%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW473+3 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:32:31 PM UTC 2026
% Result : Theorem 3.53s 2.85s
% Output : CNFRefutation 7.01s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_1640)
% Comments :
%------------------------------------------------------------------------------
fof(fact_272_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X5)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X9)),hAPP_n1699378549t_bool(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_pigeonhole__infinite) ).
fof(fact_271_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X5)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X9)),hAPP_n1082236369t_bool(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_pigeonhole__infinite) ).
fof(fact_273_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X5)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X9)),hAPP_n1025906991e_bool(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_pigeonhole__infinite) ).
fof(fact_274_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X5)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X9)),hAPP_nat_fun_a_bool(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_pigeonhole__infinite) ).
fof(fact_281_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X5)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X9)),hAPP_nat_int(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_pigeonhole__infinite) ).
fof(fact_277_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X5))
& ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X5)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X9)),hAPP_i418383825t_bool(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_pigeonhole__infinite) ).
fof(fact_276_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X5))
& ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X5)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X9)),hAPP_i1948725293t_bool(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_pigeonhole__infinite) ).
fof(fact_278_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X5))
& ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X5)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X9)),hAPP_i7355787e_bool(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_pigeonhole__infinite) ).
fof(fact_279_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X5))
& ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X5)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X9)),hAPP_int_fun_a_bool(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_pigeonhole__infinite) ).
fof(fact_275_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X5))
& ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X5)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X9)),hAPP_int_a(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_pigeonhole__infinite) ).
fof(fact_965_card__less__Suc2,axiom,
! [X33,X131] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X131))
=> hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),X131)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X33)))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X131)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,X33))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_965_card__less__Suc2) ).
fof(fact_1155_nat__number__of__add__left,axiom,
! [X156,X22,X133] :
( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X133)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X156)),X22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X156)),X22) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> ( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X156)))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X133)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X156)),X22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X133)),X22) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X156)))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X133)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X156)),X22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X133),X156))),X22) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1155_nat__number__of__add__left) ).
fof(fact_1164_nat__number__of__Bit1,axiom,
! [X135] :
( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X135)))
=> number_number_of_nat(bit1(X135)) = zero_zero_nat )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X135)))
=> number_number_of_nat(bit1(X135)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X135)),number_number_of_nat(X135))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1164_nat__number__of__Bit1) ).
fof(fact_1161_Suc__nat__number__of__add,axiom,
! [X14,X133] :
( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X133)),X14)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X14) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X133)),X14)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(X133))),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1161_Suc__nat__number__of__add) ).
fof(fact_1165_nat__1__add__number__of,axiom,
! [X133] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X133),pls))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X133)) = one_one_nat )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X133),pls))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X133)) = number_number_of_nat(succ(X133)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1165_nat__1__add__number__of) ).
fof(fact_631_Collect__conv__if,axiom,
! [X13,X8] :
( ( hBOOL(hAPP_int_bool(X13,X8))
=> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X8)),X13)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool) )
& ( ~ hBOOL(hAPP_int_bool(X13,X8))
=> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X8)),X13)) = bot_bot_fun_int_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_Collect__conv__if) ).
fof(fact_632_Collect__conv__if,axiom,
! [X13,X8] :
( ( hBOOL(hAPP_nat_bool(X13,X8))
=> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X8)),X13)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool) )
& ( ~ hBOOL(hAPP_nat_bool(X13,X8))
=> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X8)),X13)) = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_Collect__conv__if) ).
fof(fact_1154_eq__nat__number__of,axiom,
! [X154,X155] :
( number_number_of_nat(X154) = number_number_of_nat(X155)
<=> ( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X154)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X155)),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X154)))
=> ( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X155)))
=> number_number_of_int(X154) = zero_zero_int )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X155)))
=> X154 = X155 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1154_eq__nat__number__of) ).
fof(fact_634_Collect__conv__if2,axiom,
! [X13,X8] :
( ( hBOOL(hAPP_int_bool(X13,X8))
=> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X8)),X13)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool) )
& ( ~ hBOOL(hAPP_int_bool(X13,X8))
=> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X8)),X13)) = bot_bot_fun_int_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_Collect__conv__if2) ).
fof(fact_635_Collect__conv__if2,axiom,
! [X13,X8] :
( ( hBOOL(hAPP_nat_bool(X13,X8))
=> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X8)),X13)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool) )
& ( ~ hBOOL(hAPP_nat_bool(X13,X8))
=> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X8)),X13)) = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_Collect__conv__if2) ).
fof(fact_1163_Suc__nat__number__of,axiom,
! [X133] :
( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> hAPP_nat_nat(suc,number_number_of_nat(X133)) = one_one_nat )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> hAPP_nat_nat(suc,number_number_of_nat(X133)) = number_number_of_nat(succ(X133)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1163_Suc__nat__number__of) ).
fof(fact_1156_int__nat__number__of,axiom,
! [X133] :
( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X133)) = zero_zero_int )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X133)) = number_number_of_int(X133) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1156_int__nat__number__of) ).
fof(fact_522_empty__Collect__eq,axiom,
! [X13] :
( bot_bot_fun_nat_bool = collect_nat(X13)
<=> ! [X30] : ~ hBOOL(hAPP_nat_bool(X13,X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_empty__Collect__eq) ).
fof(fact_521_empty__Collect__eq,axiom,
! [X13] :
( bot_bot_fun_int_bool = collect_int(X13)
<=> ! [X30] : ~ hBOOL(hAPP_int_bool(X13,X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_empty__Collect__eq) ).
fof(fact_509_Collect__empty__eq,axiom,
! [X13] :
( collect_nat(X13) = bot_bot_fun_nat_bool
<=> ! [X30] : ~ hBOOL(hAPP_nat_bool(X13,X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_Collect__empty__eq) ).
fof(fact_508_Collect__empty__eq,axiom,
! [X13] :
( collect_int(X13) = bot_bot_fun_int_bool
<=> ! [X30] : ~ hBOOL(hAPP_int_bool(X13,X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_Collect__empty__eq) ).
fof(fact_1172_Suc3__eq__add__3,axiom,
! [X14] : hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X14))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1172_Suc3__eq__add__3) ).
fof(fact_1177_Bit1__def,axiom,
! [X22] : bit1(X22) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X22)),X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1177_Bit1__def) ).
fof(fact_1071_number__of__is__id,axiom,
! [X22] : number_number_of_int(X22) = X22,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1071_number__of__is__id) ).
fof(fact_280_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X9,X5)))
=> ? [X30] :
( is_pname(X30)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X5)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X9)),hAPP_pname_a(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_pigeonhole__infinite) ).
fof(fact_1196_less__int__code_I16_J,axiom,
! [X157,X158] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X157)),bit1(X158)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X157),X158)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1196_less__int__code_I16_J) ).
fof(fact_1195_rel__simps_I17_J,axiom,
! [X16,X134] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X16)),bit1(X134)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X16),X134)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1195_rel__simps_I17_J) ).
fof(fact_1192_less__eq__int__code_I16_J,axiom,
! [X157,X158] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X157)),bit1(X158)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X157),X158)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1192_less__eq__int__code_I16_J) ).
fof(fact_1191_rel__simps_I34_J,axiom,
! [X16,X134] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X16)),bit1(X134)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X16),X134)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1191_rel__simps_I34_J) ).
fof(fact_381_Collect__def,axiom,
! [X13] : collect_nat(X13) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_Collect__def) ).
fof(fact_380_Collect__def,axiom,
! [X13] : collect_int(X13) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_Collect__def) ).
fof(fact_680_finite__subset__induct,axiom,
! [X13,X5,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),X5))
=> ( hBOOL(hAPP_f54304608l_bool(X13,bot_bot_fun_nat_bool))
=> ( ! [X78,X79] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X79))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X78),X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X78),X79))
=> ( hBOOL(hAPP_f54304608l_bool(X13,X79))
=> hBOOL(hAPP_f54304608l_bool(X13,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X78),X79))) ) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X13,X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_finite__subset__induct) ).
fof(fact_679_finite__subset__induct,axiom,
! [X13,X5,X7] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),X5))
=> ( hBOOL(hAPP_f448129468l_bool(X13,bot_bot_fun_int_bool))
=> ( ! [X78,X79] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X79))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X78),X5))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X78),X79))
=> ( hBOOL(hAPP_f448129468l_bool(X13,X79))
=> hBOOL(hAPP_f448129468l_bool(X13,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X78),X79))) ) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X13,X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_finite__subset__induct) ).
fof(fact_681_finite__subset__induct,axiom,
! [X13,X5,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),X5))
=> ( hBOOL(hAPP_f1664156314l_bool(X13,bot_bo844097828e_bool))
=> ( ! [X78,X79] :
( ( is_pname(X78)
& is_fun_pname_bool(X79) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X79))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X78),X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X78),X79))
=> ( hBOOL(hAPP_f1664156314l_bool(X13,X79))
=> hBOOL(hAPP_f1664156314l_bool(X13,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X78),X79))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X13,X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_finite__subset__induct) ).
fof(fact_678_finite__subset__induct,axiom,
! [X13,X5,X7] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(X13,bot_bot_fun_a_bool))
=> ( ! [X78,X79] :
( ( is_a(X78)
& is_fun_a_bool(X79) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X79))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X78),X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X78),X79))
=> ( hBOOL(hAPP_fun_a_bool_bool(X13,X79))
=> hBOOL(hAPP_fun_a_bool_bool(X13,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X78),X79))) ) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X13,X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_finite__subset__induct) ).
fof(fact_1194_rel__simps_I12_J,axiom,
! [X16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X16)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X16),pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1194_rel__simps_I12_J) ).
fof(fact_1197_rel__simps_I29_J,axiom,
! [X16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X16)),pls))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X16),pls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1197_rel__simps_I29_J) ).
fof(fact_567_subset__insert__iff,axiom,
! [X5,X11,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X10)))
<=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool))),X10)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_subset__insert__iff) ).
fof(fact_566_subset__insert__iff,axiom,
! [X5,X11,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X10)))
<=> ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool))),X10)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_subset__insert__iff) ).
fof(fact_568_subset__insert__iff,axiom,
! [X5,X11,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X10)))
<=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool))),X10)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_subset__insert__iff) ).
fof(fact_565_subset__insert__iff,axiom,
! [X5,X11,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X10)))
<=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool))),X10)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_subset__insert__iff) ).
fof(fact_963_card__less__Suc,axiom,
! [X33,X131] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X131))
=> hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),X131)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X33))))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X131)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,X33))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_963_card__less__Suc) ).
fof(fact_782_finite__ne__induct,axiom,
! [X13,X7] :
( is_fun_pname_bool(X7)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> ( X7 != bot_bo844097828e_bool
=> ( ! [X30] :
( is_pname(X30)
=> hBOOL(hAPP_f1664156314l_bool(X13,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X30),bot_bo844097828e_bool))) )
=> ( ! [X30,X79] :
( ( is_pname(X30)
& is_fun_pname_bool(X79) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X79))
=> ( X79 != bot_bo844097828e_bool
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X79))
=> ( hBOOL(hAPP_f1664156314l_bool(X13,X79))
=> hBOOL(hAPP_f1664156314l_bool(X13,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X30),X79))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X13,X7)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_782_finite__ne__induct) ).
fof(fact_779_finite__ne__induct,axiom,
! [X13,X7] :
( is_fun_a_bool(X7)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> ( X7 != bot_bot_fun_a_bool
=> ( ! [X30] :
( is_a(X30)
=> hBOOL(hAPP_fun_a_bool_bool(X13,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X30),bot_bot_fun_a_bool))) )
=> ( ! [X30,X79] :
( ( is_a(X30)
& is_fun_a_bool(X79) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X79))
=> ( X79 != bot_bot_fun_a_bool
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X79))
=> ( hBOOL(hAPP_fun_a_bool_bool(X13,X79))
=> hBOOL(hAPP_fun_a_bool_bool(X13,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X30),X79))) ) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X13,X7)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_779_finite__ne__induct) ).
