : 'member$'(X2,X0) ) ),
inference(rectify,[],[f1315]) ).
tff(f1315,plain,
! [X0: 'C_option_set$'] :
( ( ! [X1: 'C_option$'] : ~ 'member$'(X1,X0)
| ( 'bot$b' != X0 ) )
& ( ( 'bot$b' = X0 )
| ? [X1: 'C_option$'] : 'member$'(X1,X0) ) ),
inference(nnf_transformation,[],[f576]) ).
tff(f576,axiom,
! [X0: 'C_option_set$'] :
( ! [X1: 'C_option$'] : ~ 'member$'(X1,X0)
<=> ( 'bot$b' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom574) ).
tff(f4383,plain,
spl249_178,
inference(avatar_split_clause,[],[f2175,f4381]) ).
tff(f4381,plain,
( spl249_178
<=> ! [X0: 'B_option_set$'] :
( ( 'bot$a' = X0 )
| 'member$a'(sK90(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_178])]) ).
tff(f2175,plain,
! [X0: 'B_option_set$'] :
( ( 'bot$a' = X0 )
| 'member$a'(sK90(X0),X0) ),
inference(cnf_transformation,[],[f1314]) ).
tff(f1314,plain,
! [X0: 'B_option_set$'] :
( ( ! [X1: 'B_option$'] : ~ 'member$a'(X1,X0)
| ( 'bot$a' != X0 ) )
& ( ( 'bot$a' = X0 )
| 'member$a'(sK90(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK90])],[f1312,f1313]) ).
tff(f1313,plain,
! [X0: 'B_option_set$'] :
( ? [X2: 'B_option$'] : 'member$a'(X2,X0)
=> 'member$a'(sK90(X0),X0) ),
introduced(choice_axiom,[]) ).
tff(f1312,plain,
! [X0: 'B_option_set$'] :
( ( ! [X1: 'B_option$'] : ~ 'member$a'(X1,X0)
| ( 'bot$a' != X0 ) )
& ( ( 'bot$a' = X0 )
| ? [X2: 'B_option$'] : 'member$a'(X2,X0) ) ),
inference(rectify,[],[f1311]) ).
tff(f1311,plain,
! [X0: 'B_option_set$'] :
( ( ! [X1: 'B_option$'] : ~ 'member$a'(X1,X0)
| ( 'bot$a' != X0 ) )
& ( ( 'bot$a' = X0 )
| ? [X1: 'B_option$'] : 'member$a'(X1,X0) ) ),
inference(nnf_transformation,[],[f575]) ).
tff(f575,axiom,
! [X0: 'B_option_set$'] :
( ! [X1: 'B_option$'] : ~ 'member$a'(X1,X0)
<=> ( 'bot$a' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom573) ).
tff(f4379,plain,
spl249_177,
inference(avatar_split_clause,[],[f2170,f4377]) ).
tff(f4377,plain,
( spl249_177
<=> ! [X0: 'B_option$'] :
( ( 'none$a' = X0 )
| ( 'set_option$d'(X0) != 'bot$d' ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_177])]) ).
tff(f2170,plain,
! [X0: 'B_option$'] :
( ( 'none$a' = X0 )
| ( 'set_option$d'(X0) != 'bot$d' ) ),
inference(cnf_transformation,[],[f1310]) ).
tff(f1310,plain,
! [X0: 'B_option$'] :
( ( ( 'set_option$d'(X0) = 'bot$d' )
| ( 'none$a' != X0 ) )
& ( ( 'none$a' = X0 )
| ( 'set_option$d'(X0) != 'bot$d' ) ) ),
inference(nnf_transformation,[],[f490]) ).
tff(f490,axiom,
! [X0: 'B_option$'] :
( ( 'set_option$d'(X0) = 'bot$d' )
<=> ( 'none$a' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom488) ).
tff(f4375,plain,
spl249_176,
inference(avatar_split_clause,[],[f2168,f4373]) ).
tff(f4373,plain,
( spl249_176
<=> ! [X0: 'A_option$'] :
( ( 'none$b' = X0 )
| ( 'set_option$b'(X0) != 'bot$' ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_176])]) ).
tff(f2168,plain,
! [X0: 'A_option$'] :
( ( 'none$b' = X0 )
| ( 'set_option$b'(X0) != 'bot$' ) ),
inference(cnf_transformation,[],[f1309]) ).
tff(f1309,plain,
! [X0: 'A_option$'] :
( ( ( 'set_option$b'(X0) = 'bot$' )
| ( 'none$b' != X0 ) )
& ( ( 'none$b' = X0 )
| ( 'set_option$b'(X0) != 'bot$' ) ) ),
inference(nnf_transformation,[],[f486]) ).
tff(f486,axiom,
! [X0: 'A_option$'] :
( ( 'set_option$b'(X0) = 'bot$' )
<=> ( 'none$b' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom484) ).
tff(f4371,plain,
spl249_175,
inference(avatar_split_clause,[],[f2166,f4369]) ).
tff(f4369,plain,
( spl249_175
<=> ! [X0: 'C_option$'] :
( ( 'none$' = X0 )
| ( 'set_option$c'(X0) != 'bot$c' ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_175])]) ).
tff(f2166,plain,
! [X0: 'C_option$'] :
( ( 'none$' = X0 )
| ( 'set_option$c'(X0) != 'bot$c' ) ),
inference(cnf_transformation,[],[f1308]) ).
tff(f1308,plain,
! [X0: 'C_option$'] :
( ( ( 'set_option$c'(X0) = 'bot$c' )
| ( 'none$' != X0 ) )
& ( ( 'none$' = X0 )
| ( 'set_option$c'(X0) != 'bot$c' ) ) ),
inference(nnf_transformation,[],[f489]) ).
tff(f489,axiom,
! [X0: 'C_option$'] :
( ( 'set_option$c'(X0) = 'bot$c' )
<=> ( 'none$' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom487) ).
tff(f4367,plain,
spl249_174,
inference(avatar_split_clause,[],[f2164,f4365]) ).
tff(f4365,plain,
( spl249_174
<=> ! [X0: 'B_option_option$'] :
( ( 'none$c' = X0 )
| ( 'set_option$'(X0) != 'bot$a' ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_174])]) ).
tff(f2164,plain,
! [X0: 'B_option_option$'] :
( ( 'none$c' = X0 )
| ( 'set_option$'(X0) != 'bot$a' ) ),
inference(cnf_transformation,[],[f1307]) ).
tff(f1307,plain,
! [X0: 'B_option_option$'] :
( ( ( 'set_option$'(X0) = 'bot$a' )
| ( 'none$c' != X0 ) )
& ( ( 'none$c' = X0 )
| ( 'set_option$'(X0) != 'bot$a' ) ) ),
inference(nnf_transformation,[],[f487]) ).
tff(f487,axiom,
! [X0: 'B_option_option$'] :
( ( 'set_option$'(X0) = 'bot$a' )
<=> ( 'none$c' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom485) ).
tff(f4363,plain,
spl249_173,
inference(avatar_split_clause,[],[f2162,f4361]) ).
tff(f4361,plain,
( spl249_173
<=> ! [X0: 'C_option_option$'] :
( ( 'none$d' = X0 )
| ( 'set_option$a'(X0) != 'bot$b' ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_173])]) ).
tff(f2162,plain,
! [X0: 'C_option_option$'] :
( ( 'none$d' = X0 )
| ( 'set_option$a'(X0) != 'bot$b' ) ),
inference(cnf_transformation,[],[f1306]) ).
tff(f1306,plain,
! [X0: 'C_option_option$'] :
( ( ( 'set_option$a'(X0) = 'bot$b' )
| ( 'none$d' != X0 ) )
& ( ( 'none$d' = X0 )
| ( 'set_option$a'(X0) != 'bot$b' ) ) ),
inference(nnf_transformation,[],[f488]) ).
tff(f488,axiom,
! [X0: 'C_option_option$'] :
( ( 'set_option$a'(X0) = 'bot$b' )
<=> ( 'none$d' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom486) ).
tff(f4359,plain,
spl249_172,
inference(avatar_split_clause,[],[f2158,f4357]) ).
tff(f2158,plain,
! [X2: 'B_option$',X0: 'B_option_bool_fun$'] :
( ~ 'fun_app$a'(X0,X2)
| ( 'bot$a' != 'collect$b'(X0) ) ),
inference(cnf_transformation,[],[f1301]) ).
tff(f4355,plain,
spl249_171,
inference(avatar_split_clause,[],[f2154,f4353]) ).
tff(f2154,plain,
! [X2: 'C_option$',X0: 'C_option_bool_fun$'] :
( ~ 'fun_app$'(X0,X2)
| ( 'bot$b' != 'collect$c'(X0) ) ),
inference(cnf_transformation,[],[f1293]) ).
tff(f4351,plain,
spl249_170,
inference(avatar_split_clause,[],[f2150,f4349]) ).
tff(f2150,plain,
! [X2: 'B$',X0: 'B_bool_fun$'] :
( ~ 'fun_app$c'(X0,X2)
| ( 'bot$d' != 'collect$'(X0) ) ),
inference(cnf_transformation,[],[f1285]) ).
tff(f4347,plain,
spl249_169,
inference(avatar_split_clause,[],[f2146,f4345]) ).
tff(f2146,plain,
! [X2: 'C$',X0: 'C_bool_fun$'] :
( ~ 'fun_app$b'(X0,X2)
| ( 'bot$c' != 'collect$a'(X0) ) ),
inference(cnf_transformation,[],[f1277]) ).
tff(f4343,plain,
spl249_168,
inference(avatar_split_clause,[],[f2082,f4341]) ).
tff(f4341,plain,
( spl249_168
<=> ! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( 'valid_getter_setter$a'(sK65(X0),sK66(X0))
| ~ 'register$'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_168])]) ).
tff(f2082,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( 'valid_getter_setter$a'(sK65(X0),sK66(X0))
| ~ 'register$'(X0) ),
inference(cnf_transformation,[],[f1225]) ).
tff(f4339,plain,
spl249_167,
inference(avatar_split_clause,[],[f2079,f4337]) ).
tff(f2079,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( 'valid_getter_setter$'(sK63(X0),sK64(X0))
| ~ 'register$a'(X0) ),
inference(cnf_transformation,[],[f1221]) ).
tff(f4335,plain,
spl249_166,
inference(avatar_split_clause,[],[f2076,f4333]) ).
tff(f4333,plain,
( spl249_166
<=> ! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( 'valid_getter_setter$b'(sK61(X0),sK62(X0))
| ~ 'register$h'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_166])]) ).
tff(f2076,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( 'valid_getter_setter$b'(sK61(X0),sK62(X0))
| ~ 'register$h'(X0) ),
inference(cnf_transformation,[],[f1217]) ).
tff(f4331,plain,
spl249_165,
inference(avatar_split_clause,[],[f2073,f4329]) ).
tff(f4329,plain,
( spl249_165
<=> ! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( 'valid_getter_setter$d'(sK59(X0),sK60(X0))
| ~ 'register$f'(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_165])]) ).
tff(f2073,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( 'valid_getter_setter$d'(sK59(X0),sK60(X0))
| ~ 'register$f'(X0) ),
inference(cnf_transformation,[],[f1213]) ).
tff(f4327,plain,
spl249_164,
inference(avatar_split_clause,[],[f2069,f4325]) ).
tff(f4325,plain,
( spl249_164
<=> ! [X0: 'B_set$'] :
( ( 'bot$d' = X0 )
| 'member$c'(sK54(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_164])]) ).
tff(f2069,plain,
! [X0: 'B_set$'] :
( ( 'bot$d' = X0 )
| 'member$c'(sK54(X0),X0) ),
inference(cnf_transformation,[],[f1204]) ).
tff(f1204,plain,
! [X0: 'B_set$'] :
( ( 'bot$d' = X0 )
| 'member$c'(sK54(X0),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54])],[f892,f1203]) ).
tff(f1203,plain,
! [X0: 'B_set$'] :
( ? [X1: 'B$'] : 'member$c'(X1,X0)
=> 'member$c'(sK54(X0),X0) ),
introduced(choice_axiom,[]) ).
tff(f892,plain,
! [X0: 'B_set$'] :
( ( 'bot$d' = X0 )
| ? [X1: 'B$'] : 'member$c'(X1,X0) ),
inference(ennf_transformation,[],[f776]) ).
tff(f776,plain,
! [X0: 'B_set$'] :
( ! [X1: 'B$'] : ~ 'member$c'(X1,X0)
=> ( 'bot$d' = X0 ) ),
inference(flattening,[],[f775]) ).
tff(f775,plain,
! [X0: 'B_set$'] :
( ! [X1: 'B$'] : ~ 'member$c'(X1,X0)
=> ( 'bot$d' = X0 ) ),
inference(true_and_false_elimination,[],[f593]) ).
tff(f593,axiom,
! [X0: 'B_set$'] :
( ! [X1: 'B$'] :
( 'member$c'(X1,X0)
=> $false )
=> ( 'bot$d' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom591) ).
tff(f4323,plain,
spl249_163,
inference(avatar_split_clause,[],[f2068,f4321]) ).
tff(f4321,plain,
( spl249_163
<=> ! [X0: 'C_set$'] :
( ( 'bot$c' = X0 )
| 'member$b'(sK53(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_163])]) ).
tff(f2068,plain,
! [X0: 'C_set$'] :
( ( 'bot$c' = X0 )
| 'member$b'(sK53(X0),X0) ),
inference(cnf_transformation,[],[f1202]) ).
tff(f1202,plain,
! [X0: 'C_set$'] :
( ( 'bot$c' = X0 )
| 'member$b'(sK53(X0),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f891,f1201]) ).
tff(f1201,plain,
! [X0: 'C_set$'] :
( ? [X1: 'C$'] : 'member$b'(X1,X0)
=> 'member$b'(sK53(X0),X0) ),
introduced(choice_axiom,[]) ).
tff(f891,plain,
! [X0: 'C_set$'] :
( ( 'bot$c' = X0 )
| ? [X1: 'C$'] : 'member$b'(X1,X0) ),
inference(ennf_transformation,[],[f774]) ).
tff(f774,plain,
! [X0: 'C_set$'] :
( ! [X1: 'C$'] : ~ 'member$b'(X1,X0)
=> ( 'bot$c' = X0 ) ),
inference(flattening,[],[f773]) ).
tff(f773,plain,
! [X0: 'C_set$'] :
( ! [X1: 'C$'] : ~ 'member$b'(X1,X0)
=> ( 'bot$c' = X0 ) ),
inference(true_and_false_elimination,[],[f594]) ).
tff(f594,axiom,
! [X0: 'C_set$'] :
( ! [X1: 'C$'] :
( 'member$b'(X1,X0)
=> $false )
=> ( 'bot$c' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom592) ).
tff(f4319,plain,
spl249_162,
inference(avatar_split_clause,[],[f2067,f4317]) ).
tff(f4317,plain,
( spl249_162
<=> ! [X0: 'B_option_set$'] :
( ( 'bot$a' = X0 )
| 'member$a'(sK52(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_162])]) ).
tff(f2067,plain,
! [X0: 'B_option_set$'] :
( ( 'bot$a' = X0 )
| 'member$a'(sK52(X0),X0) ),
inference(cnf_transformation,[],[f1200]) ).
tff(f1200,plain,
! [X0: 'B_option_set$'] :
( ( 'bot$a' = X0 )
| 'member$a'(sK52(X0),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f890,f1199]) ).
tff(f1199,plain,
! [X0: 'B_option_set$'] :
( ? [X1: 'B_option$'] : 'member$a'(X1,X0)
=> 'member$a'(sK52(X0),X0) ),
introduced(choice_axiom,[]) ).
tff(f890,plain,
! [X0: 'B_option_set$'] :
( ( 'bot$a' = X0 )
| ? [X1: 'B_option$'] : 'member$a'(X1,X0) ),
inference(ennf_transformation,[],[f772]) ).
tff(f772,plain,
! [X0: 'B_option_set$'] :
( ! [X1: 'B_option$'] : ~ 'member$a'(X1,X0)
=> ( 'bot$a' = X0 ) ),
inference(flattening,[],[f771]) ).
tff(f771,plain,
! [X0: 'B_option_set$'] :
( ! [X1: 'B_option$'] : ~ 'member$a'(X1,X0)
=> ( 'bot$a' = X0 ) ),
inference(true_and_false_elimination,[],[f595]) ).
tff(f595,axiom,
! [X0: 'B_option_set$'] :
( ! [X1: 'B_option$'] :
( 'member$a'(X1,X0)
=> $false )
=> ( 'bot$a' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom593) ).
tff(f4315,plain,
spl249_161,
inference(avatar_split_clause,[],[f2066,f4313]) ).
tff(f4313,plain,
( spl249_161
<=> ! [X0: 'C_option_set$'] :
( ( 'bot$b' = X0 )
| 'member$'(sK51(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_161])]) ).
tff(f2066,plain,
! [X0: 'C_option_set$'] :
( ( 'bot$b' = X0 )
| 'member$'(sK51(X0),X0) ),
inference(cnf_transformation,[],[f1198]) ).
tff(f1198,plain,
! [X0: 'C_option_set$'] :
( ( 'bot$b' = X0 )
| 'member$'(sK51(X0),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f889,f1197]) ).
tff(f1197,plain,
! [X0: 'C_option_set$'] :
( ? [X1: 'C_option$'] : 'member$'(X1,X0)
=> 'member$'(sK51(X0),X0) ),
introduced(choice_axiom,[]) ).
tff(f889,plain,
! [X0: 'C_option_set$'] :
( ( 'bot$b' = X0 )
| ? [X1: 'C_option$'] : 'member$'(X1,X0) ),
inference(ennf_transformation,[],[f770]) ).
tff(f770,plain,
! [X0: 'C_option_set$'] :
( ! [X1: 'C_option$'] : ~ 'member$'(X1,X0)
=> ( 'bot$b' = X0 ) ),
inference(flattening,[],[f769]) ).
tff(f769,plain,
! [X0: 'C_option_set$'] :
( ! [X1: 'C_option$'] : ~ 'member$'(X1,X0)
=> ( 'bot$b' = X0 ) ),
inference(true_and_false_elimination,[],[f596]) ).
tff(f596,axiom,
! [X0: 'C_option_set$'] :
( ! [X1: 'C_option$'] :
( 'member$'(X1,X0)
=> $false )
=> ( 'bot$b' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom594) ).
tff(f4311,plain,
spl249_160,
inference(avatar_split_clause,[],[f2044,f4309]) ).
tff(f2044,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ( 'some$' = 'fun_app$ad'(X0,'some$') )
| ~ 'register$h'(X0) ),
inference(cnf_transformation,[],[f871]) ).
tff(f871,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( ( 'some$' = 'fun_app$ad'(X0,'some$') )
| ~ 'register$h'(X0) ),
inference(ennf_transformation,[],[f92]) ).
tff(f92,axiom,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( 'register$h'(X0)
=> ( 'some$' = 'fun_app$ad'(X0,'some$') ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom90) ).
tff(f4307,plain,
spl249_159,
inference(avatar_split_clause,[],[f2043,f4305]) ).
tff(f2043,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( 'some$' = 'fun_app$au'(X0,'some$b') )
| ~ 'register$'(X0) ),
inference(cnf_transformation,[],[f870]) ).
tff(f870,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( ( 'some$' = 'fun_app$au'(X0,'some$b') )
| ~ 'register$'(X0) ),
inference(ennf_transformation,[],[f93]) ).
tff(f93,axiom,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( 'register$'(X0)
=> ( 'some$' = 'fun_app$au'(X0,'some$b') ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom91) ).
tff(f4303,plain,
spl249_158,
inference(avatar_split_clause,[],[f2042,f4301]) ).
tff(f2042,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( 'some$a' = 'fun_app$am'(X0,'some$') )
| ~ 'register$a'(X0) ),
inference(cnf_transformation,[],[f869]) ).
tff(f869,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( ( 'some$a' = 'fun_app$am'(X0,'some$') )
| ~ 'register$a'(X0) ),
inference(ennf_transformation,[],[f94]) ).
tff(f94,axiom,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( 'register$a'(X0)
=> ( 'some$a' = 'fun_app$am'(X0,'some$') ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom92) ).
tff(f4299,plain,
spl249_157,
inference(avatar_split_clause,[],[f2041,f4297]) ).
tff(f2041,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ( 'some$a' = 'fun_app$aa'(X0,'some$a') )
| ~ 'register$f'(X0) ),
inference(cnf_transformation,[],[f868]) ).
tff(f868,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( ( 'some$a' = 'fun_app$aa'(X0,'some$a') )
| ~ 'register$f'(X0) ),
inference(ennf_transformation,[],[f90]) ).
tff(f90,axiom,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( 'register$f'(X0)
=> ( 'some$a' = 'fun_app$aa'(X0,'some$a') ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom88) ).
tff(f4295,plain,
spl249_156,
inference(avatar_split_clause,[],[f2026,f4293]) ).
tff(f2026,plain,
! [X0: 'B$'] : ( 'fun_app$al'('the$','fun_app$g'('some$',X0)) = X0 ),
inference(cnf_transformation,[],[f301]) ).
tff(f301,axiom,
! [X0: 'B$'] : ( 'fun_app$al'('the$','fun_app$g'('some$',X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom299) ).
tff(f4291,plain,
spl249_155,
inference(avatar_split_clause,[],[f2025,f4289]) ).
tff(f2025,plain,
! [X0: 'C$'] : ( 'fun_app$ak'('the$a','fun_app$j'('some$a',X0)) = X0 ),
inference(cnf_transformation,[],[f300]) ).
tff(f300,axiom,
! [X0: 'C$'] : ( 'fun_app$ak'('the$a','fun_app$j'('some$a',X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom298) ).
tff(f4287,plain,
spl249_154,
inference(avatar_split_clause,[],[f2024,f4285]) ).
tff(f4285,plain,
( spl249_154
<=> ! [X0: 'A$'] : ( 'fun_app$bf'('the$b','fun_app$q'('some$b',X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_154])]) ).
tff(f2024,plain,
! [X0: 'A$'] : ( 'fun_app$bf'('the$b','fun_app$q'('some$b',X0)) = X0 ),
inference(cnf_transformation,[],[f299]) ).
tff(f299,axiom,
! [X0: 'A$'] : ( 'fun_app$bf'('the$b','fun_app$q'('some$b',X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom297) ).
tff(f4283,plain,
spl249_153,
inference(avatar_split_clause,[],[f2023,f4281]) ).
tff(f2023,plain,
! [X0: 'B_option_set$'] : ( 'these$a'('insert$b'('none$a',X0)) = 'these$a'(X0) ),
inference(cnf_transformation,[],[f699]) ).
tff(f699,axiom,
! [X0: 'B_option_set$'] : ( 'these$a'('insert$b'('none$a',X0)) = 'these$a'(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom697) ).
tff(f4279,plain,
spl249_152,
inference(avatar_split_clause,[],[f2022,f4277]) ).
tff(f2022,plain,
! [X0: 'C_option_set$'] : ( 'these$'('insert$c'('none$',X0)) = 'these$'(X0) ),
inference(cnf_transformation,[],[f698]) ).
tff(f698,axiom,
! [X0: 'C_option_set$'] : ( 'these$'('insert$c'('none$',X0)) = 'these$'(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom696) ).
tff(f4275,plain,
spl249_151,
inference(avatar_split_clause,[],[f2021,f4273]) ).
tff(f4273,plain,
( spl249_151
<=> ! [X0: 'B$'] : ( 'insert$'(X0,'bot$d') = 'collect$'('uwp$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_151])]) ).
tff(f2021,plain,
! [X0: 'B$'] : ( 'insert$'(X0,'bot$d') = 'collect$'('uwp$'(X0)) ),
inference(cnf_transformation,[],[f690]) ).
tff(f690,axiom,
! [X0: 'B$'] : ( 'insert$'(X0,'bot$d') = 'collect$'('uwp$'(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom688) ).
tff(f4271,plain,
spl249_150,
inference(avatar_split_clause,[],[f2020,f4269]) ).
tff(f4269,plain,
( spl249_150
<=> ! [X0: 'C$'] : ( 'insert$a'(X0,'bot$c') = 'collect$a'('uwq$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_150])]) ).
tff(f2020,plain,
! [X0: 'C$'] : ( 'insert$a'(X0,'bot$c') = 'collect$a'('uwq$'(X0)) ),
inference(cnf_transformation,[],[f691]) ).
tff(f691,axiom,
! [X0: 'C$'] : ( 'insert$a'(X0,'bot$c') = 'collect$a'('uwq$'(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom689) ).
tff(f4267,plain,
spl249_149,
inference(avatar_split_clause,[],[f2019,f4265]) ).
tff(f4265,plain,
( spl249_149
<=> ! [X0: 'B$'] : ( 'insert$'(X0,'bot$d') = 'collect$'('uwl$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_149])]) ).
tff(f2019,plain,
! [X0: 'B$'] : ( 'insert$'(X0,'bot$d') = 'collect$'('uwl$'(X0)) ),
inference(cnf_transformation,[],[f686]) ).
tff(f686,axiom,
! [X0: 'B$'] : ( 'insert$'(X0,'bot$d') = 'collect$'('uwl$'(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom684) ).
tff(f4263,plain,
spl249_148,
inference(avatar_split_clause,[],[f2018,f4261]) ).
tff(f4261,plain,
( spl249_148
<=> ! [X0: 'C$'] : ( 'insert$a'(X0,'bot$c') = 'collect$a'('uwm$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_148])]) ).
tff(f2018,plain,
! [X0: 'C$'] : ( 'insert$a'(X0,'bot$c') = 'collect$a'('uwm$'(X0)) ),
inference(cnf_transformation,[],[f687]) ).
tff(f687,axiom,
! [X0: 'C$'] : ( 'insert$a'(X0,'bot$c') = 'collect$a'('uwm$'(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom685) ).
tff(f4259,plain,
spl249_147,
inference(avatar_split_clause,[],[f1952,f4256]) ).
tff(f1952,plain,
'top$b' = 'insert$b'('none$a','image$a'('some$','top$c')),
inference(cnf_transformation,[],[f709]) ).
tff(f709,axiom,
'top$b' = 'insert$b'('none$a','image$a'('some$','top$c')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom707) ).
tff(f4254,plain,
spl249_146,
inference(avatar_split_clause,[],[f1951,f4251]) ).