fof(fact_781_finite__ne__induct,axiom,
! [X13,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> ( X7 != bot_bot_fun_nat_bool
=> ( ! [X30] : hBOOL(hAPP_f54304608l_bool(X13,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),bot_bot_fun_nat_bool)))
=> ( ! [X30,X79] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X79))
=> ( X79 != bot_bot_fun_nat_bool
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X79))
=> ( hBOOL(hAPP_f54304608l_bool(X13,X79))
=> hBOOL(hAPP_f54304608l_bool(X13,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),X79))) ) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X13,X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_781_finite__ne__induct) ).
fof(fact_780_finite__ne__induct,axiom,
! [X13,X7] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
=> ( X7 != bot_bot_fun_int_bool
=> ( ! [X30] : hBOOL(hAPP_f448129468l_bool(X13,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),bot_bot_fun_int_bool)))
=> ( ! [X30,X79] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X79))
=> ( X79 != bot_bot_fun_int_bool
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X79))
=> ( hBOOL(hAPP_f448129468l_bool(X13,X79))
=> hBOOL(hAPP_f448129468l_bool(X13,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),X79))) ) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X13,X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_780_finite__ne__induct) ).
fof(fact_1198_rel__simps_I5_J,axiom,
! [X16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X16)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1198_rel__simps_I5_J) ).
fof(fact_1190_rel__simps_I22_J,axiom,
! [X16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X16)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1190_rel__simps_I22_J) ).
fof(fact_1167_neg__number__of__Bit1,axiom,
! [X139] :
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X139))))
<=> hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X139))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1167_neg__number__of__Bit1) ).
fof(fact_689_finite__induct,axiom,
! [X13,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> ( hBOOL(hAPP_f54304608l_bool(X13,bot_bot_fun_nat_bool))
=> ( ! [X30,X79] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X79))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X79))
=> ( hBOOL(hAPP_f54304608l_bool(X13,X79))
=> hBOOL(hAPP_f54304608l_bool(X13,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),X79))) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X13,X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_finite__induct) ).
fof(fact_688_finite__induct,axiom,
! [X13,X7] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
=> ( hBOOL(hAPP_f448129468l_bool(X13,bot_bot_fun_int_bool))
=> ( ! [X30,X79] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X79))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X79))
=> ( hBOOL(hAPP_f448129468l_bool(X13,X79))
=> hBOOL(hAPP_f448129468l_bool(X13,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),X79))) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X13,X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_finite__induct) ).
fof(fact_690_finite__induct,axiom,
! [X13,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> ( hBOOL(hAPP_f1664156314l_bool(X13,bot_bo844097828e_bool))
=> ( ! [X30,X79] :
( ( is_pname(X30)
& is_fun_pname_bool(X79) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X79))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X79))
=> ( hBOOL(hAPP_f1664156314l_bool(X13,X79))
=> hBOOL(hAPP_f1664156314l_bool(X13,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X30),X79))) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X13,X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_finite__induct) ).
fof(fact_687_finite__induct,axiom,
! [X13,X7] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(X13,bot_bot_fun_a_bool))
=> ( ! [X30,X79] :
( ( is_a(X30)
& is_fun_a_bool(X79) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X79))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X79))
=> ( hBOOL(hAPP_fun_a_bool_bool(X13,X79))
=> hBOOL(hAPP_fun_a_bool_bool(X13,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X30),X79))) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X13,X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_finite__induct) ).
fof(fact_752_card__Diff__insert,axiom,
! [X10,X8,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X5))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X10))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X10))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10))),one_one_nat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_752_card__Diff__insert) ).
fof(fact_753_card__Diff__insert,axiom,
! [X10,X8,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X10))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X10))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10))),one_one_nat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_753_card__Diff__insert) ).
fof(fact_751_card__Diff__insert,axiom,
! [X10,X8,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X10))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X10))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10))),one_one_nat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_751_card__Diff__insert) ).
fof(fact_754_card__Diff__insert,axiom,
! [X10,X8,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X10))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X10))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10))),one_one_nat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_754_card__Diff__insert) ).
fof(fact_695_finite__less__ub,axiom,
! [X82,X9] :
( ! [X29] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X29),hAPP_nat_nat(X9,X29)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X9)),X82)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_finite__less__ub) ).
fof(fact_476_imageE,axiom,
! [X31,X9,X5] :
( is_a(X31)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),image_pname_a(X9,X5)))
=> ~ ! [X30] :
( is_pname(X30)
=> ( X31 = hAPP_pname_a(X9,X30)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_imageE) ).
fof(fact_475_imageE,axiom,
! [X31,X9,X5] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X31),image_nat_int(X9,X5)))
=> ~ ! [X30] :
( X31 = hAPP_nat_int(X9,X30)
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_imageE) ).
fof(fact_964_card__less,axiom,
! [X33,X131] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X131))
=> hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X131)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,X33))))) != zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_964_card__less) ).
fof(fact_832_add__leE,axiom,
! [X15,X22,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X22)),X14))
=> ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_832_add__leE) ).
fof(fact_962_nat__diff__split__asm,axiom,
! [X13,X8,X31] :
( hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X8),X31)))
<=> ~ ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8),X31))
& ~ hBOOL(hAPP_nat_bool(X13,zero_zero_nat)) )
| ? [X130] :
( X8 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X31),X130)
& ~ hBOOL(hAPP_nat_bool(X13,X130)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_962_nat__diff__split__asm) ).
fof(fact_876_not__add__less1,axiom,
! [X23,X24] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X24)),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_876_not__add__less1) ).
fof(fact_877_not__add__less2,axiom,
! [X24,X23] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X23)),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_877_not__add__less2) ).
fof(fact_1181_rel__simps_I51_J,axiom,
! [X16,X134] :
( bit1(X16) = bit1(X134)
<=> X16 = X134 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1181_rel__simps_I51_J) ).
fof(fact_459_subset__insert,axiom,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X10)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_subset__insert) ).
fof(fact_458_subset__insert,axiom,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X10)))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_subset__insert) ).
fof(fact_460_subset__insert,axiom,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X10)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_subset__insert) ).
fof(fact_457_subset__insert,axiom,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X10)))
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_subset__insert) ).
fof(fact_737_card__Diff__singleton__if,axiom,
! [X11,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,X5)),one_one_nat) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool))) = hAPP_f957591787ol_nat(finite_card_int,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_737_card__Diff__singleton__if) ).
fof(fact_738_card__Diff__singleton__if,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,X5)),one_one_nat) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool))) = hAPP_f22106695ol_nat(finite_card_nat,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_738_card__Diff__singleton__if) ).
fof(fact_736_card__Diff__singleton__if,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,X5)),one_one_nat) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool))) = hAPP_fun_a_bool_nat(finite_card_a,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_736_card__Diff__singleton__if) ).
fof(fact_739_card__Diff__singleton__if,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,X5)),one_one_nat) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool))) = hAPP_f921600141ol_nat(finite_card_pname,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_739_card__Diff__singleton__if) ).
fof(fact_721_Diff__iff,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X5))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_721_Diff__iff) ).
fof(fact_713_DiffD2,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_713_DiffD2) ).
fof(fact_720_Diff__iff,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10)))
<=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X5))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_720_Diff__iff) ).
fof(fact_712_DiffD2,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10)))
=> ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_712_DiffD2) ).
fof(fact_723_Diff__iff,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10)))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X5))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_723_Diff__iff) ).
fof(fact_715_DiffD2,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10)))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_715_DiffD2) ).
fof(fact_722_Diff__iff,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X5))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_722_Diff__iff) ).
fof(fact_714_DiffD2,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10)))
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_714_DiffD2) ).
fof(fact_1162_succ__def,axiom,
! [X22] : succ(X22) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X22),one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1162_succ__def) ).
fof(fact_969_ex__least__nat__less,axiom,
! [X17,X13] :
( ~ hBOOL(hAPP_nat_bool(X13,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(X13,X17))
=> ? [X119] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X119),X17))
& ! [X126] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X126),X119))
=> ~ hBOOL(hAPP_nat_bool(X13,X126)) )
& hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X119),one_one_nat))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_969_ex__least__nat__less) ).
fof(fact_709_DiffI,axiom,
! [X10,X32,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X10))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_709_DiffI) ).
fof(fact_708_DiffI,axiom,
! [X10,X32,X5] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X5))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X10))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_708_DiffI) ).
fof(fact_711_DiffI,axiom,
! [X10,X32,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X10))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_711_DiffI) ).
fof(fact_710_DiffI,axiom,
! [X10,X32,X5] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_710_DiffI) ).
fof(fact_1087_transfer__nat__int__set__cong,axiom,
! [X148,X13] :
( ! [X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X30))
=> ( hBOOL(hAPP_int_bool(X13,X30))
<=> hBOOL(hAPP_int_bool(X148,X30)) ) )
=> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X13)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X148)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1087_transfer__nat__int__set__cong) ).
fof(fact_169_not__less__eq__eq,axiom,
! [X25,X17] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X17)),X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_not__less__eq__eq) ).
fof(fact_577_insert__Diff__if,axiom,
! [X5,X11,X10] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X10))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)),X10) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X10))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)),X10) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_insert__Diff__if) ).
fof(fact_578_insert__Diff__if,axiom,
! [X5,X11,X10] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)),X10) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)),X10) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_insert__Diff__if) ).
fof(fact_579_insert__Diff__if,axiom,
! [X5,X11,X10] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)),X10) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)),X10) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_insert__Diff__if) ).
fof(fact_576_insert__Diff__if,axiom,
! [X5,X11,X10] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10))
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)),X10) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10))
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)),X10) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_insert__Diff__if) ).
fof(fact_293_insertCI,axiom,
! [X31,X8,X10] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X10))
=> X8 = X31 )
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X31),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_insertCI) ).
fof(fact_292_insertCI,axiom,
! [X31,X8,X10] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X10))
=> X8 = X31 )
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X31),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_insertCI) ).
fof(fact_294_insertCI,axiom,
! [X31,X8,X10] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X10))
=> X8 = X31 )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X31),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_insertCI) ).
fof(fact_291_insertCI,axiom,
! [X31,X8,X10] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X10))
=> X8 = X31 )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X31),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_insertCI) ).
fof(fact_551_Diff__insert__absorb,axiom,
! [X11,X5] :
( is_fun_pname_bool(X5)
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool)) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_Diff__insert__absorb) ).
fof(fact_548_Diff__insert__absorb,axiom,
! [X11,X5] :
( is_fun_a_bool(X5)
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_Diff__insert__absorb) ).
fof(fact_758_folding__one_Oinsert,axiom,
! [X11,X5,X9,X7] :
( is_fun_pname_bool(X5)
=> ( hBOOL(finite1282449217_pname(X9,X7))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( X5 != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(X7,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)) = hAPP_pname_pname(hAPP_p1170154830_pname(X9,X11),hAPP_f1297739591_pname(X7,X5)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_758_folding__one_Oinsert) ).
fof(fact_755_folding__one_Oinsert,axiom,
! [X11,X5,X9,X7] :
( is_fun_a_bool(X5)
=> ( hBOOL(finite_folding_one_a(X9,X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( X5 != bot_bot_fun_a_bool
=> hAPP_fun_a_bool_a(X7,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)) = hAPP_a_a(hAPP_a_fun_a_a(X9,X11),hAPP_fun_a_bool_a(X7,X5)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_755_folding__one_Oinsert) ).
fof(fact_549_Diff__insert__absorb,axiom,
! [X11,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_Diff__insert__absorb) ).