tff(f1951,plain,
'top$' = 'insert$c'('none$','image$'('some$a','top$a')),
inference(cnf_transformation,[],[f708]) ).
tff(f708,axiom,
'top$' = 'insert$c'('none$','image$'('some$a','top$a')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom706) ).
tff(f4233,plain,
spl249_145,
inference(avatar_split_clause,[],[f3323,f4230]) ).
tff(f4230,plain,
( spl249_145
<=> ( 'bot$d' = 'these$a'('insert$b'('none$a','bot$a')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_145])]) ).
tff(f3323,plain,
'bot$d' = 'these$a'('insert$b'('none$a','bot$a')),
inference(equality_resolution,[],[f2138]) ).
tff(f2138,plain,
! [X0: 'B_option_set$'] :
( ( 'insert$b'('none$a','bot$a') != X0 )
| ( 'bot$d' = 'these$a'(X0) ) ),
inference(cnf_transformation,[],[f1269]) ).
tff(f4228,plain,
spl249_144,
inference(avatar_split_clause,[],[f3321,f4225]) ).
tff(f4225,plain,
( spl249_144
<=> ( 'bot$c' = 'these$'('insert$c'('none$','bot$b')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_144])]) ).
tff(f3321,plain,
'bot$c' = 'these$'('insert$c'('none$','bot$b')),
inference(equality_resolution,[],[f2135]) ).
tff(f2135,plain,
! [X0: 'C_option_set$'] :
( ( 'insert$c'('none$','bot$b') != X0 )
| ( 'bot$c' = 'these$'(X0) ) ),
inference(cnf_transformation,[],[f1267]) ).
tff(f4223,plain,
spl249_143,
inference(avatar_split_clause,[],[f2218,f4221]) ).
tff(f4221,plain,
( spl249_143
<=> ! [X0: 'B$',X1: 'B_option$'] : ( 'fun_app$al'('uwj$'(X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_143])]) ).
tff(f2218,plain,
! [X0: 'B$',X1: 'B_option$'] : ( 'fun_app$al'('uwj$'(X0),X1) = X0 ),
inference(cnf_transformation,[],[f55]) ).
tff(f55,axiom,
! [X0: 'B$',X1: 'B_option$'] : ( 'fun_app$al'('uwj$'(X0),X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom54) ).
tff(f4219,plain,
spl249_142,
inference(avatar_split_clause,[],[f2217,f4217]) ).
tff(f4217,plain,
( spl249_142
<=> ! [X0: 'C$',X1: 'C_option$'] : ( 'fun_app$ak'('uwk$'(X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_142])]) ).
tff(f2217,plain,
! [X0: 'C$',X1: 'C_option$'] : ( 'fun_app$ak'('uwk$'(X0),X1) = X0 ),
inference(cnf_transformation,[],[f54]) ).
tff(f54,axiom,
! [X0: 'C$',X1: 'C_option$'] : ( 'fun_app$ak'('uwk$'(X0),X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom53) ).
tff(f4215,plain,
spl249_141,
inference(avatar_split_clause,[],[f2215,f4213]) ).
tff(f4213,plain,
( spl249_141
<=> ! [X0: 'B_option$',X1: 'A$'] : ( 'fun_app$f'('uwh$'(X0),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_141])]) ).
tff(f2215,plain,
! [X0: 'B_option$',X1: 'A$'] : ( 'fun_app$f'('uwh$'(X0),X1) = X0 ),
inference(cnf_transformation,[],[f53]) ).
tff(f53,axiom,
! [X0: 'B_option$',X1: 'A$'] : ( 'fun_app$f'('uwh$'(X0),X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom52) ).
tff(f4211,plain,
spl249_140,
inference(avatar_split_clause,[],[f2130,f4209]) ).
tff(f2130,plain,
! [X0: 'B_option$'] :
( ( 'none$a' = X0 )
| ~ 'fun_app$a'('is_none$',X0) ),
inference(cnf_transformation,[],[f1265]) ).
tff(f1265,plain,
! [X0: 'B_option$'] :
( ( 'fun_app$a'('is_none$',X0)
| ( 'none$a' != X0 ) )
& ( ( 'none$a' = X0 )
| ~ 'fun_app$a'('is_none$',X0) ) ),
inference(nnf_transformation,[],[f464]) ).
tff(f464,axiom,
! [X0: 'B_option$'] :
( 'fun_app$a'('is_none$',X0)
<=> ( 'none$a' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom462) ).
tff(f4207,plain,
spl249_139,
inference(avatar_split_clause,[],[f2127,f4205]) ).
tff(f4205,plain,
( spl249_139
<=> ! [X0: 'B_option$'] :
( 'member$a'(X0,'bot$a')
| ~ 'fun_app$a'('bot$g',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_139])]) ).
tff(f2127,plain,
! [X0: 'B_option$'] :
( 'member$a'(X0,'bot$a')
| ~ 'fun_app$a'('bot$g',X0) ),
inference(cnf_transformation,[],[f1264]) ).
tff(f1264,plain,
! [X0: 'B_option$'] :
( ( 'fun_app$a'('bot$g',X0)
| ~ 'member$a'(X0,'bot$a') )
& ( 'member$a'(X0,'bot$a')
| ~ 'fun_app$a'('bot$g',X0) ) ),
inference(nnf_transformation,[],[f678]) ).
tff(f678,axiom,
! [X0: 'B_option$'] :
( 'fun_app$a'('bot$g',X0)
<=> 'member$a'(X0,'bot$a') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom676) ).
tff(f4203,plain,
spl249_138,
inference(avatar_split_clause,[],[f2125,f4201]) ).
tff(f2125,plain,
! [X0: 'C_option$'] :
( ( 'none$' = X0 )
| ~ 'fun_app$'('is_none$a',X0) ),
inference(cnf_transformation,[],[f1263]) ).
tff(f1263,plain,
! [X0: 'C_option$'] :
( ( 'fun_app$'('is_none$a',X0)
| ( 'none$' != X0 ) )
& ( ( 'none$' = X0 )
| ~ 'fun_app$'('is_none$a',X0) ) ),
inference(nnf_transformation,[],[f463]) ).
tff(f463,axiom,
! [X0: 'C_option$'] :
( 'fun_app$'('is_none$a',X0)
<=> ( 'none$' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom461) ).
tff(f4199,plain,
spl249_137,
inference(avatar_split_clause,[],[f2122,f4197]) ).
tff(f4197,plain,
( spl249_137
<=> ! [X0: 'C_option$'] :
( 'member$'(X0,'bot$b')
| ~ 'fun_app$'('bot$h',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_137])]) ).
tff(f2122,plain,
! [X0: 'C_option$'] :
( 'member$'(X0,'bot$b')
| ~ 'fun_app$'('bot$h',X0) ),
inference(cnf_transformation,[],[f1262]) ).
tff(f1262,plain,
! [X0: 'C_option$'] :
( ( 'fun_app$'('bot$h',X0)
| ~ 'member$'(X0,'bot$b') )
& ( 'member$'(X0,'bot$b')
| ~ 'fun_app$'('bot$h',X0) ) ),
inference(nnf_transformation,[],[f679]) ).
tff(f679,axiom,
! [X0: 'C_option$'] :
( 'fun_app$'('bot$h',X0)
<=> 'member$'(X0,'bot$b') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom677) ).
tff(f4195,plain,
spl249_136,
inference(avatar_split_clause,[],[f2120,f4193]) ).
tff(f2120,plain,
! [X0: 'A_option$'] :
( ( 'none$b' = X0 )
| ~ 'fun_app$aw'('is_none$b',X0) ),
inference(cnf_transformation,[],[f1261]) ).
tff(f1261,plain,
! [X0: 'A_option$'] :
( ( 'fun_app$aw'('is_none$b',X0)
| ( 'none$b' != X0 ) )
& ( ( 'none$b' = X0 )
| ~ 'fun_app$aw'('is_none$b',X0) ) ),
inference(nnf_transformation,[],[f462]) ).
tff(f462,axiom,
! [X0: 'A_option$'] :
( 'fun_app$aw'('is_none$b',X0)
<=> ( 'none$b' = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom460) ).
tff(f4191,plain,
spl249_135,
inference(avatar_split_clause,[],[f2114,f4189]) ).
tff(f4189,plain,
( spl249_135
<=> ! [X0: 'B$'] :
( 'member$c'(X0,'bot$d')
| ~ 'fun_app$c'('bot$e',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_135])]) ).
tff(f2114,plain,
! [X0: 'B$'] :
( 'member$c'(X0,'bot$d')
| ~ 'fun_app$c'('bot$e',X0) ),
inference(cnf_transformation,[],[f1260]) ).
tff(f1260,plain,
! [X0: 'B$'] :
( ( 'fun_app$c'('bot$e',X0)
| ~ 'member$c'(X0,'bot$d') )
& ( 'member$c'(X0,'bot$d')
| ~ 'fun_app$c'('bot$e',X0) ) ),
inference(nnf_transformation,[],[f676]) ).
tff(f676,axiom,
! [X0: 'B$'] :
( 'fun_app$c'('bot$e',X0)
<=> 'member$c'(X0,'bot$d') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom674) ).
tff(f4187,plain,
spl249_134,
inference(avatar_split_clause,[],[f2110,f4185]) ).
tff(f4185,plain,
( spl249_134
<=> ! [X0: 'C$'] :
( 'member$b'(X0,'bot$c')
| ~ 'fun_app$b'('bot$f',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_134])]) ).
tff(f2110,plain,
! [X0: 'C$'] :
( 'member$b'(X0,'bot$c')
| ~ 'fun_app$b'('bot$f',X0) ),
inference(cnf_transformation,[],[f1259]) ).
tff(f1259,plain,
! [X0: 'C$'] :
( ( 'fun_app$b'('bot$f',X0)
| ~ 'member$b'(X0,'bot$c') )
& ( 'member$b'(X0,'bot$c')
| ~ 'fun_app$b'('bot$f',X0) ) ),
inference(nnf_transformation,[],[f677]) ).
tff(f677,axiom,
! [X0: 'C$'] :
( 'fun_app$b'('bot$f',X0)
<=> 'member$b'(X0,'bot$c') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom675) ).
tff(f4183,plain,
spl249_133,
inference(avatar_split_clause,[],[f2036,f4181]) ).
tff(f2036,plain,
! [X0: tlbool] :
( ( tlfalse = X0 )
| ( tltrue = X0 ) ),
inference(cnf_transformation,[],[f742]) ).
tff(f742,plain,
! [X0: tlbool] :
( ( tlfalse = X0 )
| ( tltrue = X0 ) ),
inference(rectify,[],[f735]) ).
tff(f735,axiom,
! [X7: tlbool] :
( ( tlfalse = X7 )
| ( tltrue = X7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_734) ).
tff(f4178,plain,
spl249_132,
inference(avatar_split_clause,[],[f2017,f4176]) ).
tff(f4176,plain,
( spl249_132
<=> ! [X0: 'B$'] : 'member$c'(X0,'set_option$d'('fun_app$g'('some$',X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_132])]) ).
tff(f2017,plain,
! [X0: 'B$'] : 'member$c'(X0,'set_option$d'('fun_app$g'('some$',X0))),
inference(cnf_transformation,[],[f436]) ).
tff(f436,axiom,
! [X0: 'B$'] : 'member$c'(X0,'set_option$d'('fun_app$g'('some$',X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom434) ).
tff(f4173,plain,
spl249_131,
inference(avatar_split_clause,[],[f2016,f4171]) ).
tff(f4171,plain,
( spl249_131
<=> ! [X0: 'C$'] : 'member$b'(X0,'set_option$c'('fun_app$j'('some$a',X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_131])]) ).
tff(f2016,plain,
! [X0: 'C$'] : 'member$b'(X0,'set_option$c'('fun_app$j'('some$a',X0))),
inference(cnf_transformation,[],[f435]) ).
tff(f435,axiom,
! [X0: 'C$'] : 'member$b'(X0,'set_option$c'('fun_app$j'('some$a',X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom433) ).
tff(f4169,plain,
spl249_130,
inference(avatar_split_clause,[],[f2015,f4167]) ).
tff(f4167,plain,
( spl249_130
<=> ! [X0: 'A$'] : 'member$d'(X0,'set_option$b'('fun_app$q'('some$b',X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_130])]) ).
tff(f2015,plain,
! [X0: 'A$'] : 'member$d'(X0,'set_option$b'('fun_app$q'('some$b',X0))),
inference(cnf_transformation,[],[f434]) ).
tff(f434,axiom,
! [X0: 'A$'] : 'member$d'(X0,'set_option$b'('fun_app$q'('some$b',X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom432) ).
tff(f4165,plain,
spl249_129,
inference(avatar_split_clause,[],[f2011,f4163]) ).
tff(f2011,plain,
! [X0: 'B_option$'] : ( 'fun_app$ac'('bind$c'(X0),'some$') = X0 ),
inference(cnf_transformation,[],[f370]) ).
tff(f370,axiom,
! [X0: 'B_option$'] : ( 'fun_app$ac'('bind$c'(X0),'some$') = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom368) ).
tff(f4161,plain,
spl249_128,
inference(avatar_split_clause,[],[f2010,f4159]) ).
tff(f2010,plain,
! [X0: 'C_option$'] : ( 'fun_app$ab'('bind$'(X0),'some$a') = X0 ),
inference(cnf_transformation,[],[f369]) ).
tff(f369,axiom,
! [X0: 'C_option$'] : ( 'fun_app$ab'('bind$'(X0),'some$a') = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom367) ).
tff(f4157,plain,
spl249_127,
inference(avatar_split_clause,[],[f2007,f4155]) ).
tff(f2007,plain,
! [X0: 'A_option$'] : ( 'fun_app$bp'('bind$h'(X0),'some$b') = X0 ),
inference(cnf_transformation,[],[f368]) ).
tff(f368,axiom,
! [X0: 'A_option$'] : ( 'fun_app$bp'('bind$h'(X0),'some$b') = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom366) ).
tff(f4153,plain,
spl249_126,
inference(avatar_split_clause,[],[f2006,f4151]) ).
tff(f2006,plain,
! [X0: 'B_set$'] : ( 'these$a'('image$a'('some$',X0)) = X0 ),
inference(cnf_transformation,[],[f711]) ).
tff(f711,axiom,
! [X0: 'B_set$'] : ( 'these$a'('image$a'('some$',X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom709) ).
tff(f4149,plain,
spl249_125,
inference(avatar_split_clause,[],[f2005,f4147]) ).
tff(f2005,plain,
! [X0: 'C_set$'] : ( 'these$'('image$'('some$a',X0)) = X0 ),
inference(cnf_transformation,[],[f710]) ).
tff(f710,axiom,
! [X0: 'C_set$'] : ( 'these$'('image$'('some$a',X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom708) ).
tff(f4145,plain,
spl249_124,
inference(avatar_split_clause,[],[f2004,f4143]) ).
tff(f4143,plain,
( spl249_124
<=> ! [X0: 'B_b_fun$'] : ( 'none$a' = 'fun_app$s'('map_option$b'(X0),'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_124])]) ).
tff(f2004,plain,
! [X0: 'B_b_fun$'] : ( 'none$a' = 'fun_app$s'('map_option$b'(X0),'none$a') ),
inference(cnf_transformation,[],[f281]) ).
tff(f281,axiom,
! [X0: 'B_b_fun$'] : ( 'none$a' = 'fun_app$s'('map_option$b'(X0),'none$a') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom279) ).
tff(f4141,plain,
spl249_123,
inference(avatar_split_clause,[],[f2003,f4139]) ).
tff(f4139,plain,
( spl249_123
<=> ! [X0: 'A_b_fun$'] : ( 'none$a' = 'fun_app$av'('map_option$e'(X0),'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_123])]) ).
tff(f2003,plain,
! [X0: 'A_b_fun$'] : ( 'none$a' = 'fun_app$av'('map_option$e'(X0),'none$b') ),
inference(cnf_transformation,[],[f276]) ).
tff(f276,axiom,
! [X0: 'A_b_fun$'] : ( 'none$a' = 'fun_app$av'('map_option$e'(X0),'none$b') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom274) ).
tff(f4137,plain,
spl249_122,
inference(avatar_split_clause,[],[f2002,f4135]) ).
tff(f4135,plain,
( spl249_122
<=> ! [X0: 'C_b_fun$'] : ( 'none$a' = 'fun_app$bg'('map_option$'(X0),'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_122])]) ).
tff(f2002,plain,
! [X0: 'C_b_fun$'] : ( 'none$a' = 'fun_app$bg'('map_option$'(X0),'none$') ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,axiom,
! [X0: 'C_b_fun$'] : ( 'none$a' = 'fun_app$bg'('map_option$'(X0),'none$') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom277) ).
tff(f4133,plain,
spl249_121,
inference(avatar_split_clause,[],[f2001,f4131]) ).
tff(f2001,plain,
! [X0: 'B_option$'] : ( 'none$a' = 'fun_app$ac'('bind$c'(X0),'uwd$') ),
inference(cnf_transformation,[],[f385]) ).
tff(f385,axiom,
! [X0: 'B_option$'] : ( 'none$a' = 'fun_app$ac'('bind$c'(X0),'uwd$') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom383) ).
tff(f4129,plain,
spl249_120,
inference(avatar_split_clause,[],[f2000,f4127]) ).
tff(f2000,plain,
! [X0: 'B_b_option_fun$'] : ( 'none$a' = 'fun_app$ac'('bind$c'('none$a'),X0) ),
inference(cnf_transformation,[],[f409]) ).
tff(f409,axiom,
! [X0: 'B_b_option_fun$'] : ( 'none$a' = 'fun_app$ac'('bind$c'('none$a'),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom407) ).
tff(f4125,plain,
spl249_119,
inference(avatar_split_clause,[],[f1999,f4123]) ).
tff(f1999,plain,
! [X0: 'B_c_fun$'] : ( 'none$' = 'fun_app$an'('map_option$d'(X0),'none$a') ),
inference(cnf_transformation,[],[f280]) ).
tff(f280,axiom,
! [X0: 'B_c_fun$'] : ( 'none$' = 'fun_app$an'('map_option$d'(X0),'none$a') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom278) ).
tff(f4121,plain,
spl249_118,
inference(avatar_split_clause,[],[f1998,f4119]) ).
tff(f4119,plain,
( spl249_118
<=> ! [X0: 'C_c_fun$'] : ( 'none$' = 'fun_app$u'('map_option$c'(X0),'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_118])]) ).
tff(f1998,plain,
! [X0: 'C_c_fun$'] : ( 'none$' = 'fun_app$u'('map_option$c'(X0),'none$') ),
inference(cnf_transformation,[],[f278]) ).
tff(f278,axiom,
! [X0: 'C_c_fun$'] : ( 'none$' = 'fun_app$u'('map_option$c'(X0),'none$') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom276) ).
tff(f4117,plain,
spl249_117,
inference(avatar_split_clause,[],[f1997,f4115]) ).
tff(f1997,plain,
! [X0: 'C_option$'] : ( 'none$' = 'fun_app$ab'('bind$'(X0),'uwc$') ),
inference(cnf_transformation,[],[f384]) ).
tff(f384,axiom,
! [X0: 'C_option$'] : ( 'none$' = 'fun_app$ab'('bind$'(X0),'uwc$') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom382) ).
tff(f4113,plain,
spl249_116,
inference(avatar_split_clause,[],[f1996,f4111]) ).
tff(f1996,plain,
! [X0: 'C_c_option_fun$'] : ( 'none$' = 'fun_app$ab'('bind$'('none$'),X0) ),
inference(cnf_transformation,[],[f406]) ).
tff(f406,axiom,
! [X0: 'C_c_option_fun$'] : ( 'none$' = 'fun_app$ab'('bind$'('none$'),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom404) ).
tff(f4109,plain,
spl249_115,
inference(avatar_split_clause,[],[f1995,f4107]) ).
tff(f4107,plain,
( spl249_115
<=> ! [X0: 'A_c_fun$'] : ( 'none$' = 'fun_app$bh'('map_option$f'(X0),'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_115])]) ).
tff(f1995,plain,
! [X0: 'A_c_fun$'] : ( 'none$' = 'fun_app$bh'('map_option$f'(X0),'none$b') ),
inference(cnf_transformation,[],[f275]) ).
tff(f275,axiom,
! [X0: 'A_c_fun$'] : ( 'none$' = 'fun_app$bh'('map_option$f'(X0),'none$b') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom273) ).
tff(f4105,plain,
spl249_114,
inference(avatar_split_clause,[],[f1994,f4103]) ).
tff(f4103,plain,
( spl249_114
<=> ! [X0: 'A_a_fun$'] : ( 'none$b' = 'fun_app$be'('map_option$a'(X0),'none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_114])]) ).
tff(f1994,plain,
! [X0: 'A_a_fun$'] : ( 'none$b' = 'fun_app$be'('map_option$a'(X0),'none$b') ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,axiom,
! [X0: 'A_a_fun$'] : ( 'none$b' = 'fun_app$be'('map_option$a'(X0),'none$b') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom275) ).
tff(f4101,plain,
spl249_113,
inference(avatar_split_clause,[],[f1993,f4099]) ).
tff(f4099,plain,
( spl249_113
<=> ! [X0: 'B_a_fun$'] : ( 'none$b' = 'fun_app$bj'('map_option$h'(X0),'none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_113])]) ).
tff(f1993,plain,
! [X0: 'B_a_fun$'] : ( 'none$b' = 'fun_app$bj'('map_option$h'(X0),'none$a') ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,axiom,
! [X0: 'B_a_fun$'] : ( 'none$b' = 'fun_app$bj'('map_option$h'(X0),'none$a') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom272) ).
tff(f4097,plain,
spl249_112,
inference(avatar_split_clause,[],[f1992,f4095]) ).
tff(f4095,plain,
( spl249_112
<=> ! [X0: 'C_a_fun$'] : ( 'none$b' = 'fun_app$bi'('map_option$g'(X0),'none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_112])]) ).
tff(f1992,plain,
! [X0: 'C_a_fun$'] : ( 'none$b' = 'fun_app$bi'('map_option$g'(X0),'none$') ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,axiom,
! [X0: 'C_a_fun$'] : ( 'none$b' = 'fun_app$bi'('map_option$g'(X0),'none$') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom271) ).
tff(f4093,plain,
spl249_111,
inference(avatar_split_clause,[],[f1991,f4091]) ).
tff(f1991,plain,
! [X0: 'A_a_option_fun$'] : ( 'none$b' = 'fun_app$bp'('bind$h'('none$b'),X0) ),
inference(cnf_transformation,[],[f405]) ).
tff(f405,axiom,
! [X0: 'A_a_option_fun$'] : ( 'none$b' = 'fun_app$bp'('bind$h'('none$b'),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom403) ).
tff(f4089,plain,
spl249_110,
inference(avatar_split_clause,[],[f3576,f4087]) ).
tff(f3576,plain,
! [X0: 'B_option$'] : ( 'fun_app$s'('id$d',X0) = X0 ),
inference(forward_demodulation,[],[f2013,f1946]) ).
tff(f1946,plain,
'map_option$b'('uvm$') = 'id$d',
inference(cnf_transformation,[],[f670]) ).
tff(f670,axiom,
'map_option$b'('uvm$') = 'id$d',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom668) ).
tff(f2013,plain,
! [X0: 'B_option$'] : ( 'fun_app$s'('map_option$b'('uvm$'),X0) = X0 ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,axiom,
! [X0: 'B_option$'] : ( 'fun_app$s'('map_option$b'('uvm$'),X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom260) ).
tff(f4085,plain,
spl249_109,
inference(avatar_split_clause,[],[f3575,f4083]) ).
tff(f3575,plain,
! [X0: 'C_option$'] : ( 'fun_app$u'('id$c',X0) = X0 ),
inference(forward_demodulation,[],[f2012,f1945]) ).
tff(f1945,plain,
'map_option$c'('id$a') = 'id$c',
inference(cnf_transformation,[],[f654]) ).
tff(f654,axiom,
'map_option$c'('id$a') = 'id$c',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom652) ).
tff(f2012,plain,
! [X0: 'C_option$'] : ( 'fun_app$u'('map_option$c'('id$a'),X0) = X0 ),
inference(cnf_transformation,[],[f661]) ).
tff(f661,axiom,
! [X0: 'C_option$'] : ( 'fun_app$u'('map_option$c'('id$a'),X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom659) ).
tff(f4081,plain,
spl249_108,
inference(avatar_split_clause,[],[f3573,f4079]) ).
tff(f4079,plain,
( spl249_108
<=> ! [X0: 'A_option$'] : ( 'fun_app$be'('id$e',X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_108])]) ).
tff(f3573,plain,
! [X0: 'A_option$'] : ( 'fun_app$be'('id$e',X0) = X0 ),
inference(forward_demodulation,[],[f2008,f1944]) ).
tff(f1944,plain,
'map_option$a'('id$') = 'id$e',
inference(cnf_transformation,[],[f656]) ).
tff(f656,axiom,
'map_option$a'('id$') = 'id$e',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom654) ).
tff(f2008,plain,
! [X0: 'A_option$'] : ( 'fun_app$be'('map_option$a'('id$'),X0) = X0 ),
inference(cnf_transformation,[],[f663]) ).
tff(f663,axiom,
! [X0: 'A_option$'] : ( 'fun_app$be'('map_option$a'('id$'),X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom661) ).
tff(f4077,plain,
spl249_107,
inference(avatar_split_clause,[],[f3384,f4075]) ).
tff(f3384,plain,
! [X1: 'B_bool_fun$'] : 'fun_app$a'('case_option$e'(tltrue,X1),'none$a'),
inference(equality_resolution,[],[f2457]) ).
tff(f2457,plain,
! [X0: tlbool,X1: 'B_bool_fun$'] :
( 'fun_app$a'('case_option$e'(X0,X1),'none$a')
| ( tltrue != X0 ) ),
inference(cnf_transformation,[],[f1486]) ).
tff(f4073,plain,
spl249_106,
inference(avatar_split_clause,[],[f3383,f4071]) ).
tff(f3383,plain,
! [X1: 'B_option$'] : 'fun_app$a'('fun_app$e'('uwr$',X1),X1),
inference(equality_resolution,[],[f2455]) ).
tff(f2455,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( 'fun_app$a'('fun_app$e'('uwr$',X0),X1)
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1485]) ).
tff(f4069,plain,
spl249_105,
inference(avatar_split_clause,[],[f3382,f4067]) ).