fof(fact_550_Diff__insert__absorb,axiom,
! [X11,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_Diff__insert__absorb) ).
fof(fact_970_ex__least__nat__le,axiom,
! [X17,X13] :
( ~ hBOOL(hAPP_nat_bool(X13,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(X13,X17))
=> ? [X119] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X119),X17))
& ! [X126] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X126),X119))
=> ~ hBOOL(hAPP_nat_bool(X13,X126)) )
& hBOOL(hAPP_nat_bool(X13,X119)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_970_ex__least__nat__le) ).
fof(fact_757_folding__one_Oinsert,axiom,
! [X11,X5,X9,X7] :
( hBOOL(finite988810631ne_nat(X9,X7))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( X5 != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(X7,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X9,X11),hAPP_f22106695ol_nat(X7,X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_757_folding__one_Oinsert) ).
fof(fact_756_folding__one_Oinsert,axiom,
! [X11,X5,X9,X7] :
( hBOOL(finite1626084323ne_int(X9,X7))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> ( X5 != bot_bot_fun_int_bool
=> hAPP_f1594865479ol_int(X7,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)) = hAPP_int_int(hAPP_int_fun_int_int(X9,X11),hAPP_f1594865479ol_int(X7,X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_756_folding__one_Oinsert) ).
fof(fact_865_not__less__eq,axiom,
! [X25,X17] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),hAPP_nat_nat(suc,X25))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_865_not__less__eq) ).
fof(fact_897_finite__M__bounded__by__nat,axiom,
! [X13,X33] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X13),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X33))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_897_finite__M__bounded__by__nat) ).
fof(fact_138_finite__Collect__disjI,axiom,
! [X13,X12] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X13)))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_finite__Collect__disjI) ).
fof(fact_139_finite__Collect__disjI,axiom,
! [X13,X12] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X13)))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_finite__Collect__disjI) ).
fof(fact_630_Collect__conv__if,axiom,
! [X13,X8] :
( ( hBOOL(hAPP_a_bool(X13,X8))
=> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8)),X13)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool) )
& ( ~ hBOOL(hAPP_a_bool(X13,X8))
=> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8)),X13)) = bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_Collect__conv__if) ).
fof(fact_392_insert__ident,axiom,
! [X10,X11,X5] :
( ( is_fun_pname_bool(X10)
& is_fun_pname_bool(X5) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10))
=> ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X10)
<=> X5 = X10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_insert__ident) ).
fof(fact_389_insert__ident,axiom,
! [X10,X11,X5] :
( ( is_fun_a_bool(X10)
& is_fun_a_bool(X5) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10))
=> ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X10)
<=> X5 = X10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_insert__ident) ).
fof(fact_165_le__SucE,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),hAPP_nat_nat(suc,X14)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> X15 = hAPP_nat_nat(suc,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_le__SucE) ).
fof(fact_391_insert__ident,axiom,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10))
=> ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X10)
<=> X5 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_insert__ident) ).
fof(fact_390_insert__ident,axiom,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X10))
=> ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X10)
<=> X5 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_insert__ident) ).
fof(fact_873_less__SucE,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_nat_nat(suc,X14)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> X15 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_873_less__SucE) ).
fof(fact_869_less__antisym,axiom,
! [X14,X15] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X15))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),hAPP_nat_nat(suc,X15)))
=> X15 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_869_less__antisym) ).
fof(fact_868_not__less__less__Suc__eq,axiom,
! [X17,X25] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),X25))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),hAPP_nat_nat(suc,X25)))
<=> X17 = X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_868_not__less__less__Suc__eq) ).
fof(fact_1182_rel__simps_I46_J,axiom,
! [X22] : bit1(X22) != pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1182_rel__simps_I46_J) ).
fof(fact_1183_rel__simps_I39_J,axiom,
! [X26] : pls != bit1(X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1183_rel__simps_I39_J) ).
fof(fact_170_Suc__n__not__le__n,axiom,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X14)),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_Suc__n__not__le__n) ).
fof(fact_101_card__insert__if,axiom,
! [X11,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)) = hAPP_f957591787ol_nat(finite_card_int,X5) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_card__insert__if) ).
fof(fact_100_card__insert__if,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)) = hAPP_f22106695ol_nat(finite_card_nat,X5) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_card__insert__if) ).
fof(fact_98_card__insert__if,axiom,
! [X11,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X11),X5))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X11),X5)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X5) )
& ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X11),X5))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_card__insert__if) ).
fof(fact_97_card__insert__if,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X11),X5))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X11),X5)) = hAPP_f55526627ol_nat(finite1340463720e_bool,X5) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X11),X5))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_card__insert__if) ).
fof(fact_96_card__insert__if,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X11),X5))
=> hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X11),X5)) = hAPP_f696928925ol_nat(finite346522414t_bool,X5) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X11),X5))
=> hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_card__insert__if) ).
fof(fact_95_card__insert__if,axiom,
! [X11,X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5))
=> ( ( hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X11),X5))
=> hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X11),X5)) = hAPP_f521865025ol_nat(finite1876863882t_bool,X5) )
& ( ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X11),X5))
=> hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_card__insert__if) ).
fof(fact_102_card__insert__if,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)) = hAPP_fun_a_bool_nat(finite_card_a,X5) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_card__insert__if) ).
fof(fact_99_card__insert__if,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)) = hAPP_f921600141ol_nat(finite_card_pname,X5) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_card__insert__if) ).
fof(fact_1097_int__less__0__conv,axiom,
! [X22] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X22)),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1097_int__less__0__conv) ).
fof(fact_633_Collect__conv__if2,axiom,
! [X13,X8] :
( ( hBOOL(hAPP_a_bool(X13,X8))
=> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X8)),X13)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool) )
& ( ~ hBOOL(hAPP_a_bool(X13,X8))
=> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X8)),X13)) = bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_Collect__conv__if2) ).
fof(fact_374_insert__Collect,axiom,
! [X8,X13] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),collect_int(X13)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X8))),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_insert__Collect) ).
fof(fact_375_insert__Collect,axiom,
! [X8,X13] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),collect_nat(X13)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X8))),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_insert__Collect) ).
fof(fact_109_card__insert__disjoint,axiom,
! [X11,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_card__insert__disjoint) ).
fof(fact_108_card__insert__disjoint,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_card__insert__disjoint) ).
fof(fact_106_card__insert__disjoint,axiom,
! [X11,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X11),X5))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_card__insert__disjoint) ).
fof(fact_105_card__insert__disjoint,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X11),X5))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_card__insert__disjoint) ).
fof(fact_104_card__insert__disjoint,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X11),X5))
=> hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_card__insert__disjoint) ).
fof(fact_103_card__insert__disjoint,axiom,
! [X11,X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5))
=> ( ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X11),X5))
=> hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_card__insert__disjoint) ).
fof(fact_110_card__insert__disjoint,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_card__insert__disjoint) ).
fof(fact_107_card__insert__disjoint,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_card__insert__disjoint) ).
fof(fact_724_set__diff__eq,axiom,
! [X5,X10] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X5)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X10)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_724_set__diff__eq) ).
fof(fact_725_set__diff__eq,axiom,
! [X5,X10] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X5)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X10)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_725_set__diff__eq) ).
fof(fact_117_finite__Collect__conjI,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X13)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X12))) )
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X13),X12)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_finite__Collect__conjI) ).
fof(fact_118_finite__Collect__conjI,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X13)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X12))) )
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X13),X12)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_finite__Collect__conjI) ).
fof(fact_1095_tsub__def,axiom,
! [X19,X18] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X18))
=> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X18),X19) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X18),X19) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X18))
=> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X18),X19) = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1095_tsub__def) ).
fof(fact_702_nonempty__iff,axiom,
! [X5] :
( is_fun_pname_bool(X5)
=> ( X5 != bot_bo844097828e_bool
<=> ? [X30,X83] :
( is_pname(X30)
& is_fun_pname_bool(X83)
& X5 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X30),X83)
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X83)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_702_nonempty__iff) ).
fof(fact_699_nonempty__iff,axiom,
! [X5] :
( is_fun_a_bool(X5)
=> ( X5 != bot_bot_fun_a_bool
<=> ? [X30,X83] :
( is_a(X30)
& is_fun_a_bool(X83)
& X5 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X30),X83)
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X83)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_nonempty__iff) ).
fof(fact_910_add__diff__inverse,axiom,
! [X15,X14] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14)) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_910_add__diff__inverse) ).
fof(fact_701_nonempty__iff,axiom,
! [X5] :
( X5 != bot_bot_fun_nat_bool
<=> ? [X30,X83] :
( X5 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),X83)
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X83)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_701_nonempty__iff) ).
fof(fact_700_nonempty__iff,axiom,
! [X5] :
( X5 != bot_bot_fun_int_bool
<=> ? [X30,X83] :
( X5 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),X83)
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X83)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_700_nonempty__iff) ).
fof(fact_438_insert__compr__raw,axiom,
! [X30,X68] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),X68) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X30)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X68))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_insert__compr__raw) ).
fof(fact_370_insert__compr,axiom,
! [X8,X10] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X10) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X8)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_insert__compr) ).
fof(fact_439_insert__compr__raw,axiom,
! [X30,X68] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),X68) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X30)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X68))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_insert__compr__raw) ).
fof(fact_371_insert__compr,axiom,
! [X8,X10] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X10) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X8)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_insert__compr) ).
fof(fact_860_linorder__neqE__nat,axiom,
! [X18,X19] :
( X18 != X19
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X18),X19))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X19),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_860_linorder__neqE__nat) ).
fof(fact_1147_not__neg__eq__ge__0,axiom,
! [X11] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X11))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1147_not__neg__eq__ge__0) ).
fof(fact_364_linorder__le__cases,axiom,
! [X65,X66] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X65),X66))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X66),X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_linorder__le__cases) ).
fof(fact_363_linorder__le__cases,axiom,
! [X65,X66] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X65),X66))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X66),X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_linorder__le__cases) ).
fof(fact_534_all__not__in__conv,axiom,
! [X5] :
( is_fun_pname_bool(X5)
=> ( ! [X30] :
( is_pname(X30)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5)) )
<=> X5 = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_all__not__in__conv) ).
fof(fact_533_all__not__in__conv,axiom,
! [X5] :
( is_fun_a_bool(X5)
=> ( ! [X30] :
( is_a(X30)
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5)) )
<=> X5 = bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_all__not__in__conv) ).
fof(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
! [X18,X19] :
( ( is_pname(X18)
& is_pname(X19) )
=> ( ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X18),X19))
| X18 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).
fof(help_fequal_1_1_fequal_000t__a_T,axiom,
! [X18,X19] :
( ( is_a(X18)
& is_a(X19) )
=> ( ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X18),X19))
| X18 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000t__a_T) ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom,
! [X18,X19] :
( ( is_fun_pname_bool(X18)
& is_fun_pname_bool(X19) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X18),X19))
| X18 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
fof(help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,axiom,
! [X18,X19] :
( ( is_fun_a_bool(X18)
& is_fun_a_bool(X19) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X18),X19))
| X18 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
fof(fact_1138_int__if__cong,axiom,
! [X11,X39,X13] :
( ( hBOOL(X13)
=> hAPP_nat_int(semiri1621563631at_int,X11) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X13),X11),X39)) )
& ( ~ hBOOL(X13)
=> hAPP_nat_int(semiri1621563631at_int,X39) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X13),X11),X39)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1138_int__if__cong) ).