tff(f3382,plain,
! [X1: 'B_option$'] : 'fun_app$a'('fun_app$e'('uwn$',X1),X1),
inference(equality_resolution,[],[f2453]) ).
tff(f2453,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( 'fun_app$a'('fun_app$e'('uwn$',X0),X1)
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1484]) ).
tff(f4065,plain,
spl249_104,
inference(avatar_split_clause,[],[f3381,f4063]) ).
tff(f3381,plain,
! [X1: 'C_bool_fun$'] : 'fun_app$'('case_option$f'(tltrue,X1),'none$'),
inference(equality_resolution,[],[f2445]) ).
tff(f2445,plain,
! [X0: tlbool,X1: 'C_bool_fun$'] :
( 'fun_app$'('case_option$f'(X0,X1),'none$')
| ( tltrue != X0 ) ),
inference(cnf_transformation,[],[f1479]) ).
tff(f4061,plain,
spl249_103,
inference(avatar_split_clause,[],[f3380,f4059]) ).
tff(f3380,plain,
! [X1: 'C_option$'] : 'fun_app$'('fun_app$d'('uws$',X1),X1),
inference(equality_resolution,[],[f2443]) ).
tff(f2443,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( 'fun_app$'('fun_app$d'('uws$',X0),X1)
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1478]) ).
tff(f4057,plain,
spl249_102,
inference(avatar_split_clause,[],[f3379,f4055]) ).
tff(f3379,plain,
! [X1: 'C_option$'] : 'fun_app$'('fun_app$d'('uwo$',X1),X1),
inference(equality_resolution,[],[f2441]) ).
tff(f2441,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( 'fun_app$'('fun_app$d'('uwo$',X0),X1)
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1477]) ).
tff(f4053,plain,
spl249_101,
inference(avatar_split_clause,[],[f3315,f4050]) ).
tff(f4050,plain,
( spl249_101
<=> 'fun_app$aw'('case_option$g'(tltrue,'uub$'),'none$b') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_101])]) ).
tff(f3315,plain,
'fun_app$aw'('case_option$g'(tltrue,'uub$'),'none$b'),
inference(equality_resolution,[],[f2102]) ).
tff(f2102,plain,
! [X0: 'A_option$'] :
( 'fun_app$aw'('case_option$g'(tltrue,'uub$'),X0)
| ( 'none$b' != X0 ) ),
inference(cnf_transformation,[],[f1256]) ).
tff(f4048,plain,
~ spl249_100,
inference(avatar_split_clause,[],[f3313,f4045]) ).
tff(f3313,plain,
~ 'fun_app$a'('case_option$e'(tlfalse,'uug$'),'none$a'),
inference(equality_resolution,[],[f2099]) ).
tff(f2099,plain,
! [X0: 'B_option$'] :
( ( 'none$a' != X0 )
| ~ 'fun_app$a'('case_option$e'(tlfalse,'uug$'),X0) ),
inference(cnf_transformation,[],[f1251]) ).
tff(f4043,plain,
~ spl249_99,
inference(avatar_split_clause,[],[f3311,f4040]) ).
tff(f3311,plain,
~ 'fun_app$'('case_option$f'(tlfalse,'uuf$'),'none$'),
inference(equality_resolution,[],[f2095]) ).
tff(f2095,plain,
! [X0: 'C_option$'] :
( ( 'none$' != X0 )
| ~ 'fun_app$'('case_option$f'(tlfalse,'uuf$'),X0) ),
inference(cnf_transformation,[],[f1246]) ).
tff(f4038,plain,
~ spl249_98,
inference(avatar_split_clause,[],[f3309,f4035]) ).
tff(f4035,plain,
( spl249_98
<=> 'fun_app$aw'('case_option$g'(tlfalse,'uue$'),'none$b') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_98])]) ).
tff(f3309,plain,
~ 'fun_app$aw'('case_option$g'(tlfalse,'uue$'),'none$b'),
inference(equality_resolution,[],[f2091]) ).
tff(f2091,plain,
! [X0: 'A_option$'] :
( ( 'none$b' != X0 )
| ~ 'fun_app$aw'('case_option$g'(tlfalse,'uue$'),X0) ),
inference(cnf_transformation,[],[f1241]) ).
tff(f4033,plain,
spl249_97,
inference(avatar_split_clause,[],[f1990,f4031]) ).
tff(f4031,plain,
( spl249_97
<=> ! [X0: 'B$'] : 'member$c'(X0,'insert$'(X0,'bot$d')) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_97])]) ).
tff(f1990,plain,
! [X0: 'B$'] : 'member$c'(X0,'insert$'(X0,'bot$d')),
inference(cnf_transformation,[],[f682]) ).
tff(f682,axiom,
! [X0: 'B$'] : 'member$c'(X0,'insert$'(X0,'bot$d')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom680) ).
tff(f4029,plain,
spl249_96,
inference(avatar_split_clause,[],[f1989,f4027]) ).
tff(f4027,plain,
( spl249_96
<=> ! [X0: 'C$'] : 'member$b'(X0,'insert$a'(X0,'bot$c')) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_96])]) ).
tff(f1989,plain,
! [X0: 'C$'] : 'member$b'(X0,'insert$a'(X0,'bot$c')),
inference(cnf_transformation,[],[f683]) ).
tff(f683,axiom,
! [X0: 'C$'] : 'member$b'(X0,'insert$a'(X0,'bot$c')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom681) ).
tff(f4025,plain,
spl249_95,
inference(avatar_split_clause,[],[f1988,f4023]) ).
tff(f4023,plain,
( spl249_95
<=> ! [X0: 'B_option$'] : 'member$a'(X0,'insert$b'(X0,'bot$a')) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_95])]) ).
tff(f1988,plain,
! [X0: 'B_option$'] : 'member$a'(X0,'insert$b'(X0,'bot$a')),
inference(cnf_transformation,[],[f684]) ).
tff(f684,axiom,
! [X0: 'B_option$'] : 'member$a'(X0,'insert$b'(X0,'bot$a')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom682) ).
tff(f4021,plain,
spl249_94,
inference(avatar_split_clause,[],[f1987,f4019]) ).
tff(f4019,plain,
( spl249_94
<=> ! [X0: 'C_option$'] : 'member$'(X0,'insert$c'(X0,'bot$b')) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_94])]) ).
tff(f1987,plain,
! [X0: 'C_option$'] : 'member$'(X0,'insert$c'(X0,'bot$b')),
inference(cnf_transformation,[],[f685]) ).
tff(f685,axiom,
! [X0: 'C_option$'] : 'member$'(X0,'insert$c'(X0,'bot$b')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom683) ).
tff(f4017,plain,
spl249_93,
inference(avatar_split_clause,[],[f1986,f4015]) ).
tff(f4015,plain,
( spl249_93
<=> ! [X0: 'C_option$'] : 'member$'(X0,'set_option$a'('some$d'(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_93])]) ).
tff(f1986,plain,
! [X0: 'C_option$'] : 'member$'(X0,'set_option$a'('some$d'(X0))),
inference(cnf_transformation,[],[f433]) ).
tff(f433,axiom,
! [X0: 'C_option$'] : 'member$'(X0,'set_option$a'('some$d'(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom431) ).
tff(f4013,plain,
spl249_92,
inference(avatar_split_clause,[],[f1985,f4011]) ).
tff(f4011,plain,
( spl249_92
<=> ! [X0: 'B_option$'] : 'member$a'(X0,'set_option$'('some$c'(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_92])]) ).
tff(f1985,plain,
! [X0: 'B_option$'] : 'member$a'(X0,'set_option$'('some$c'(X0))),
inference(cnf_transformation,[],[f432]) ).
tff(f432,axiom,
! [X0: 'B_option$'] : 'member$a'(X0,'set_option$'('some$c'(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom430) ).
tff(f4009,plain,
spl249_91,
inference(avatar_split_clause,[],[f1984,f4007]) ).
tff(f4007,plain,
( spl249_91
<=> ! [X0: 'C$'] : ( 'fun_app$j'('uwc$',X0) = 'none$' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_91])]) ).
tff(f1984,plain,
! [X0: 'C$'] : ( 'fun_app$j'('uwc$',X0) = 'none$' ),
inference(cnf_transformation,[],[f61]) ).
tff(f61,axiom,
! [X0: 'C$'] : ( 'fun_app$j'('uwc$',X0) = 'none$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom60) ).
tff(f4005,plain,
spl249_90,
inference(avatar_split_clause,[],[f1983,f4003]) ).
tff(f4003,plain,
( spl249_90
<=> ! [X0: 'B$'] : ( 'fun_app$h'('uvm$',X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_90])]) ).
tff(f1983,plain,
! [X0: 'B$'] : ( 'fun_app$h'('uvm$',X0) = X0 ),
inference(cnf_transformation,[],[f59]) ).
tff(f59,axiom,
! [X0: 'B$'] : ( 'fun_app$h'('uvm$',X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom58) ).
tff(f4001,plain,
spl249_89,
inference(avatar_split_clause,[],[f1982,f3999]) ).
tff(f1982,plain,
! [X0: 'C$'] : ( 'fun_app$k'('uvs$',X0) = X0 ),
inference(cnf_transformation,[],[f58]) ).
tff(f58,axiom,
! [X0: 'C$'] : ( 'fun_app$k'('uvs$',X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom57) ).
tff(f3997,plain,
spl249_88,
inference(avatar_split_clause,[],[f1981,f3995]) ).
tff(f1981,plain,
! [X0: 'B_c_option_fun$'] : ( 'comp$f'(X0,'id$b') = X0 ),
inference(cnf_transformation,[],[f653]) ).
tff(f653,axiom,
! [X0: 'B_c_option_fun$'] : ( 'comp$f'(X0,'id$b') = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom651) ).
tff(f3993,plain,
spl249_87,
inference(avatar_split_clause,[],[f1980,f3991]) ).
tff(f3991,plain,
( spl249_87
<=> ! [X0: 'A$'] : ( 'fun_app$r'('uvn$',X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_87])]) ).
tff(f1980,plain,
! [X0: 'A$'] : ( 'fun_app$r'('uvn$',X0) = X0 ),
inference(cnf_transformation,[],[f60]) ).
tff(f60,axiom,
! [X0: 'A$'] : ( 'fun_app$r'('uvn$',X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom59) ).
tff(f3989,plain,
( spl249_86
| ~ spl249_4
| ~ spl249_51 ),
inference(avatar_split_clause,[],[f3874,f3834,f3620,f3986]) ).
tff(f3986,plain,
( spl249_86
<=> 'preregister$b'('g$') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_86])]) ).
tff(f3874,plain,
( 'preregister$b'('g$')
| ~ spl249_4
| ~ spl249_51 ),
inference(resolution,[],[f3835,f3622]) ).
tff(f3984,plain,
spl249_85,
inference(avatar_split_clause,[],[f1979,f3982]) ).
tff(f3982,plain,
( spl249_85
<=> ! [X0: 'A_b_option_fun$'] : ( 'comp$g'(X0,'id$') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_85])]) ).
tff(f1979,plain,
! [X0: 'A_b_option_fun$'] : ( 'comp$g'(X0,'id$') = X0 ),
inference(cnf_transformation,[],[f652]) ).
tff(f652,axiom,
! [X0: 'A_b_option_fun$'] : ( 'comp$g'(X0,'id$') = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom650) ).
tff(f3980,plain,
spl249_84,
inference(avatar_split_clause,[],[f1977,f3978]) ).
tff(f1977,plain,
! [X0: 'C_set$'] : ( 'collect$a'('uvj$'(X0)) = X0 ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,axiom,
! [X0: 'C_set$'] : ( 'collect$a'('uvj$'(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom253) ).
tff(f3976,plain,
spl249_83,
inference(avatar_split_clause,[],[f1976,f3974]) ).
tff(f1976,plain,
! [X0: 'B_set$'] : ( 'collect$'('uvi$'(X0)) = X0 ),
inference(cnf_transformation,[],[f254]) ).
tff(f254,axiom,
! [X0: 'B_set$'] : ( 'collect$'('uvi$'(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom252) ).
tff(f3972,plain,
spl249_82,
inference(avatar_split_clause,[],[f1975,f3970]) ).
tff(f1975,plain,
! [X0: 'B_option_set$'] : ( 'collect$b'('uvk$'(X0)) = X0 ),
inference(cnf_transformation,[],[f256]) ).
tff(f256,axiom,
! [X0: 'B_option_set$'] : ( 'collect$b'('uvk$'(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom254) ).
tff(f3968,plain,
spl249_81,
inference(avatar_split_clause,[],[f1974,f3966]) ).
tff(f1974,plain,
! [X0: 'C_option_set$'] : ( 'collect$c'('uvl$'(X0)) = X0 ),
inference(cnf_transformation,[],[f257]) ).
tff(f257,axiom,
! [X0: 'C_option_set$'] : ( 'collect$c'('uvl$'(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom255) ).
tff(f3964,plain,
spl249_80,
inference(avatar_split_clause,[],[f1973,f3962]) ).
tff(f3962,plain,
( spl249_80
<=> ! [X0: 'B$'] : ( 'none$a' = 'fun_app$g'('uwd$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_80])]) ).
tff(f1973,plain,
! [X0: 'B$'] : ( 'none$a' = 'fun_app$g'('uwd$',X0) ),
inference(cnf_transformation,[],[f64]) ).