fof(help_fimplies_3_1_U,axiom,
! [X159,X160] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X159),X160))
| ~ hBOOL(X159)
| hBOOL(X160) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
fof(help_fdisj_3_1_U,axiom,
! [X159,X160] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X159),X160))
| hBOOL(X159)
| hBOOL(X160) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
fof(help_fconj_2_1_U,axiom,
! [X159,X160] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X159),X160))
| hBOOL(X159) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
fof(help_fconj_3_1_U,axiom,
! [X159,X160] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X159),X160))
| hBOOL(X160) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
fof(fact_532_all__not__in__conv,axiom,
! [X5] :
( ! [X30] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
<=> X5 = bot_bot_fun_nat_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_all__not__in__conv) ).
fof(fact_505_equals0D,axiom,
! [X8,X5] :
( X5 = bot_bot_fun_nat_bool
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_equals0D) ).
fof(fact_531_all__not__in__conv,axiom,
! [X5] :
( ! [X30] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X5))
<=> X5 = bot_bot_fun_int_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_all__not__in__conv) ).
fof(fact_504_equals0D,axiom,
! [X8,X5] :
( X5 = bot_bot_fun_int_bool
=> ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_equals0D) ).
fof(fact_507_equals0D,axiom,
! [X8,X5] :
( X5 = bot_bo844097828e_bool
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_equals0D) ).
fof(fact_506_equals0D,axiom,
! [X8,X5] :
( X5 = bot_bot_fun_a_bool
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_equals0D) ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,axiom,
! [X18,X19] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X18),X19))
| X18 = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T,axiom,
! [X18,X19] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X18),X19))
| X18 = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T) ).
fof(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
! [X18,X19] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X18),X19))
| X18 = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
fof(help_fequal_1_1_fequal_000tc__Int__Oint_T,axiom,
! [X18,X19] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X18),X19))
| X18 = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Int__Oint_T) ).
fof(fact_861_less__irrefl__nat,axiom,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_861_less__irrefl__nat) ).
fof(fact_858_less__not__refl,axiom,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_858_less__not__refl) ).
fof(fact_518_empty__iff,axiom,
! [X32] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),bot_bot_fun_nat_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_empty__iff) ).
fof(fact_491_emptyE,axiom,
! [X8] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),bot_bot_fun_nat_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_emptyE) ).
fof(fact_517_empty__iff,axiom,
! [X32] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),bot_bot_fun_int_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_empty__iff) ).
fof(fact_490_emptyE,axiom,
! [X8] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),bot_bot_fun_int_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_emptyE) ).
fof(fact_520_empty__iff,axiom,
! [X32] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),bot_bo844097828e_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_empty__iff) ).
fof(fact_493_emptyE,axiom,
! [X8] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),bot_bo844097828e_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_emptyE) ).
fof(fact_519_empty__iff,axiom,
! [X32] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),bot_bot_fun_a_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_empty__iff) ).
fof(fact_492_emptyE,axiom,
! [X8] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),bot_bot_fun_a_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_emptyE) ).
fof(fact_939_not__less0,axiom,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),zero_zero_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_939_not__less0) ).
fof(fact_937_less__nat__zero__code,axiom,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),zero_zero_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_937_less__nat__zero__code) ).
fof(fact_921_less__zeroE,axiom,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),zero_zero_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_921_less__zeroE) ).
fof(fact_1151_not__neg__int,axiom,
! [X14] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,X14))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1151_not__neg__int) ).
fof(fact_1117_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
! [X13] : collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X13)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(X13,semiri1621563631at_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1117_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) ).
fof(fact_857_finite__Collect__less__nat,axiom,
! [X16] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X16)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_857_finite__Collect__less__nat) ).
fof(fact_120_finite__Collect__le__nat,axiom,
! [X16] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X16)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_finite__Collect__le__nat) ).
fof(help_fconj_1_1_U,axiom,
! [X160,X159] :
( ~ hBOOL(X159)
| ~ hBOOL(X160)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X159),X160)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
fof(help_fimplies_2_1_U,axiom,
! [X159,X160] :
( ~ hBOOL(X160)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X159),X160)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
fof(help_fdisj_1_1_U,axiom,
! [X160,X159] :
( ~ hBOOL(X159)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X159),X160)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
fof(help_fdisj_2_1_U,axiom,
! [X159,X160] :
( ~ hBOOL(X160)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X159),X160)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
fof(fact_429_equalityE,axiom,
! [X5,X10] :
( X5 = X10
=> ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_equalityE) ).
fof(fact_428_equalityE,axiom,
! [X5,X10] :
( X5 = X10
=> ~ ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
=> ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_equalityE) ).
fof(fact_430_equalityE,axiom,
! [X5,X10] :
( X5 = X10
=> ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_equalityE) ).
fof(fact_510_Collect__empty__eq,axiom,
! [X13] :
( collect_a(X13) = bot_bot_fun_a_bool
<=> ! [X30] :
( is_a(X30)
=> ~ hBOOL(hAPP_a_bool(X13,X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_Collect__empty__eq) ).
fof(fact_523_empty__Collect__eq,axiom,
! [X13] :
( bot_bot_fun_a_bool = collect_a(X13)
<=> ! [X30] :
( is_a(X30)
=> ~ hBOOL(hAPP_a_bool(X13,X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_empty__Collect__eq) ).
fof(fact_121_card__Collect__le__nat,axiom,
! [X17] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X17))) = hAPP_nat_nat(suc,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_card__Collect__le__nat) ).
fof(fact_637_singleton__conv,axiom,
! [X8] : collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X8)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_singleton__conv) ).
fof(fact_638_singleton__conv,axiom,
! [X8] : collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X8)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_singleton__conv) ).
fof(help_fNot_1_1_U,axiom,
! [X159] :
( ~ hBOOL(hAPP_bool_bool(fNot,X159))
| ~ hBOOL(X159) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
fof(fact_640_singleton__conv2,axiom,
! [X8] : collect_int(hAPP_i1948725293t_bool(fequal_int,X8)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_singleton__conv2) ).
fof(fact_641_singleton__conv2,axiom,
! [X8] : collect_nat(hAPP_n1699378549t_bool(fequal_nat,X8)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_singleton__conv2) ).
fof(fact_1153_neg__imp__number__of__eq__0,axiom,
! [X133] :
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> number_number_of_nat(X133) = zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1153_neg__imp__number__of__eq__0) ).
fof(fact_896_card__Collect__less__nat,axiom,
! [X17] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X17))) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_896_card__Collect__less__nat) ).
fof(fact_1168_not__neg__number__of__Pls,axiom,
~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1168_not__neg__number__of__Pls) ).
fof(fact_1160_nat__intermed__int__val,axiom,
! [X16,X9,X17,X25] :
( ! [X126] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X126))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X126),X17)) )
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X9,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X126),one_one_nat))),hAPP_nat_int(X9,X126)))),one_one_int)) )
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X9,X25)),X16))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X16),hAPP_nat_int(X9,X17)))
=> ? [X126] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X126))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X126),X17))
& hAPP_nat_int(X9,X126) = X16 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1160_nat__intermed__int__val) ).
fof(fact_1159_nat0__intermed__int__val,axiom,
! [X16,X9,X17] :
( ! [X126] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X126),X17))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X9,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X126),one_one_nat))),hAPP_nat_int(X9,X126)))),one_one_int)) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X9,zero_zero_nat)),X16))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X16),hAPP_nat_int(X9,X17)))
=> ? [X126] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X126),X17))
& hAPP_nat_int(X9,X126) = X16 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1159_nat0__intermed__int__val) ).
fof(fact_1158_int__val__lemma,axiom,
! [X16,X9,X17] :
( ! [X126] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X126),X17))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X9,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X126),one_one_nat))),hAPP_nat_int(X9,X126)))),one_one_int)) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X9,zero_zero_nat)),X16))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X16),hAPP_nat_int(X9,X17)))
=> ? [X126] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X126),X17))
& hAPP_nat_int(X9,X126) = X16 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1158_int__val__lemma) ).
fof(fact_1144_decr__lemma,axiom,
! [X18,X98,X152] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X152))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X18),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X18),X98))),one_one_int)),X152))),X98)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1144_decr__lemma) ).
fof(fact_1068_nat__less__add__iff1,axiom,
! [X82,X25,X17,X120,X33] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X120),X33))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X33),X82)),X25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X120),X82)),X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X33),X120)),X82)),X25)),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1068_nat__less__add__iff1) ).
fof(fact_1062_nat__le__add__iff1,axiom,
! [X82,X25,X17,X120,X33] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X120),X33))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X33),X82)),X25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X120),X82)),X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X33),X120)),X82)),X25)),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1062_nat__le__add__iff1) ).
fof(fact_1157_incr__lemma,axiom,
! [X98,X18,X152] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X152))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X98),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X18),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X18),X98))),one_one_int)),X152)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1157_incr__lemma) ).
fof(fact_762_folding__one_Oclosed,axiom,
! [X5,X9,X7] :
( is_fun_pname_bool(X5)
=> ( hBOOL(finite1282449217_pname(X9,X7))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( X5 != bot_bo844097828e_bool
=> ( ! [X30,X84] :
( ( is_pname(X30)
& is_pname(X84) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(X9,X30),X84)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X30),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X84),bot_bo844097828e_bool)))) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(X7,X5)),X5)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_762_folding__one_Oclosed) ).
fof(fact_759_folding__one_Oclosed,axiom,
! [X5,X9,X7] :
( is_fun_a_bool(X5)
=> ( hBOOL(finite_folding_one_a(X9,X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( X5 != bot_bot_fun_a_bool
=> ( ! [X30,X84] :
( ( is_a(X30)
& is_a(X84) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_a_a(hAPP_a_fun_a_a(X9,X30),X84)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X30),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X84),bot_bot_fun_a_bool)))) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(X7,X5)),X5)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_759_folding__one_Oclosed) ).
fof(fact_761_folding__one_Oclosed,axiom,
! [X5,X9,X7] :
( hBOOL(finite988810631ne_nat(X9,X7))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( X5 != bot_bot_fun_nat_bool
=> ( ! [X30,X84] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(X9,X30),X84)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X84),bot_bot_fun_nat_bool))))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(X7,X5)),X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_761_folding__one_Oclosed) ).
fof(fact_760_folding__one_Oclosed,axiom,
! [X5,X9,X7] :
( hBOOL(finite1626084323ne_int(X9,X7))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( X5 != bot_bot_fun_int_bool
=> ( ! [X30,X84] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(X9,X30),X84)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X84),bot_bot_fun_int_bool))))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(X7,X5)),X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_760_folding__one_Oclosed) ).
fof(fact_1169_transfer__int__nat__numerals_I4_J,axiom,
number_number_of_int(bit1(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit1(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1169_transfer__int__nat__numerals_I4_J) ).
fof(fact_1094_plusinfinity,axiom,
! [X13,X148,X73] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X73))
=> ( ! [X30,X119] :
( hBOOL(hAPP_int_bool(X148,X30))
<=> hBOOL(hAPP_int_bool(X148,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X30),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X119),X73)))) )
=> ( ? [X150] :
! [X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X150),X30))
=> ( hBOOL(hAPP_int_bool(X13,X30))
<=> hBOOL(hAPP_int_bool(X148,X30)) ) )
=> ( ? [X151] : hBOOL(hAPP_int_bool(X148,X151))
=> ? [X151] : hBOOL(hAPP_int_bool(X13,X151)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1094_plusinfinity) ).
fof(fact_1093_minusinfinity,axiom,
! [X13,X149,X73] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X73))
=> ( ! [X30,X119] :
( hBOOL(hAPP_int_bool(X149,X30))
<=> hBOOL(hAPP_int_bool(X149,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X30),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X119),X73)))) )
=> ( ? [X150] :
! [X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X30),X150))
=> ( hBOOL(hAPP_int_bool(X13,X30))
<=> hBOOL(hAPP_int_bool(X149,X30)) ) )
=> ( ? [X151] : hBOOL(hAPP_int_bool(X149,X151))
=> ? [X151] : hBOOL(hAPP_int_bool(X13,X151)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1093_minusinfinity) ).