tff(f64,axiom,
! [X0: 'B$'] : ( 'none$a' = 'fun_app$g'('uwd$',X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom63) ).
tff(f3960,plain,
spl249_79,
inference(avatar_split_clause,[],[f1972,f3958]) ).
tff(f1972,plain,
! [X0: 'C_b_option_fun$'] : ( 'none$a' = 'bind$a'('none$',X0) ),
inference(cnf_transformation,[],[f407]) ).
tff(f407,axiom,
! [X0: 'C_b_option_fun$'] : ( 'none$a' = 'bind$a'('none$',X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom405) ).
tff(f3956,plain,
spl249_78,
inference(avatar_split_clause,[],[f1971,f3954]) ).
tff(f1971,plain,
! [X0: 'C_option$'] : ( 'none$a' = 'bind$a'(X0,'uwe$') ),
inference(cnf_transformation,[],[f386]) ).
tff(f386,axiom,
! [X0: 'C_option$'] : ( 'none$a' = 'bind$a'(X0,'uwe$') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom384) ).
tff(f3952,plain,
spl249_77,
inference(avatar_split_clause,[],[f1970,f3950]) ).
tff(f1970,plain,
! [X0: 'A_b_option_fun$'] : ( 'none$a' = 'bind$e'('none$b',X0) ),
inference(cnf_transformation,[],[f404]) ).
tff(f404,axiom,
! [X0: 'A_b_option_fun$'] : ( 'none$a' = 'bind$e'('none$b',X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom402) ).
tff(f3948,plain,
spl249_76,
inference(avatar_split_clause,[],[f1968,f3946]) ).
tff(f1968,plain,
! [X0: 'B_c_option_fun$'] : ( 'none$' = 'bind$b'('none$a',X0) ),
inference(cnf_transformation,[],[f408]) ).
tff(f408,axiom,
! [X0: 'B_c_option_fun$'] : ( 'none$' = 'bind$b'('none$a',X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom406) ).
tff(f3944,plain,
( spl249_75
| ~ spl249_5
| ~ spl249_50 ),
inference(avatar_split_clause,[],[f3873,f3830,f3625,f3941]) ).
tff(f3941,plain,
( spl249_75
<=> 'preregister$c'('f$') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_75])]) ).
tff(f3873,plain,
( 'preregister$c'('f$')
| ~ spl249_5
| ~ spl249_50 ),
inference(resolution,[],[f3831,f3627]) ).
tff(f3939,plain,
spl249_74,
inference(avatar_split_clause,[],[f1967,f3937]) ).
tff(f1967,plain,
! [X0: 'B_option$'] : ( 'none$' = 'bind$b'(X0,'uwb$') ),
inference(cnf_transformation,[],[f383]) ).
tff(f383,axiom,
! [X0: 'B_option$'] : ( 'none$' = 'bind$b'(X0,'uwb$') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom381) ).
tff(f3935,plain,
spl249_73,
inference(avatar_split_clause,[],[f1966,f3933]) ).
tff(f1966,plain,
! [X0: 'A_c_option_fun$'] : ( 'none$' = 'bind$d'('none$b',X0) ),
inference(cnf_transformation,[],[f403]) ).
tff(f403,axiom,
! [X0: 'A_c_option_fun$'] : ( 'none$' = 'bind$d'('none$b',X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom401) ).
tff(f3931,plain,
spl249_72,
inference(avatar_split_clause,[],[f1965,f3929]) ).
tff(f1965,plain,
! [X0: 'B_a_option_fun$'] : ( 'none$b' = 'bind$g'('none$a',X0) ),
inference(cnf_transformation,[],[f402]) ).
tff(f402,axiom,
! [X0: 'B_a_option_fun$'] : ( 'none$b' = 'bind$g'('none$a',X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom400) ).
tff(f3927,plain,
spl249_71,
inference(avatar_split_clause,[],[f1964,f3925]) ).
tff(f1964,plain,
! [X0: 'C_a_option_fun$'] : ( 'none$b' = 'bind$f'('none$',X0) ),
inference(cnf_transformation,[],[f401]) ).
tff(f401,axiom,
! [X0: 'C_a_option_fun$'] : ( 'none$b' = 'bind$f'('none$',X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom399) ).
tff(f3923,plain,
spl249_70,
inference(avatar_split_clause,[],[f1963,f3921]) ).
tff(f1963,plain,
! [X0: 'B$'] : ~ 'fun_app$a'('is_none$','fun_app$g'('some$',X0)),
inference(cnf_transformation,[],[f470]) ).
tff(f470,axiom,
! [X0: 'B$'] : ~ 'fun_app$a'('is_none$','fun_app$g'('some$',X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom468) ).
tff(f3919,plain,
spl249_69,
inference(avatar_split_clause,[],[f1962,f3917]) ).
tff(f1962,plain,
! [X0: 'C$'] : ~ 'fun_app$'('is_none$a','fun_app$j'('some$a',X0)),
inference(cnf_transformation,[],[f469]) ).
tff(f469,axiom,
! [X0: 'C$'] : ~ 'fun_app$'('is_none$a','fun_app$j'('some$a',X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom467) ).
tff(f3915,plain,
spl249_68,
inference(avatar_split_clause,[],[f1961,f3913]) ).
tff(f1961,plain,
! [X0: 'A$'] : ~ 'fun_app$aw'('is_none$b','fun_app$q'('some$b',X0)),
inference(cnf_transformation,[],[f468]) ).
tff(f468,axiom,
! [X0: 'A$'] : ~ 'fun_app$aw'('is_none$b','fun_app$q'('some$b',X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom466) ).
tff(f3911,plain,
spl249_67,
inference(avatar_split_clause,[],[f1960,f3909]) ).
tff(f1960,plain,
! [X0: 'B$'] : ( 'none$a' != 'fun_app$g'('some$',X0) ),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
! [X0: 'B$'] : ( 'none$a' != 'fun_app$g'('some$',X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom112) ).
tff(f3907,plain,
spl249_66,
inference(avatar_split_clause,[],[f1959,f3905]) ).
tff(f1959,plain,
! [X0: 'C$'] : ( 'none$' != 'fun_app$j'('some$a',X0) ),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
! [X0: 'C$'] : ( 'none$' != 'fun_app$j'('some$a',X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom111) ).
tff(f3903,plain,
spl249_65,
inference(avatar_split_clause,[],[f1958,f3901]) ).
tff(f1958,plain,
! [X0: 'A$'] : ( 'none$b' != 'fun_app$q'('some$b',X0) ),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
! [X0: 'A$'] : ( 'none$b' != 'fun_app$q'('some$b',X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom110) ).
tff(f3899,plain,
( spl249_64
| ~ spl249_3
| ~ spl249_49 ),
inference(avatar_split_clause,[],[f3872,f3826,f3615,f3896]) ).
tff(f3896,plain,
( spl249_64
<=> 'preregister$'('id$f') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_64])]) ).
tff(f3872,plain,
( 'preregister$'('id$f')
| ~ spl249_3
| ~ spl249_49 ),
inference(resolution,[],[f3827,f3617]) ).
tff(f3894,plain,
spl249_63,
inference(avatar_split_clause,[],[f1950,f3891]) ).
tff(f1950,plain,
'comp$m'('the$','some$') = 'id$b',
inference(cnf_transformation,[],[f651]) ).
tff(f651,axiom,
'comp$m'('the$','some$') = 'id$b',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom649) ).
tff(f3889,plain,
spl249_62,
inference(avatar_split_clause,[],[f1949,f3886]) ).
tff(f1949,plain,
'comp$n'('the$a','some$a') = 'id$a',
inference(cnf_transformation,[],[f650]) ).
tff(f650,axiom,
'comp$n'('the$a','some$a') = 'id$a',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom648) ).
tff(f3884,plain,
spl249_61,
inference(avatar_split_clause,[],[f1948,f3881]) ).
tff(f3881,plain,
( spl249_61
<=> ( 'comp$bi'('the$b','some$b') = 'id$' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_61])]) ).
tff(f1948,plain,
'comp$bi'('the$b','some$b') = 'id$',
inference(cnf_transformation,[],[f649]) ).
tff(f649,axiom,
'comp$bi'('the$b','some$b') = 'id$',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom647) ).
tff(f3879,plain,
( spl249_60
| ~ spl249_2
| ~ spl249_48 ),
inference(avatar_split_clause,[],[f3871,f3822,f3610,f3876]) ).
tff(f3876,plain,
( spl249_60
<=> 'preregister$a'('id$g') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_60])]) ).
tff(f3871,plain,
( 'preregister$a'('id$g')
| ~ spl249_2
| ~ spl249_48 ),
inference(resolution,[],[f3823,f3612]) ).
tff(f3870,plain,
spl249_59,
inference(avatar_split_clause,[],[f3470,f3868]) ).
tff(f3470,plain,
! [X1: 'B_bool_fun$'] : sP25('none$a',X1,tltrue),
inference(equality_resolution,[],[f3469]) ).
tff(f3469,plain,
! [X2: tlbool,X1: 'B_bool_fun$'] :
( sP25('none$a',X1,X2)
| ( tltrue != X2 ) ),
inference(equality_resolution,[],[f2904]) ).
tff(f2904,plain,
! [X2: tlbool,X0: 'B_option$',X1: 'B_bool_fun$'] :
( sP25(X0,X1,X2)
| ( 'none$a' != X0 )
| ( tltrue != X2 ) ),
inference(cnf_transformation,[],[f1684]) ).
tff(f3866,plain,
spl249_58,
inference(avatar_split_clause,[],[f3457,f3864]) ).
tff(f3457,plain,
! [X1: 'C_bool_fun$'] : sP20('none$',X1,tltrue),
inference(equality_resolution,[],[f3456]) ).
tff(f3456,plain,
! [X2: tlbool,X1: 'C_bool_fun$'] :
( sP20('none$',X1,X2)
| ( tltrue != X2 ) ),
inference(equality_resolution,[],[f2864]) ).
tff(f2864,plain,
! [X2: tlbool,X0: 'C_option$',X1: 'C_bool_fun$'] :
( sP20(X0,X1,X2)
| ( 'none$' != X0 )
| ( tltrue != X2 ) ),
inference(cnf_transformation,[],[f1656]) ).
tff(f3862,plain,
spl249_57,
inference(avatar_split_clause,[],[f3367,f3860]) ).
tff(f3367,plain,
! [X1: 'B$'] : 'fun_app$c'('uwl$'(X1),X1),
inference(equality_resolution,[],[f2359]) ).
tff(f2359,plain,
! [X0: 'B$',X1: 'B$'] :
( 'fun_app$c'('uwl$'(X0),X1)
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1432]) ).
tff(f3858,plain,
spl249_56,
inference(avatar_split_clause,[],[f3366,f3856]) ).
tff(f3366,plain,
! [X1: 'B$'] : 'fun_app$c'('uwp$'(X1),X1),
inference(equality_resolution,[],[f2357]) ).
tff(f2357,plain,
! [X0: 'B$',X1: 'B$'] :
( 'fun_app$c'('uwp$'(X0),X1)
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1431]) ).
tff(f3854,plain,
spl249_55,
inference(avatar_split_clause,[],[f3365,f3852]) ).
tff(f3365,plain,
! [X1: 'C$'] : 'fun_app$b'('uwm$'(X1),X1),
inference(equality_resolution,[],[f2353]) ).
tff(f2353,plain,
! [X0: 'C$',X1: 'C$'] :
( 'fun_app$b'('uwm$'(X0),X1)
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1429]) ).
tff(f3850,plain,
spl249_54,
inference(avatar_split_clause,[],[f3364,f3848]) ).
tff(f3364,plain,
! [X1: 'C$'] : 'fun_app$b'('uwq$'(X1),X1),
inference(equality_resolution,[],[f2351]) ).
tff(f2351,plain,
! [X0: 'C$',X1: 'C$'] :
( 'fun_app$b'('uwq$'(X0),X1)
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1428]) ).
tff(f3846,plain,
spl249_53,
inference(avatar_split_clause,[],[f3324,f3843]) ).
tff(f3843,plain,
( spl249_53
<=> ( 'bot$d' = 'these$a'('bot$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_53])]) ).
tff(f3324,plain,
'bot$d' = 'these$a'('bot$a'),
inference(equality_resolution,[],[f2137]) ).
tff(f2137,plain,
! [X0: 'B_option_set$'] :
( ( 'bot$a' != X0 )
| ( 'bot$d' = 'these$a'(X0) ) ),
inference(cnf_transformation,[],[f1269]) ).
tff(f3841,plain,
spl249_52,
inference(avatar_split_clause,[],[f3322,f3838]) ).
tff(f3838,plain,
( spl249_52
<=> ( 'bot$c' = 'these$'('bot$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_52])]) ).
tff(f3322,plain,
'bot$c' = 'these$'('bot$b'),
inference(equality_resolution,[],[f2134]) ).
tff(f2134,plain,
! [X0: 'C_option_set$'] :
( ( 'bot$b' != X0 )
| ( 'bot$c' = 'these$'(X0) ) ),
inference(cnf_transformation,[],[f1267]) ).
tff(f3836,plain,
spl249_51,
inference(avatar_split_clause,[],[f2040,f3834]) ).
tff(f2040,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( 'preregister$b'(X0)
| ~ 'register$a'(X0) ),
inference(cnf_transformation,[],[f867]) ).