fof(fact_1015_nat__less__add__iff2,axiom,
! [X82,X25,X17,X33,X120] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X33),X120))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X33),X82)),X25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X120),X82)),X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X120),X33)),X82)),X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1015_nat__less__add__iff2) ).
fof(fact_1065_nat__le__add__iff2,axiom,
! [X82,X25,X17,X33,X120] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X33),X120))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X33),X82)),X25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X120),X82)),X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X120),X33)),X82)),X17))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1065_nat__le__add__iff2) ).
fof(fact_1188_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1188_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
fof(fact_1063_nat__diff__add__eq1,axiom,
! [X142,X15,X14,X24,X23] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X23))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X23),X142)),X15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X24),X142)),X14)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X23),X24)),X142)),X15)),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1063_nat__diff__add__eq1) ).
fof(fact_1070_unique__quotient__lemma__neg,axiom,
! [X125,X146,X147,X143,X144] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X125),X146)),X147)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X125),X143)),X144)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X144),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X125),X144))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X125),X147))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X143),X146)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1070_unique__quotient__lemma__neg) ).
fof(fact_1077_unique__quotient__lemma,axiom,
! [X125,X146,X147,X143,X144] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X125),X146)),X147)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X125),X143)),X144)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X147))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X147),X125))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X144),X125))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X146),X143)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1077_unique__quotient__lemma) ).
fof(fact_1171_numeral__3__eq__3,axiom,
number_number_of_nat(bit1(bit1(pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1171_numeral__3__eq__3) ).
fof(fact_269_lift__Suc__mono__le,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X9,X29)),hAPP_n1699378549t_bool(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X9,X17)),hAPP_n1699378549t_bool(X9,X28))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_lift__Suc__mono__le) ).
fof(fact_270_lift__Suc__mono__le,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(X9,X29)),hAPP_n1082236369t_bool(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(X9,X17)),hAPP_n1082236369t_bool(X9,X28))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_lift__Suc__mono__le) ).
fof(fact_264_lift__Suc__mono__le,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X9,X29)),hAPP_n1025906991e_bool(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X9,X17)),hAPP_n1025906991e_bool(X9,X28))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_lift__Suc__mono__le) ).
fof(fact_266_lift__Suc__mono__le,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X9,X29)),hAPP_nat_fun_a_bool(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X9,X17)),hAPP_nat_fun_a_bool(X9,X28))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_lift__Suc__mono__le) ).
fof(fact_267_lift__Suc__mono__le,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X9,X29)),hAPP_nat_nat(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X9,X17)),hAPP_nat_nat(X9,X28))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_lift__Suc__mono__le) ).
fof(fact_268_lift__Suc__mono__le,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X9,X29)),hAPP_nat_int(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X9,X17)),hAPP_nat_int(X9,X28))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_lift__Suc__mono__le) ).
fof(fact_265_lift__Suc__mono__le,axiom,
! [X17,X28,X9] :
( ! [X29] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X9,X29)),hAPP_nat_bool(X9,hAPP_nat_nat(suc,X29))))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X28))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X9,X17)),hAPP_nat_bool(X9,X28))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_lift__Suc__mono__le) ).
fof(fact_914_mono__nat__linear__lb,axiom,
! [X25,X16,X9] :
( ! [X35,X29] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X35),X29))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X9,X35)),hAPP_nat_nat(X9,X29))) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(X9,X25)),X16)),hAPP_nat_nat(X9,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X25),X16)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_914_mono__nat__linear__lb) ).
fof(fact_1069_zdiv__mono2__neg__lemma,axiom,
! [X125,X143,X144,X145,X146,X147] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X125),X143)),X144) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X145),X146)),X147)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X145),X146)),X147)),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X144),X125))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X147))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X145))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X145),X125))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X146),X143)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1069_zdiv__mono2__neg__lemma) ).
fof(fact_1092_int__induct,axiom,
! [X33,X13,X16] :
( hBOOL(hAPP_int_bool(X13,X16))
=> ( ! [X126] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X16),X126))
=> ( hBOOL(hAPP_int_bool(X13,X126))
=> hBOOL(hAPP_int_bool(X13,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X126),one_one_int))) ) )
=> ( ! [X126] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X126),X16))
=> ( hBOOL(hAPP_int_bool(X13,X126))
=> hBOOL(hAPP_int_bool(X13,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X126),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X13,X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1092_int__induct) ).
fof(fact_1066_nat__diff__add__eq2,axiom,
! [X142,X15,X14,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X24))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X23),X142)),X15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X24),X142)),X14)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X24),X23)),X142)),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1066_nat__diff__add__eq2) ).
fof(fact_918_less__mono__imp__le__mono,axiom,
! [X33,X120,X9] :
( ! [X126,X127] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X126),X127))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X9,X126)),hAPP_nat_nat(X9,X127))) )
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X33),X120))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X9,X33)),hAPP_nat_nat(X9,X120))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_918_less__mono__imp__le__mono) ).
fof(fact_1076_q__neg__lemma,axiom,
! [X145,X146,X147] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X145),X146)),X147)),zero_zero_int))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X147))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X145))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X146),zero_zero_int)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1076_q__neg__lemma) ).
fof(fact_1091_incr__mult__lemma,axiom,
! [X16,X13,X73] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X73))
=> ( ! [X30] :
( hBOOL(hAPP_int_bool(X13,X30))
=> hBOOL(hAPP_int_bool(X13,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X30),X73))) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X16))
=> ! [X30] :
( hBOOL(hAPP_int_bool(X13,X30))
=> hBOOL(hAPP_int_bool(X13,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X30),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X16),X73)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1091_incr__mult__lemma) ).
fof(fact_1088_decr__mult__lemma,axiom,
! [X16,X13,X73] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X73))
=> ( ! [X30] :
( hBOOL(hAPP_int_bool(X13,X30))
=> hBOOL(hAPP_int_bool(X13,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X30),X73))) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X16))
=> ! [X30] :
( hBOOL(hAPP_int_bool(X13,X30))
=> hBOOL(hAPP_int_bool(X13,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X30),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X16),X73)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1088_decr__mult__lemma) ).
fof(fact_1078_zdiv__mono2__lemma,axiom,
! [X125,X143,X144,X145,X146,X147] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X125),X143)),X144) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X145),X146)),X147)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X145),X146)),X147)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X147),X145))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X144))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X145))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X145),X125))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X143),X146)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1078_zdiv__mono2__lemma) ).
fof(fact_1039_odd__less__0,axiom,
! [X56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X56)),X56)),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X56),zero_zero_int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1039_odd__less__0) ).
fof(fact_682_assms_I2_J,axiom,
! [X80,X4] :
( hBOOL(hAPP_fun_a_bool_bool(p(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X80)),X4)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(the_com(body(X80)))),bot_bot_fun_a_bool)))
=> hBOOL(hAPP_fun_a_bool_bool(p(X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X80)),bot_bot_fun_a_bool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_assms_I2_J) ).
fof(fact_1079_int__less__induct,axiom,
! [X13,X33,X16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X33),X16))
=> ( hBOOL(hAPP_int_bool(X13,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X16),one_one_int)))
=> ( ! [X126] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X126),X16))
=> ( hBOOL(hAPP_int_bool(X13,X126))
=> hBOOL(hAPP_int_bool(X13,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X126),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X13,X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1079_int__less__induct) ).
fof(fact_1081_int__gr__induct,axiom,
! [X13,X16,X33] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X16),X33))
=> ( hBOOL(hAPP_int_bool(X13,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X16),one_one_int)))
=> ( ! [X126] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X16),X126))
=> ( hBOOL(hAPP_int_bool(X13,X126))
=> hBOOL(hAPP_int_bool(X13,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X126),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X13,X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1081_int__gr__induct) ).
fof(fact_651_card__Diff1__le,axiom,
! [X11,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_card__Diff1__le) ).
fof(fact_652_card__Diff1__le,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_card__Diff1__le) ).
fof(fact_650_card__Diff1__le,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_card__Diff1__le) ).
fof(fact_653_card__Diff1__le,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_card__Diff1__le) ).
fof(fact_481_image__subsetI,axiom,
! [X9,X10,X5] :
( ! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X9,X30)),X10)) )
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X9,X5)),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_image__subsetI) ).
fof(fact_482_image__subsetI,axiom,
! [X9,X10,X5] :
( ! [X30] :
( is_pname(X30)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X9,X30)),X10)) ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X9,X5)),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_image__subsetI) ).
fof(fact_1080_int__le__induct,axiom,
! [X13,X33,X16] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X33),X16))
=> ( hBOOL(hAPP_int_bool(X13,X16))
=> ( ! [X126] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X126),X16))
=> ( hBOOL(hAPP_int_bool(X13,X126))
=> hBOOL(hAPP_int_bool(X13,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X126),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X13,X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1080_int__le__induct) ).
fof(fact_1082_int__ge__induct,axiom,
! [X13,X16,X33] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X16),X33))
=> ( hBOOL(hAPP_int_bool(X13,X16))
=> ( ! [X126] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X16),X126))
=> ( hBOOL(hAPP_int_bool(X13,X126))
=> hBOOL(hAPP_int_bool(X13,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X126),one_one_int))) ) )
=> hBOOL(hAPP_int_bool(X13,X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1082_int__ge__induct) ).
fof(fact_685_finite__empty__induct,axiom,
! [X13,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f54304608l_bool(X13,X5))
=> ( ! [X78,X81] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X81))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X78),X81))
=> ( hBOOL(hAPP_f54304608l_bool(X13,X81))
=> hBOOL(hAPP_f54304608l_bool(X13,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X81),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X78),bot_bot_fun_nat_bool)))) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X13,bot_bot_fun_nat_bool)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_finite__empty__induct) ).
fof(fact_684_finite__empty__induct,axiom,
! [X13,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f448129468l_bool(X13,X5))
=> ( ! [X78,X81] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X81))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X78),X81))
=> ( hBOOL(hAPP_f448129468l_bool(X13,X81))
=> hBOOL(hAPP_f448129468l_bool(X13,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X81),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X78),bot_bot_fun_int_bool)))) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X13,bot_bot_fun_int_bool)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_finite__empty__induct) ).
fof(fact_686_finite__empty__induct,axiom,
! [X13,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(X13,X5))
=> ( ! [X78,X81] :
( ( is_pname(X78)
& is_fun_pname_bool(X81) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X81))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X78),X81))
=> ( hBOOL(hAPP_f1664156314l_bool(X13,X81))
=> hBOOL(hAPP_f1664156314l_bool(X13,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X81),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X78),bot_bo844097828e_bool)))) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X13,bot_bo844097828e_bool)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_finite__empty__induct) ).
fof(fact_683_finite__empty__induct,axiom,
! [X13,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(X13,X5))
=> ( ! [X78,X81] :
( ( is_a(X78)
& is_fun_a_bool(X81) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X81))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X78),X81))
=> ( hBOOL(hAPP_fun_a_bool_bool(X13,X81))
=> hBOOL(hAPP_fun_a_bool_bool(X13,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X81),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X78),bot_bot_fun_a_bool)))) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X13,bot_bot_fun_a_bool)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_finite__empty__induct) ).
fof(fact_563_diff__single__insert,axiom,
! [X5,X11,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool))),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_diff__single__insert) ).
fof(fact_562_diff__single__insert,axiom,
! [X5,X11,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool))),X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_diff__single__insert) ).
fof(fact_564_diff__single__insert,axiom,
! [X5,X11,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool))),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_diff__single__insert) ).
fof(fact_561_diff__single__insert,axiom,
! [X5,X11,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool))),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_561_diff__single__insert) ).
fof(fact_1003_Suc__mult__less__cancel1,axiom,
! [X16,X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X16)),X25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X16)),X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1003_Suc__mult__less__cancel1) ).