tff(f867,plain,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( 'preregister$b'(X0)
| ~ 'register$a'(X0) ),
inference(ennf_transformation,[],[f315]) ).
tff(f315,axiom,
! [X0: 'B_b_option_fun_c_c_option_fun_fun$'] :
( 'register$a'(X0)
=> 'preregister$b'(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom313) ).
tff(f3832,plain,
spl249_50,
inference(avatar_split_clause,[],[f2039,f3830]) ).
tff(f2039,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( 'preregister$c'(X0)
| ~ 'register$'(X0) ),
inference(cnf_transformation,[],[f866]) ).
tff(f866,plain,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( 'preregister$c'(X0)
| ~ 'register$'(X0) ),
inference(ennf_transformation,[],[f314]) ).
tff(f314,axiom,
! [X0: 'A_a_option_fun_b_b_option_fun_fun$'] :
( 'register$'(X0)
=> 'preregister$c'(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom312) ).
tff(f3828,plain,
spl249_49,
inference(avatar_split_clause,[],[f2038,f3826]) ).
tff(f2038,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( 'preregister$'(X0)
| ~ 'register$h'(X0) ),
inference(cnf_transformation,[],[f865]) ).
tff(f865,plain,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( 'preregister$'(X0)
| ~ 'register$h'(X0) ),
inference(ennf_transformation,[],[f311]) ).
tff(f311,axiom,
! [X0: 'B_b_option_fun_b_b_option_fun_fun$'] :
( 'register$h'(X0)
=> 'preregister$'(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom309) ).
tff(f3824,plain,
spl249_48,
inference(avatar_split_clause,[],[f2037,f3822]) ).
tff(f2037,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( 'preregister$a'(X0)
| ~ 'register$f'(X0) ),
inference(cnf_transformation,[],[f864]) ).
tff(f864,plain,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( 'preregister$a'(X0)
| ~ 'register$f'(X0) ),
inference(ennf_transformation,[],[f313]) ).
tff(f313,axiom,
! [X0: 'C_c_option_fun_c_c_option_fun_fun$'] :
( 'register$f'(X0)
=> 'preregister$a'(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom311) ).
tff(f3820,plain,
spl249_47,
inference(avatar_split_clause,[],[f1947,f3817]) ).
tff(f3817,plain,
( spl249_47
<=> ( 'map_option$b'('id$b') = 'id$d' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_47])]) ).
tff(f1947,plain,
'map_option$b'('id$b') = 'id$d',
inference(cnf_transformation,[],[f655]) ).
tff(f655,axiom,
'map_option$b'('id$b') = 'id$d',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom653) ).
tff(f3815,plain,
spl249_46,
inference(avatar_split_clause,[],[f1946,f3812]) ).
tff(f3812,plain,
( spl249_46
<=> ( 'map_option$b'('uvm$') = 'id$d' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_46])]) ).
tff(f3810,plain,
spl249_45,
inference(avatar_split_clause,[],[f1945,f3807]) ).
tff(f3807,plain,
( spl249_45
<=> ( 'map_option$c'('id$a') = 'id$c' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_45])]) ).
tff(f3805,plain,
spl249_44,
inference(avatar_split_clause,[],[f1944,f3802]) ).
tff(f3802,plain,
( spl249_44
<=> ( 'map_option$a'('id$') = 'id$e' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_44])]) ).
tff(f3800,plain,
spl249_43,
inference(avatar_split_clause,[],[f1943,f3797]) ).
tff(f3797,plain,
( spl249_43
<=> ( 'map_option$a'('uvn$') = 'id$e' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_43])]) ).
tff(f1943,plain,
'map_option$a'('uvn$') = 'id$e',
inference(cnf_transformation,[],[f671]) ).
tff(f671,axiom,
'map_option$a'('uvn$') = 'id$e',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom669) ).
tff(f3795,plain,
spl249_42,
inference(avatar_split_clause,[],[f1942,f3792]) ).
tff(f3792,plain,
( spl249_42
<=> ( 'bot$a' = 'set_option$'('none$c') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_42])]) ).
tff(f1942,plain,
'bot$a' = 'set_option$'('none$c'),
inference(cnf_transformation,[],[f557]) ).
tff(f557,axiom,
'bot$a' = 'set_option$'('none$c'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom555) ).
tff(f3790,plain,
spl249_41,
inference(avatar_split_clause,[],[f1941,f3787]) ).
tff(f3787,plain,
( spl249_41
<=> ( 'bot$b' = 'set_option$a'('none$d') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_41])]) ).
tff(f1941,plain,
'bot$b' = 'set_option$a'('none$d'),
inference(cnf_transformation,[],[f558]) ).
tff(f558,axiom,
'bot$b' = 'set_option$a'('none$d'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom556) ).
tff(f3785,plain,
spl249_40,
inference(avatar_split_clause,[],[f1940,f3782]) ).
tff(f1940,plain,
'bot$a' = 'collect$b'('bot$g'),
inference(cnf_transformation,[],[f583]) ).
tff(f583,axiom,
'bot$a' = 'collect$b'('bot$g'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom581) ).
tff(f3780,plain,
spl249_39,
inference(avatar_split_clause,[],[f1939,f3777]) ).
tff(f1939,plain,
'bot$b' = 'collect$c'('bot$h'),
inference(cnf_transformation,[],[f584]) ).
tff(f584,axiom,
'bot$b' = 'collect$c'('bot$h'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom582) ).
tff(f3775,plain,
spl249_38,
inference(avatar_split_clause,[],[f1938,f3772]) ).
tff(f3772,plain,
( spl249_38
<=> ( 'bot$b' = 'collect$c'('uwg$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_38])]) ).
tff(f1938,plain,
'bot$b' = 'collect$c'('uwg$'),
inference(cnf_transformation,[],[f640]) ).
tff(f640,axiom,
'bot$b' = 'collect$c'('uwg$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom638) ).
tff(f3770,plain,
spl249_37,
inference(avatar_split_clause,[],[f1937,f3767]) ).
tff(f3767,plain,
( spl249_37
<=> ( 'bot$a' = 'collect$b'('uwf$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_37])]) ).
tff(f1937,plain,
'bot$a' = 'collect$b'('uwf$'),
inference(cnf_transformation,[],[f639]) ).
tff(f639,axiom,
'bot$a' = 'collect$b'('uwf$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom637) ).
tff(f3765,plain,
spl249_36,
inference(avatar_split_clause,[],[f1936,f3762]) ).
tff(f3762,plain,
( spl249_36
<=> ( 'bot$d' = 'set_option$d'('none$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_36])]) ).
tff(f1936,plain,
'bot$d' = 'set_option$d'('none$a'),
inference(cnf_transformation,[],[f560]) ).
tff(f560,axiom,
'bot$d' = 'set_option$d'('none$a'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom558) ).
tff(f3760,plain,
spl249_35,
inference(avatar_split_clause,[],[f1935,f3757]) ).
tff(f3757,plain,
( spl249_35
<=> ( 'bot$c' = 'set_option$c'('none$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_35])]) ).
tff(f1935,plain,
'bot$c' = 'set_option$c'('none$'),
inference(cnf_transformation,[],[f559]) ).
tff(f559,axiom,
'bot$c' = 'set_option$c'('none$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom557) ).
tff(f3755,plain,
spl249_34,
inference(avatar_split_clause,[],[f1934,f3752]) ).
tff(f3752,plain,
( spl249_34
<=> ( 'bot$c' = 'collect$a'('uuc$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_34])]) ).
tff(f1934,plain,
'bot$c' = 'collect$a'('uuc$'),
inference(cnf_transformation,[],[f638]) ).
tff(f638,axiom,
'bot$c' = 'collect$a'('uuc$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom636) ).
tff(f3750,plain,
spl249_33,
inference(avatar_split_clause,[],[f1933,f3747]) ).
tff(f3747,plain,
( spl249_33
<=> ( 'bot$d' = 'collect$'('uud$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_33])]) ).
tff(f1933,plain,
'bot$d' = 'collect$'('uud$'),
inference(cnf_transformation,[],[f637]) ).
tff(f637,axiom,
'bot$d' = 'collect$'('uud$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom635) ).
tff(f3745,plain,
spl249_32,
inference(avatar_split_clause,[],[f1932,f3742]) ).
tff(f1932,plain,
'bot$d' = 'collect$'('bot$e'),
inference(cnf_transformation,[],[f581]) ).
tff(f581,axiom,
'bot$d' = 'collect$'('bot$e'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom579) ).
tff(f3740,plain,
spl249_31,
inference(avatar_split_clause,[],[f1931,f3737]) ).
tff(f1931,plain,
'bot$c' = 'collect$a'('bot$f'),
inference(cnf_transformation,[],[f582]) ).
tff(f582,axiom,
'bot$c' = 'collect$a'('bot$f'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom580) ).
tff(f3735,plain,
spl249_30,
inference(avatar_split_clause,[],[f1930,f3732]) ).
tff(f3732,plain,
( spl249_30
<=> ( 'bot$' = 'set_option$b'('none$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_30])]) ).
tff(f1930,plain,
'bot$' = 'set_option$b'('none$b'),
inference(cnf_transformation,[],[f556]) ).
tff(f556,axiom,
'bot$' = 'set_option$b'('none$b'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom554) ).
tff(f3730,plain,
spl249_29,
inference(avatar_split_clause,[],[f3361,f3728]) ).
tff(f3728,plain,
( spl249_29
<=> ! [X0: 'B_option$'] : ~ sP2(X0,'none$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_29])]) ).
tff(f3361,plain,
! [X0: 'B_option$'] : ~ sP2(X0,'none$a'),
inference(equality_resolution,[],[f2327]) ).
tff(f2327,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( ( 'none$a' != X1 )
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1402]) ).
tff(f3726,plain,
spl249_28,
inference(avatar_split_clause,[],[f3360,f3724]) ).
tff(f3724,plain,
( spl249_28
<=> ! [X1: 'B_option$'] : ~ sP2('none$a',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_28])]) ).
tff(f3360,plain,
! [X1: 'B_option$'] : ~ sP2('none$a',X1),
inference(equality_resolution,[],[f2328]) ).
tff(f2328,plain,
! [X0: 'B_option$',X1: 'B_option$'] :
( ( 'none$a' != X0 )
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1402]) ).
tff(f3722,plain,
spl249_27,
inference(avatar_split_clause,[],[f3357,f3720]) ).
tff(f3720,plain,
( spl249_27
<=> ! [X0: 'C_option$'] : ~ sP1(X0,'none$') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_27])]) ).
tff(f3357,plain,
! [X0: 'C_option$'] : ~ sP1(X0,'none$'),
inference(equality_resolution,[],[f2322]) ).
tff(f2322,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( ( 'none$' != X1 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f1399]) ).
tff(f3718,plain,
spl249_26,
inference(avatar_split_clause,[],[f3356,f3716]) ).
tff(f3716,plain,
( spl249_26
<=> ! [X1: 'C_option$'] : ~ sP1('none$',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_26])]) ).
tff(f3356,plain,
! [X1: 'C_option$'] : ~ sP1('none$',X1),
inference(equality_resolution,[],[f2323]) ).
tff(f2323,plain,
! [X0: 'C_option$',X1: 'C_option$'] :
( ( 'none$' != X0 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f1399]) ).
tff(f3714,plain,
spl249_25,
inference(avatar_split_clause,[],[f3353,f3712]) ).
tff(f3712,plain,
( spl249_25
<=> ! [X0: 'A_option$'] : ~ sP0(X0,'none$b') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_25])]) ).
tff(f3353,plain,
! [X0: 'A_option$'] : ~ sP0(X0,'none$b'),
inference(equality_resolution,[],[f2317]) ).
tff(f2317,plain,
! [X0: 'A_option$',X1: 'A_option$'] :
( ( 'none$b' != X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f1396]) ).
tff(f3710,plain,
spl249_24,
inference(avatar_split_clause,[],[f3352,f3708]) ).
tff(f3708,plain,
( spl249_24
<=> ! [X1: 'A_option$'] : ~ sP0('none$b',X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_24])]) ).
tff(f3352,plain,
! [X1: 'A_option$'] : ~ sP0('none$b',X1),
inference(equality_resolution,[],[f2318]) ).
tff(f2318,plain,
! [X0: 'A_option$',X1: 'A_option$'] :
( ( 'none$b' != X0 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f1396]) ).
tff(f3706,plain,
spl249_23,
inference(avatar_split_clause,[],[f2129,f3704]) ).
tff(f2129,plain,
! [X0: 'B_option$'] : ~ 'fun_app$a'('uwf$',X0),
inference(cnf_transformation,[],[f793]) ).
tff(f793,plain,
! [X0: 'B_option$'] : ~ 'fun_app$a'('uwf$',X0),
inference(flattening,[],[f792]) ).
tff(f792,plain,
! [X0: 'B_option$'] : ~ 'fun_app$a'('uwf$',X0),
inference(true_and_false_elimination,[],[f66]) ).
tff(f66,axiom,
! [X0: 'B_option$'] :
( 'fun_app$a'('uwf$',X0)
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom65) ).
tff(f3702,plain,
spl249_22,
inference(avatar_split_clause,[],[f2124,f3700]) ).