fof(fact_1006_Suc__mult__le__cancel1,axiom,
! [X16,X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X16)),X25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X16)),X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1006_Suc__mult__le__cancel1) ).
fof(fact_1064_nat__eq__add__iff1,axiom,
! [X82,X25,X17,X120,X33] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X120),X33))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X33),X82)),X25) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X120),X82)),X17)
<=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X33),X120)),X82)),X25) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1064_nat__eq__add__iff1) ).
fof(fact_1067_nat__eq__add__iff2,axiom,
! [X82,X25,X17,X33,X120] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X33),X120))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X33),X82)),X25) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X120),X82)),X17)
<=> X25 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X120),X33)),X82)),X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1067_nat__eq__add__iff2) ).
fof(fact_1075_q__pos__lemma,axiom,
! [X145,X146,X147] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X145),X146)),X147)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X147),X145))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X145))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X146)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1075_q__pos__lemma) ).
fof(fact_487_assms_I3_J,axiom,
! [X4,X32] :
( hBOOL(wt(X32))
=> ( ! [X30] :
( is_pname(X30)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),u))
=> hBOOL(hAPP_fun_a_bool_bool(p(X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X30)),bot_bot_fun_a_bool))) ) )
=> hBOOL(hAPP_fun_a_bool_bool(p(X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X32)),bot_bot_fun_a_bool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_assms_I3_J) ).
fof(fact_658_image__diff__subset,axiom,
! [X9,X5,X10] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(X9,X5)),image_nat_int(X9,X10))),image_nat_int(X9,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_image__diff__subset) ).
fof(fact_659_image__diff__subset,axiom,
! [X9,X5,X10] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(X9,X5)),image_pname_a(X9,X10))),image_pname_a(X9,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_image__diff__subset) ).
fof(fact_1058_left__add__mult__distrib,axiom,
! [X23,X142,X24,X22] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X23),X142)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X24),X142)),X22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X24)),X142)),X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1058_left__add__mult__distrib) ).
fof(fact_674_diff__card__le__card__Diff,axiom,
! [X5,X10] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,X5)),hAPP_f957591787ol_nat(finite_card_int,X10))),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_diff__card__le__card__Diff) ).
fof(fact_675_diff__card__le__card__Diff,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,X5)),hAPP_f22106695ol_nat(finite_card_nat,X10))),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_diff__card__le__card__Diff) ).
fof(fact_676_diff__card__le__card__Diff,axiom,
! [X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,X5)),hAPP_fun_a_bool_nat(finite_card_a,X10))),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_diff__card__le__card__Diff) ).
fof(fact_677_diff__card__le__card__Diff,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,X5)),hAPP_f921600141ol_nat(finite_card_pname,X10))),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_diff__card__le__card__Diff) ).
fof(fact_1127_zmult__zless__mono2__lemma,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X23),X24))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X22))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X22)),X23)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X22)),X24))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1127_zmult__zless__mono2__lemma) ).
fof(fact_1129_zdiff__int__split,axiom,
! [X13,X11,X39] :
( hBOOL(hAPP_int_bool(X13,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X11),X39))))
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X39),X11))
=> hBOOL(hAPP_int_bool(X13,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X11)),hAPP_nat_int(semiri1621563631at_int,X39)))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X11),X39))
=> hBOOL(hAPP_int_bool(X13,zero_zero_int)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1129_zdiff__int__split) ).
fof(conj_6,conjecture,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
fof(fact_912_less__diff__iff,axiom,
! [X17,X16,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X25))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X17))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X25),X16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X17),X16)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_912_less__diff__iff) ).
fof(fact_173_le__diff__iff,axiom,
! [X17,X16,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X25))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X17))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X25),X16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X17),X16)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_le__diff__iff) ).
fof(fact_1060_nat__mult__less__cancel1,axiom,
! [X25,X17,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1060_nat__mult__less__cancel1) ).
fof(fact_1013_mult__le__cancel2,axiom,
! [X25,X16,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X25),X16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X17),X16)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1013_mult__le__cancel2) ).
fof(fact_1061_nat__mult__le__cancel1,axiom,
! [X25,X17,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1061_nat__mult__le__cancel1) ).
fof(fact_1012_mult__le__cancel1,axiom,
! [X16,X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X17)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1012_mult__le__cancel1) ).
fof(fact_484_le__funI,axiom,
! [X9,X69] :
( ! [X30] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X9,X30)),hAPP_nat_bool(X69,X30)))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),X69)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_le__funI) ).
fof(fact_442_le__fun__def,axiom,
! [X9,X69] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),X69))
<=> ! [X30] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X9,X30)),hAPP_nat_bool(X69,X30))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_le__fun__def) ).
fof(fact_483_le__funI,axiom,
! [X9,X69] :
( ! [X30] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X9,X30)),hAPP_int_bool(X69,X30)))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),X69)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_le__funI) ).
fof(fact_441_le__fun__def,axiom,
! [X9,X69] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),X69))
<=> ! [X30] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X9,X30)),hAPP_int_bool(X69,X30))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_le__fun__def) ).
fof(fact_485_le__funI,axiom,
! [X9,X69] :
( ! [X30] :
( is_a(X30)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X9,X30)),hAPP_a_bool(X69,X30))) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),X69)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_le__funI) ).
fof(fact_443_le__fun__def,axiom,
! [X9,X69] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),X69))
<=> ! [X30] :
( is_a(X30)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X9,X30)),hAPP_a_bool(X69,X30))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_le__fun__def) ).
fof(fact_840_le__add__diff,axiom,
! [X15,X22,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X15)),X22))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_840_le__add__diff) ).
fof(fact_843_le__diff__conv2,axiom,
! [X33,X16,X120] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X120))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X33),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X120),X16)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X33),X16)),X120)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_843_le__diff__conv2) ).
fof(fact_656_finite__Diff__insert,axiom,
! [X5,X8,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X10))))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_finite__Diff__insert) ).
fof(fact_655_finite__Diff__insert,axiom,
! [X5,X8,X10] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X10))))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_finite__Diff__insert) ).
fof(fact_657_finite__Diff__insert,axiom,
! [X5,X8,X10] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X10))))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_finite__Diff__insert) ).
fof(fact_654_finite__Diff__insert,axiom,
! [X5,X8,X10] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X10))))
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_finite__Diff__insert) ).
fof(fact_1000_mult__less__cancel2,axiom,
! [X25,X16,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X25),X16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X17),X16)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1000_mult__less__cancel2) ).
fof(fact_1001_mult__less__cancel1,axiom,
! [X16,X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X17)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1001_mult__less__cancel1) ).
fof(fact_878_nat__add__left__cancel__less,axiom,
! [X16,X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X16),X25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X16),X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_878_nat__add__left__cancel__less) ).
fof(fact_814_add__le__imp__le__right,axiom,
! [X109,X110,X111] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X109),X110)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X111),X110)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X109),X111)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_add__le__imp__le__right) ).
fof(fact_804_add__le__cancel__right,axiom,
! [X8,X32,X31] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X8),X32)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X31),X32)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8),X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_804_add__le__cancel__right) ).
fof(fact_825_nat__add__left__cancel__le,axiom,
! [X16,X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X16),X25)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X16),X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_825_nat__add__left__cancel__le) ).
fof(fact_816_add__le__imp__le__left,axiom,
! [X112,X113,X114] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X112),X113)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X112),X114)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X113),X114)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_816_add__le__imp__le__left) ).
fof(fact_806_add__le__cancel__left,axiom,
! [X32,X8,X31] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X32),X8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X32),X31)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8),X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_806_add__le__cancel__left) ).
fof(fact_813_add__le__imp__le__right,axiom,
! [X109,X110,X111] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X109),X110)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X111),X110)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X109),X111)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_813_add__le__imp__le__right) ).
fof(fact_803_add__le__cancel__right,axiom,
! [X8,X32,X31] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X8),X32)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X31),X32)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X8),X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_803_add__le__cancel__right) ).
fof(fact_815_add__le__imp__le__left,axiom,
! [X112,X113,X114] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X112),X113)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X112),X114)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X113),X114)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_815_add__le__imp__le__left) ).
fof(fact_805_add__le__cancel__left,axiom,
! [X32,X8,X31] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X32),X8)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X32),X31)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X8),X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_805_add__le__cancel__left) ).
fof(fact_735_folding__one_Oremove,axiom,
! [X11,X5,X9,X7] :
( is_pname(X11)
=> ( hBOOL(finite1282449217_pname(X9,X7))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool)) = bot_bo844097828e_bool
=> hAPP_f1297739591_pname(X7,X5) = X11 )
& ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool)) != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(X7,X5) = hAPP_pname_pname(hAPP_p1170154830_pname(X9,X11),hAPP_f1297739591_pname(X7,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool)))) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_735_folding__one_Oremove) ).
fof(fact_732_folding__one_Oremove,axiom,
! [X11,X5,X9,X7] :
( is_a(X11)
=> ( hBOOL(finite_folding_one_a(X9,X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool
=> hAPP_fun_a_bool_a(X7,X5) = X11 )
& ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool
=> hAPP_fun_a_bool_a(X7,X5) = hAPP_a_a(hAPP_a_fun_a_a(X9,X11),hAPP_fun_a_bool_a(X7,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)))) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_folding__one_Oremove) ).
fof(fact_733_folding__one_Oremove,axiom,
! [X11,X5,X9,X7] :
( hBOOL(finite1626084323ne_int(X9,X7))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool
=> hAPP_f1594865479ol_int(X7,X5) = X11 )
& ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool
=> hAPP_f1594865479ol_int(X7,X5) = hAPP_int_int(hAPP_int_fun_int_int(X9,X11),hAPP_f1594865479ol_int(X7,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_733_folding__one_Oremove) ).
fof(fact_734_folding__one_Oremove,axiom,
! [X11,X5,X9,X7] :
( hBOOL(finite988810631ne_nat(X9,X7))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(X7,X5) = X11 )
& ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(X7,X5) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X9,X11),hAPP_f22106695ol_nat(X7,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_734_folding__one_Oremove) ).
fof(fact_909_less__diff__conv,axiom,
! [X33,X120,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X33),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X120),X16)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X33),X16)),X120)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_909_less__diff__conv) ).
fof(fact_839_le__diff__conv,axiom,
! [X120,X16,X33] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X120),X16)),X33))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X120),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X33),X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_839_le__diff__conv) ).
fof(fact_1010_one__less__mult,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X14))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X15))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X14))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1010_one__less__mult) ).
fof(fact_1011_one__le__mult__iff,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X25),X17)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X25))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1011_one__le__mult__iff) ).
fof(fact_731_folding__one_Oinsert__remove,axiom,
! [X11,X5,X9,X7] :
( is_pname(X11)
=> ( hBOOL(finite1282449217_pname(X9,X7))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool)) = bot_bo844097828e_bool
=> hAPP_f1297739591_pname(X7,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)) = X11 )
& ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool)) != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(X7,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)) = hAPP_pname_pname(hAPP_p1170154830_pname(X9,X11),hAPP_f1297739591_pname(X7,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool)))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_731_folding__one_Oinsert__remove) ).
fof(fact_728_folding__one_Oinsert__remove,axiom,
! [X11,X5,X9,X7] :
( is_a(X11)
=> ( hBOOL(finite_folding_one_a(X9,X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool
=> hAPP_fun_a_bool_a(X7,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)) = X11 )
& ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool
=> hAPP_fun_a_bool_a(X7,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)) = hAPP_a_a(hAPP_a_fun_a_a(X9,X11),hAPP_fun_a_bool_a(X7,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_folding__one_Oinsert__remove) ).
fof(fact_729_folding__one_Oinsert__remove,axiom,
! [X11,X5,X9,X7] :
( hBOOL(finite1626084323ne_int(X9,X7))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool
=> hAPP_f1594865479ol_int(X7,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)) = X11 )
& ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool
=> hAPP_f1594865479ol_int(X7,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)) = hAPP_int_int(hAPP_int_fun_int_int(X9,X11),hAPP_f1594865479ol_int(X7,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_729_folding__one_Oinsert__remove) ).
fof(fact_730_folding__one_Oinsert__remove,axiom,
! [X11,X5,X9,X7] :
( hBOOL(finite988810631ne_nat(X9,X7))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(X7,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)) = X11 )
& ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(X7,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X9,X11),hAPP_f22106695ol_nat(X7,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_730_folding__one_Oinsert__remove) ).
fof(fact_230_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_pname_bool(X10)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_1921560913_pname(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X27),X5))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X27))
& X10 = image_1921560913_pname(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_finite__subset__image) ).
fof(fact_220_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_a_bool(X10)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_fun_nat_bool_a(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X27),X5))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X27))
& X10 = image_fun_nat_bool_a(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_finite__subset__image) ).
fof(fact_229_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_pname_bool(X10)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_62782965_pname(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X27),X5))
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X27))
& X10 = image_62782965_pname(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_finite__subset__image) ).
fof(fact_219_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_a_bool(X10)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_fun_int_bool_a(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X27),X5))
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X27))
& X10 = image_fun_int_bool_a(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_finite__subset__image) ).
fof(fact_231_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_pname_bool(X10)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_1283814551_pname(X9,X5)))
=> ? [X27] :
( is_fun1661590463l_bool(X27)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X27),X5))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X27))
& X10 = image_1283814551_pname(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_finite__subset__image) ).
fof(fact_221_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_a_bool(X10)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_876012084bool_a(X9,X5)))
=> ? [X27] :
( is_fun1661590463l_bool(X27)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X27),X5))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X27))
& X10 = image_876012084bool_a(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_finite__subset__image) ).
fof(fact_232_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_pname_bool(X10)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_1854862208_pname(X9,X5)))
=> ? [X27] :
( is_fun949378684l_bool(X27)
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X27),X5))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X27))
& X10 = image_1854862208_pname(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_finite__subset__image) ).
fof(fact_222_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_a_bool(X10)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_fun_a_bool_a(X9,X5)))
=> ? [X27] :
( is_fun949378684l_bool(X27)
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X27),X5))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X27))
& X10 = image_fun_a_bool_a(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_finite__subset__image) ).
fof(fact_255_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_pname_bool(X10)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_nat_pname(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X27),X5))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X27))
& X10 = image_nat_pname(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_finite__subset__image) ).
fof(fact_254_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun949378684l_bool(X10)
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X10),image_nat_fun_a_bool(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X27),X5))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X27))
& X10 = image_nat_fun_a_bool(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_finite__subset__image) ).
fof(fact_253_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun1661590463l_bool(X10)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X10),image_1655916159e_bool(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X27),X5))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X27))
& X10 = image_1655916159e_bool(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_finite__subset__image) ).
fof(fact_250_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_a_bool(X10)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_nat_a(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X27),X5))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X27))
& X10 = image_nat_a(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_finite__subset__image) ).
fof(fact_261_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_pname_bool(X10)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_int_pname(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X27),X5))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X27))
& X10 = image_int_pname(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_finite__subset__image) ).
fof(fact_260_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun949378684l_bool(X10)
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X10),image_int_fun_a_bool(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X27),X5))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X27))
& X10 = image_int_fun_a_bool(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_finite__subset__image) ).
fof(fact_259_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun1661590463l_bool(X10)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X10),image_637364955e_bool(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X27),X5))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X27))
& X10 = image_637364955e_bool(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_finite__subset__image) ).
fof(fact_256_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_a_bool(X10)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_int_a(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X27),X5))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X27))
& X10 = image_int_a(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_finite__subset__image) ).
fof(fact_262_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_a_bool(X10)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_pname_a(X9,X5)))
=> ? [X27] :
( is_fun_pname_bool(X27)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X27),X5))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X27))
& X10 = image_pname_a(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_finite__subset__image) ).
fof(fact_249_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_pname_bool(X10)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_pname_pname(X9,X5)))
=> ? [X27] :
( is_fun_pname_bool(X27)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X27),X5))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X27))
& X10 = image_pname_pname(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_finite__subset__image) ).
fof(fact_248_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun949378684l_bool(X10)
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X10),image_112932426a_bool(X9,X5)))
=> ? [X27] :
( is_fun_pname_bool(X27)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X27),X5))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X27))
& X10 = image_112932426a_bool(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_finite__subset__image) ).
fof(fact_247_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun1661590463l_bool(X10)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X10),image_47868345e_bool(X9,X5)))
=> ? [X27] :
( is_fun_pname_bool(X27)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X27),X5))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X27))
& X10 = image_47868345e_bool(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_finite__subset__image) ).
fof(fact_228_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_pname_bool(X10)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_a_pname(X9,X5)))
=> ? [X27] :
( is_fun_a_bool(X27)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X27),X5))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X27))
& X10 = image_a_pname(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_finite__subset__image) ).
fof(fact_227_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun949378684l_bool(X10)
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X10),image_a_fun_a_bool(X9,X5)))
=> ? [X27] :
( is_fun_a_bool(X27)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X27),X5))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X27))
& X10 = image_a_fun_a_bool(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_finite__subset__image) ).
fof(fact_226_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun1661590463l_bool(X10)
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X10),image_819518260e_bool(X9,X5)))
=> ? [X27] :
( is_fun_a_bool(X27)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X27),X5))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X27))
& X10 = image_819518260e_bool(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_finite__subset__image) ).
fof(fact_223_finite__subset__image,axiom,
! [X9,X5,X10] :
( is_fun_a_bool(X10)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_a_a(X9,X5)))
=> ? [X27] :
( is_fun_a_bool(X27)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X27),X5))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X27))
& X10 = image_a_a(X9,X27) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_finite__subset__image) ).
fof(fact_241_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),image_1133522419ol_int(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X27),X5))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X27))
& X10 = image_1133522419ol_int(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_finite__subset__image) ).
fof(fact_235_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),image_496248727ol_nat(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X27),X5))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X27))
& X10 = image_496248727ol_nat(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_finite__subset__image) ).
fof(fact_240_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),image_2069007511ol_int(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X27),X5))
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X27))
& X10 = image_2069007511ol_int(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_finite__subset__image) ).
fof(fact_234_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),image_1431733819ol_nat(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X27),X5))
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X27))
& X10 = image_1431733819ol_nat(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_finite__subset__image) ).
fof(fact_242_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),image_41399353ol_int(X9,X5)))
=> ? [X27] :
( is_fun1661590463l_bool(X27)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X27),X5))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X27))
& X10 = image_41399353ol_int(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_finite__subset__image) ).
fof(fact_236_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),image_1551609309ol_nat(X9,X5)))
=> ? [X27] :
( is_fun1661590463l_bool(X27)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X27),X5))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X27))
& X10 = image_1551609309ol_nat(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_finite__subset__image) ).
fof(fact_243_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),image_fun_a_bool_int(X9,X5)))
=> ? [X27] :
( is_fun949378684l_bool(X27)
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X27),X5))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X27))
& X10 = image_fun_a_bool_int(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_finite__subset__image) ).
fof(fact_237_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),image_fun_a_bool_nat(X9,X5)))
=> ? [X27] :
( is_fun949378684l_bool(X27)
& hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X27),X5))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X27))
& X10 = image_fun_a_bool_nat(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_finite__subset__image) ).
fof(fact_263_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),image_nat_int(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X27),X5))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X27))
& X10 = image_nat_int(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_finite__subset__image) ).
fof(fact_252_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X10),image_26036933t_bool(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X27),X5))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X27))
& X10 = image_26036933t_bool(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_finite__subset__image) ).
fof(fact_251_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X10))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X10),image_1556378401t_bool(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X27),X5))
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X27))
& X10 = image_1556378401t_bool(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_finite__subset__image) ).
fof(fact_258_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X10),image_892525857t_bool(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X27),X5))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X27))
& X10 = image_892525857t_bool(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_finite__subset__image) ).
fof(fact_257_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X10))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X10),image_275383677t_bool(X9,X5)))
=> ? [X27] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X27),X5))
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X27))
& X10 = image_275383677t_bool(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_finite__subset__image) ).
fof(fact_246_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X10),image_2129980159t_bool(X9,X5)))
=> ? [X27] :
( is_fun_pname_bool(X27)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X27),X5))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X27))
& X10 = image_2129980159t_bool(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_finite__subset__image) ).
fof(fact_245_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X10))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X10),image_1512837979t_bool(X9,X5)))
=> ? [X27] :
( is_fun_pname_bool(X27)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X27),X5))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X27))
& X10 = image_1512837979t_bool(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_finite__subset__image) ).
fof(fact_244_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),image_pname_int(X9,X5)))
=> ? [X27] :
( is_fun_pname_bool(X27)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X27),X5))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X27))
& X10 = image_pname_int(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_finite__subset__image) ).
fof(fact_238_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),image_pname_nat(X9,X5)))
=> ? [X27] :
( is_fun_pname_bool(X27)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X27),X5))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X27))
& X10 = image_pname_nat(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_finite__subset__image) ).
fof(fact_239_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),image_a_int(X9,X5)))
=> ? [X27] :
( is_fun_a_bool(X27)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X27),X5))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X27))
& X10 = image_a_int(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_finite__subset__image) ).
fof(fact_233_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),image_a_nat(X9,X5)))
=> ? [X27] :
( is_fun_a_bool(X27)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X27),X5))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X27))
& X10 = image_a_nat(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_finite__subset__image) ).
fof(fact_225_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X10),image_a_fun_nat_bool(X9,X5)))
=> ? [X27] :
( is_fun_a_bool(X27)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X27),X5))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X27))
& X10 = image_a_fun_nat_bool(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_finite__subset__image) ).
fof(fact_224_finite__subset__image,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X10))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X10),image_a_fun_int_bool(X9,X5)))
=> ? [X27] :
( is_fun_a_bool(X27)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X27),X5))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X27))
& X10 = image_a_fun_int_bool(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_finite__subset__image) ).
fof(fact_584_Diff__mono,axiom,
! [X70,X10,X5,X67] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X67))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X70),X10))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X67),X70))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_Diff__mono) ).
fof(fact_583_Diff__mono,axiom,
! [X70,X10,X5,X67] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X67))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X70),X10))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10)),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X67),X70))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_Diff__mono) ).
fof(fact_585_Diff__mono,axiom,
! [X70,X10,X5,X67] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X67))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X70),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10)),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X67),X70))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_Diff__mono) ).
fof(fact_882_add__less__mono,axiom,
! [X22,X26,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X24))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X26))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X26))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_882_add__less__mono) ).
fof(fact_911_diff__less__mono,axiom,
! [X123,X124,X125] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X124),X125))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X123),X124))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X124),X123)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X125),X123))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_911_diff__less__mono) ).
fof(fact_894_diff__less__mono2,axiom,
! [X26,X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X26))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X26),X14)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X26),X15))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_894_diff__less__mono2) ).
fof(fact_986_mult__le__mono,axiom,
! [X22,X26,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X24))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X26))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X23),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X24),X26))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_986_mult__le__mono) ).
fof(fact_829_add__le__mono,axiom,
! [X22,X26,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X24))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X26))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X26))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_829_add__le__mono) ).
fof(fact_812_add__mono,axiom,
! [X105,X106,X107,X108] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X107),X108))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X105),X106))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X107),X105)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X108),X106))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_812_add__mono) ).