tff(f2124,plain,
! [X0: 'C_option$'] : ~ 'fun_app$'('uwg$',X0),
inference(cnf_transformation,[],[f791]) ).
tff(f791,plain,
! [X0: 'C_option$'] : ~ 'fun_app$'('uwg$',X0),
inference(flattening,[],[f790]) ).
tff(f790,plain,
! [X0: 'C_option$'] : ~ 'fun_app$'('uwg$',X0),
inference(true_and_false_elimination,[],[f65]) ).
tff(f65,axiom,
! [X0: 'C_option$'] :
( 'fun_app$'('uwg$',X0)
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom64) ).
tff(f3698,plain,
spl249_21,
inference(avatar_split_clause,[],[f2117,f3696]) ).
tff(f3696,plain,
( spl249_21
<=> ! [X0: 'B$'] : ~ 'fun_app$c'('uud$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_21])]) ).
tff(f2117,plain,
! [X0: 'B$'] : ~ 'fun_app$c'('uud$',X0),
inference(cnf_transformation,[],[f785]) ).
tff(f785,plain,
! [X0: 'B$'] : ~ 'fun_app$c'('uud$',X0),
inference(flattening,[],[f784]) ).
tff(f784,plain,
! [X0: 'B$'] : ~ 'fun_app$c'('uud$',X0),
inference(true_and_false_elimination,[],[f68]) ).
tff(f68,axiom,
! [X0: 'B$'] :
( 'fun_app$c'('uud$',X0)
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom67) ).
tff(f3694,plain,
spl249_20,
inference(avatar_split_clause,[],[f2116,f3692]) ).
tff(f2116,plain,
! [X0: 'B$'] : 'fun_app$c'('uug$',X0),
inference(cnf_transformation,[],[f783]) ).
tff(f783,plain,
! [X0: 'B$'] : 'fun_app$c'('uug$',X0),
inference(true_and_false_elimination,[],[f71]) ).
tff(f71,axiom,
! [X0: 'B$'] :
( 'fun_app$c'('uug$',X0)
<=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom70) ).
tff(f3690,plain,
spl249_19,
inference(avatar_split_clause,[],[f2113,f3688]) ).
tff(f3688,plain,
( spl249_19
<=> ! [X0: 'C$'] : ~ 'fun_app$b'('uuc$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_19])]) ).
tff(f2113,plain,
! [X0: 'C$'] : ~ 'fun_app$b'('uuc$',X0),
inference(cnf_transformation,[],[f782]) ).
tff(f782,plain,
! [X0: 'C$'] : ~ 'fun_app$b'('uuc$',X0),
inference(flattening,[],[f781]) ).
tff(f781,plain,
! [X0: 'C$'] : ~ 'fun_app$b'('uuc$',X0),
inference(true_and_false_elimination,[],[f67]) ).
tff(f67,axiom,
! [X0: 'C$'] :
( 'fun_app$b'('uuc$',X0)
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom66) ).
tff(f3686,plain,
spl249_18,
inference(avatar_split_clause,[],[f2112,f3684]) ).
tff(f2112,plain,
! [X0: 'C$'] : 'fun_app$b'('uuf$',X0),
inference(cnf_transformation,[],[f780]) ).
tff(f780,plain,
! [X0: 'C$'] : 'fun_app$b'('uuf$',X0),
inference(true_and_false_elimination,[],[f70]) ).
tff(f70,axiom,
! [X0: 'C$'] :
( 'fun_app$b'('uuf$',X0)
<=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom69) ).
tff(f3682,plain,
spl249_17,
inference(avatar_split_clause,[],[f2109,f3680]) ).
tff(f3680,plain,
( spl249_17
<=> ! [X0: 'A$'] : 'fun_app$z'('uue$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_17])]) ).
tff(f2109,plain,
! [X0: 'A$'] : 'fun_app$z'('uue$',X0),
inference(cnf_transformation,[],[f779]) ).
tff(f779,plain,
! [X0: 'A$'] : 'fun_app$z'('uue$',X0),
inference(true_and_false_elimination,[],[f72]) ).
tff(f72,axiom,
! [X0: 'A$'] :
( 'fun_app$z'('uue$',X0)
<=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom71) ).
tff(f3678,plain,
spl249_16,
inference(avatar_split_clause,[],[f2108,f3676]) ).
tff(f3676,plain,
( spl249_16
<=> ! [X0: 'A$'] : ~ 'fun_app$z'('uub$',X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_16])]) ).
tff(f2108,plain,
! [X0: 'A$'] : ~ 'fun_app$z'('uub$',X0),
inference(cnf_transformation,[],[f778]) ).
tff(f778,plain,
! [X0: 'A$'] : ~ 'fun_app$z'('uub$',X0),
inference(flattening,[],[f777]) ).
tff(f777,plain,
! [X0: 'A$'] : ~ 'fun_app$z'('uub$',X0),
inference(true_and_false_elimination,[],[f69]) ).
tff(f69,axiom,
! [X0: 'A$'] :
( 'fun_app$z'('uub$',X0)
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom68) ).
tff(f3674,plain,
spl249_15,
inference(avatar_split_clause,[],[f2056,f3672]) ).
tff(f3672,plain,
( spl249_15
<=> ! [X0: 'B$'] : ~ 'member$c'(X0,'bot$d') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_15])]) ).
tff(f2056,plain,
! [X0: 'B$'] : ~ 'member$c'(X0,'bot$d'),
inference(cnf_transformation,[],[f750]) ).
tff(f750,plain,
! [X0: 'B$'] : ~ 'member$c'(X0,'bot$d'),
inference(flattening,[],[f749]) ).
tff(f749,plain,
! [X0: 'B$'] : ~ 'member$c'(X0,'bot$d'),
inference(true_and_false_elimination,[],[f585]) ).
tff(f585,axiom,
! [X0: 'B$'] :
( 'member$c'(X0,'bot$d')
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom583) ).
tff(f3670,plain,
spl249_14,
inference(avatar_split_clause,[],[f2055,f3668]) ).
tff(f3668,plain,
( spl249_14
<=> ! [X0: 'C$'] : ~ 'member$b'(X0,'bot$c') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_14])]) ).
tff(f2055,plain,
! [X0: 'C$'] : ~ 'member$b'(X0,'bot$c'),
inference(cnf_transformation,[],[f748]) ).
tff(f748,plain,
! [X0: 'C$'] : ~ 'member$b'(X0,'bot$c'),
inference(flattening,[],[f747]) ).
tff(f747,plain,
! [X0: 'C$'] : ~ 'member$b'(X0,'bot$c'),
inference(true_and_false_elimination,[],[f586]) ).
tff(f586,axiom,
! [X0: 'C$'] :
( 'member$b'(X0,'bot$c')
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom584) ).
tff(f3666,plain,
spl249_13,
inference(avatar_split_clause,[],[f2054,f3664]) ).
tff(f3664,plain,
( spl249_13
<=> ! [X0: 'C_option$'] : ~ 'member$'(X0,'bot$b') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_13])]) ).
tff(f2054,plain,
! [X0: 'C_option$'] : ~ 'member$'(X0,'bot$b'),
inference(cnf_transformation,[],[f746]) ).
tff(f746,plain,
! [X0: 'C_option$'] : ~ 'member$'(X0,'bot$b'),
inference(flattening,[],[f745]) ).
tff(f745,plain,
! [X0: 'C_option$'] : ~ 'member$'(X0,'bot$b'),
inference(true_and_false_elimination,[],[f588]) ).
tff(f588,axiom,
! [X0: 'C_option$'] :
( 'member$'(X0,'bot$b')
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom586) ).
tff(f3662,plain,
spl249_12,
inference(avatar_split_clause,[],[f2053,f3660]) ).
tff(f3660,plain,
( spl249_12
<=> ! [X0: 'B_option$'] : ~ 'member$a'(X0,'bot$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl249_12])]) ).
tff(f2053,plain,
! [X0: 'B_option$'] : ~ 'member$a'(X0,'bot$a'),
inference(cnf_transformation,[],[f744]) ).
tff(f744,plain,
! [X0: 'B_option$'] : ~ 'member$a'(X0,'bot$a'),
inference(flattening,[],[f743]) ).
tff(f743,plain,
! [X0: 'B_option$'] : ~ 'member$a'(X0,'bot$a'),
inference(true_and_false_elimination,[],[f587]) ).
tff(f587,axiom,
! [X0: 'B_option$'] :
( 'member$a'(X0,'bot$a')
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom585) ).
tff(f3658,plain,
spl249_11,
inference(avatar_split_clause,[],[f1954,f3655]) ).
tff(f1954,plain,
'valid_getter_setter$a'(sK47,sK46),
inference(cnf_transformation,[],[f1190]) ).
tff(f3653,plain,
spl249_10,
inference(avatar_split_clause,[],[f1929,f3650]) ).
tff(f1929,plain,
'fun_app$a'('is_none$','none$a'),
inference(cnf_transformation,[],[f467]) ).
tff(f467,axiom,
'fun_app$a'('is_none$','none$a'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom465) ).
tff(f3648,plain,
spl249_9,
inference(avatar_split_clause,[],[f1928,f3645]) ).
tff(f1928,plain,
'fun_app$'('is_none$a','none$'),
inference(cnf_transformation,[],[f466]) ).
tff(f466,axiom,
'fun_app$'('is_none$a','none$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom464) ).
tff(f3643,plain,
spl249_8,
inference(avatar_split_clause,[],[f1927,f3640]) ).
tff(f1927,plain,
'fun_app$aw'('is_none$b','none$b'),
inference(cnf_transformation,[],[f465]) ).
tff(f465,axiom,
'fun_app$aw'('is_none$b','none$b'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom463) ).
tff(f3638,plain,
spl249_7,
inference(avatar_split_clause,[],[f1926,f3635]) ).
tff(f1926,plain,
'valid_getter_setter$a'('gF$','sF$'),
inference(cnf_transformation,[],[f124]) ).
tff(f124,axiom,
'valid_getter_setter$a'('gF$','sF$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom122) ).
tff(f3633,plain,
~ spl249_6,
inference(avatar_split_clause,[],[f1925,f3630]) ).
tff(f3630,plain,
( spl249_6
<=> ( tltrue = tlfalse ) ),
introduced(avatar_definition,[new_symbols(naming,[spl249_6])]) ).
tff(f1925,plain,
tltrue != tlfalse,
inference(cnf_transformation,[],[f736]) ).
tff(f736,axiom,
tltrue != tlfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_735) ).
tff(f3628,plain,
spl249_5,
inference(avatar_split_clause,[],[f1924,f3625]) ).
tff(f1924,plain,
'register$'('f$'),
inference(cnf_transformation,[],[f76]) ).
tff(f76,axiom,
'register$'('f$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom74) ).
tff(f3623,plain,
spl249_4,
inference(avatar_split_clause,[],[f1923,f3620]) ).
tff(f1923,plain,
'register$a'('g$'),
inference(cnf_transformation,[],[f77]) ).
tff(f77,axiom,
'register$a'('g$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom75) ).
tff(f3618,plain,
spl249_3,
inference(avatar_split_clause,[],[f1922,f3615]) ).
tff(f1922,plain,
'register$h'('id$f'),
inference(cnf_transformation,[],[f664]) ).
tff(f664,axiom,
'register$h'('id$f'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom662) ).
tff(f3613,plain,
spl249_2,
inference(avatar_split_clause,[],[f1921,f3610]) ).
tff(f1921,plain,
'register$f'('id$g'),
inference(cnf_transformation,[],[f665]) ).
tff(f665,axiom,
'register$f'('id$g'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom663) ).
tff(f3608,plain,
~ spl249_1,
inference(avatar_split_clause,[],[f1919,f3605]) ).
tff(f1919,plain,
~ 'thesis$',
inference(cnf_transformation,[],[f737]) ).
tff(f737,plain,
~ 'thesis$',
inference(flattening,[],[f74]) ).
tff(f74,negated_conjecture,
~ 'thesis$',
inference(negated_conjecture,[],[f73]) ).
tff(f73,conjecture,
'thesis$',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture72) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ITP386_1 : TPTP v8.1.2. Released v8.0.0.
% 0.09/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.30 % Computer : n029.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Fri May 3 18:59:38 EDT 2024
% 0.09/0.31 % CPUTime :
% 0.09/0.31 % (13467)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.36 % (13470)WARNING: value z3 for option sas not known
% 0.15/0.36 % (13471)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.36 % (13473)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.36 % (13474)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.36 % (13469)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.36 % (13472)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.36 % (13468)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.36 % (13470)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 3.49/0.85 TRYING [1]
% 3.49/0.91 TRYING [2]
% 4.18/0.98 % (13472)First to succeed.
% 5.09/1.07 % (13472)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-13467"
% 5.09/1.08 % (13472)Refutation found. Thanks to Tanya!
% 5.09/1.08 % SZS status Theorem for theBenchmark
% 5.09/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 5.25/1.13 % (13472)------------------------------
% 5.25/1.13 % (13472)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 5.25/1.13 % (13472)Termination reason: Refutation
% 5.25/1.13
% 5.25/1.13 % (13472)Memory used [KB]: 12229
% 5.25/1.13 % (13472)Time elapsed: 0.712 s
% 5.25/1.13 % (13472)Instructions burned: 1349 (million)
% 5.25/1.13 % (13467)Success in time 0.805 s
%------------------------------------------------------------------------------