fof(fact_1052_zadd__zless__mono,axiom,
! [X140,X98,X141,X135] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X141),X135))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X140),X98))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X141),X140)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X135),X98))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1052_zadd__zless__mono) ).
fof(fact_811_add__mono,axiom,
! [X105,X106,X107,X108] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X107),X108))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X105),X106))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X107),X105)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X108),X106))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_811_add__mono) ).
fof(fact_999_mult__less__mono1,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X24))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X22))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X23),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X24),X22))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_999_mult__less__mono1) ).
fof(fact_998_mult__less__mono2,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X24))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X22))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X23)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X24))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_998_mult__less__mono2) ).
fof(fact_1030_zmult__zless__mono2,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X23),X24))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X22))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X22),X23)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X22),X24))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1030_zmult__zless__mono2) ).
fof(fact_299_zero__induct__lemma,axiom,
! [X33,X13,X16] :
( hBOOL(hAPP_nat_bool(X13,X16))
=> ( ! [X29] :
( hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(suc,X29)))
=> hBOOL(hAPP_nat_bool(X13,X29)) )
=> hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X16),X33))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_zero__induct__lemma) ).
fof(fact_472_subset__image__iff,axiom,
! [X10,X9,X5] :
( is_fun_a_bool(X10)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_pname_a(X9,X5)))
<=> ? [X71] :
( is_fun_pname_bool(X71)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X71),X5))
& X10 = image_pname_a(X9,X71) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_subset__image__iff) ).
fof(fact_432_image__iff,axiom,
! [X56,X9,X5] :
( is_a(X56)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X56),image_pname_a(X9,X5)))
<=> ? [X30] :
( is_pname(X30)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
& X56 = hAPP_pname_a(X9,X30) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_image__iff) ).
fof(fact_1009_n__less__n__mult__m,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X14))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X15))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X15))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1009_n__less__n__mult__m) ).
fof(fact_1008_n__less__m__mult__n,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X14))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X15))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X14))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1008_n__less__m__mult__n) ).
fof(fact_431_image__iff,axiom,
! [X56,X9,X5] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X56),image_nat_int(X9,X5)))
<=> ? [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
& X56 = hAPP_nat_int(X9,X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_image__iff) ).
fof(fact_471_subset__image__iff,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),image_nat_int(X9,X5)))
<=> ? [X71] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X71),X5))
& X10 = image_nat_int(X9,X71) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_subset__image__iff) ).
fof(fact_915_inc__induct,axiom,
! [X13,X33,X120] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X33),X120))
=> ( hBOOL(hAPP_nat_bool(X13,X120))
=> ( ! [X126] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X126),X120))
=> ( hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(suc,X126)))
=> hBOOL(hAPP_nat_bool(X13,X126)) ) )
=> hBOOL(hAPP_nat_bool(X13,X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_915_inc__induct) ).
fof(fact_960_diff__Suc__less,axiom,
! [X23,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),hAPP_nat_nat(suc,X23))),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_960_diff__Suc__less) ).
fof(fact_764_card_Oremove,axiom,
! [X11,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_f957591787ol_nat(finite_card_int,X5) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_764_card_Oremove) ).
fof(fact_765_card_Oremove,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,X5) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_765_card_Oremove) ).
fof(fact_763_card_Oremove,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,X5) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_763_card_Oremove) ).
fof(fact_766_card_Oremove,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,X5) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_766_card_Oremove) ).
fof(fact_455_insert__subset,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)),X10))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_insert__subset) ).
fof(fact_454_insert__subset,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)),X10))
<=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X10))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_insert__subset) ).
fof(fact_456_insert__subset,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)),X10))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_insert__subset) ).
fof(fact_453_insert__subset,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)),X10))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_insert__subset) ).
fof(fact_884_add__lessD1,axiom,
! [X23,X24,X22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X24)),X22))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_884_add__lessD1) ).
fof(fact_831_add__leD1,axiom,
! [X15,X22,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X22)),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_831_add__leD1) ).
fof(fact_830_add__leD2,axiom,
! [X15,X22,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X22)),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_830_add__leD2) ).
fof(fact_852_diff__Suc__diff__eq2,axiom,
! [X15,X22,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X24),X22))),X15) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X24)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_852_diff__Suc__diff__eq2) ).
fof(fact_1037_less__bin__lemma,axiom,
! [X16,X134] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X16),X134))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X16),X134)),zero_zero_int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1037_less__bin__lemma) ).
fof(fact_961_nat__diff__split,axiom,
! [X13,X8,X31] :
( hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X8),X31)))
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8),X31))
=> hBOOL(hAPP_nat_bool(X13,zero_zero_nat)) )
& ! [X130] :
( X8 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X31),X130)
=> hBOOL(hAPP_nat_bool(X13,X130)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_961_nat__diff__split) ).
fof(fact_643_card__Suc__Diff1,axiom,
! [X11,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)))) = hAPP_f957591787ol_nat(finite_card_int,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_card__Suc__Diff1) ).
fof(fact_644_card__Suc__Diff1,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)))) = hAPP_f22106695ol_nat(finite_card_nat,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_card__Suc__Diff1) ).
fof(fact_642_card__Suc__Diff1,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)))) = hAPP_fun_a_bool_nat(finite_card_a,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_card__Suc__Diff1) ).
fof(fact_645_card__Suc__Diff1,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool)))) = hAPP_f921600141ol_nat(finite_card_pname,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_card__Suc__Diff1) ).
fof(fact_1054_add1__zle__eq,axiom,
! [X139,X56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X139),one_one_int)),X56))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X139),X56)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1054_add1__zle__eq) ).
fof(fact_466_insert__mono,axiom,
! [X8,X67,X70] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X67),X70))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X67)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X70))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_insert__mono) ).
fof(fact_465_insert__mono,axiom,
! [X8,X67,X70] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X67),X70))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X67)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X70))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_insert__mono) ).
fof(fact_464_insert__mono,axiom,
! [X8,X67,X70] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X67),X70))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X67)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X70))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_insert__mono) ).
fof(fact_881_add__less__mono1,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X24))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X22))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_881_add__less__mono1) ).
fof(fact_988_mult__le__mono1,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X24))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X23),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X24),X22))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_988_mult__le__mono1) ).
fof(fact_987_mult__le__mono2,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X24))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X23)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_987_mult__le__mono2) ).
fof(fact_828_add__le__mono1,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X24))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X22))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_828_add__le__mono1) ).
fof(fact_808_add__right__mono,axiom,
! [X99,X100,X101] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X100),X101))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X100),X99)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X101),X99))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_808_add__right__mono) ).
fof(fact_810_add__left__mono,axiom,
! [X102,X103,X104] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X103),X104))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X102),X103)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X102),X104))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_810_add__left__mono) ).
fof(fact_177_diff__le__mono,axiom,
! [X26,X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X26)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X26))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_diff__le__mono) ).
fof(fact_178_diff__le__mono2,axiom,
! [X26,X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X26),X14)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X26),X15))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_diff__le__mono2) ).
fof(fact_1051_zadd__strict__right__mono,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X23),X24))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X23),X22)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X24),X22))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1051_zadd__strict__right__mono) ).
fof(fact_807_add__right__mono,axiom,
! [X99,X100,X101] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X100),X101))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X100),X99)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X101),X99))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_807_add__right__mono) ).
fof(fact_1040_zadd__left__mono,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X23),X24))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X22),X23)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X22),X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1040_zadd__left__mono) ).
fof(fact_809_add__left__mono,axiom,
! [X102,X103,X104] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X103),X104))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X102),X103)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X102),X104))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_809_add__left__mono) ).
fof(fact_1104_zadd__int__left,axiom,
! [X15,X14,X98] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X15)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X14)),X98)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X14))),X98),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1104_zadd__int__left) ).
fof(fact_768_card_Oinsert__remove,axiom,
! [X11,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_768_card_Oinsert__remove) ).
fof(fact_769_card_Oinsert__remove,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_769_card_Oinsert__remove) ).
fof(fact_767_card_Oinsert__remove,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_767_card_Oinsert__remove) ).
fof(fact_770_card_Oinsert__remove,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_770_card_Oinsert__remove) ).
fof(fact_953_diff__less,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X14))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X15))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14)),X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_953_diff__less) ).
fof(fact_647_card__insert,axiom,
! [X11,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_card__insert) ).
fof(fact_648_card__insert,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_card__insert) ).
fof(fact_646_card__insert,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_card__insert) ).
fof(fact_649_card__insert,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_card__insert) ).
fof(fact_171_Suc__diff__diff,axiom,
! [X15,X14,X22] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X15)),X14)),hAPP_nat_nat(suc,X22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14)),X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Suc__diff__diff) ).
fof(fact_557_Diff__insert2,axiom,
! [X5,X8,X10] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X10)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool))),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_Diff__insert2) ).
fof(fact_556_Diff__insert2,axiom,
! [X5,X8,X10] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X10)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool))),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_Diff__insert2) ).
fof(fact_555_Diff__insert2,axiom,
! [X5,X8,X10] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X10)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool))),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_Diff__insert2) ).
fof(fact_134_finite__Collect__disjI,axiom,
! [X13,X12] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X13)))
& hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_finite__Collect__disjI) ).
fof(fact_133_finite__Collect__disjI,axiom,
! [X13,X12] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X13)))
& hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_finite__Collect__disjI) ).
fof(fact_135_finite__Collect__disjI,axiom,
! [X13,X12] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X13)))
& hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_finite__Collect__disjI) ).
fof(fact_136_finite__Collect__disjI,axiom,
! [X13,X12] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X13)))
& hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_finite__Collect__disjI) ).
fof(fact_137_finite__Collect__disjI,axiom,
! [X13,X12] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X13)))
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_finite__Collect__disjI) ).
fof(fact_132_finite__Collect__disjI,axiom,
! [X13,X12] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X13),X12))))
<=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X13)))
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X12))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_finite__Collect__disjI) ).
fof(fact_93_card__insert__le,axiom,
! [X11,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X5)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_card__insert__le) ).
fof(fact_92_card__insert__le,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X5)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_card__insert__le) ).
fof(fact_90_card__insert__le,axiom,
! [X11,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X11),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_card__insert__le) ).
fof(fact_89_card__insert__le,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X11),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_card__insert__le) ).
fof(fact_88_card__insert__le,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X5)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X11),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_card__insert__le) ).
fof(fact_87_card__insert__le,axiom,
! [X11,X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X5)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X11),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_card__insert__le) ).
fof(fact_94_card__insert__le,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X5)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_card__insert__le) ).
fof(fact_91_card__insert__le,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X5)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_card__insert__le) ).
fof(fact_174_Nat_Odiff__diff__eq,axiom,
! [X14,X22,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X15))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_Nat_Odiff__diff__eq) ).
fof(fact_851_diff__Suc__diff__eq1,axiom,
! [X15,X22,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X24),X22))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X22)),hAPP_nat_nat(suc,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_851_diff__Suc__diff__eq1) ).
fof(fact_81_card__seteq,axiom,
! [X5,X10] :
( ( is_fun1661590463l_bool(X5)
& is_fun1661590463l_bool(X10) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X10)),hAPP_f55526627ol_nat(finite1340463720e_bool,X5)))
=> X5 = X10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_card__seteq) ).
fof(fact_82_card__seteq,axiom,
! [X5,X10] :
( ( is_fun949378684l_bool(X5)
& is_fun949378684l_bool(X10) )
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X10)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)))
=> X5 = X10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_card__seteq) ).
fof(fact_83_card__seteq,axiom,
! [X5,X10] :
( ( is_fun_pname_bool(X5)
& is_fun_pname_bool(X10) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X10)),hAPP_f921600141ol_nat(finite_card_pname,X5)))
=> X5 = X10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_card__seteq) ).
fof(fact_84_card__seteq,axiom,
! [X5,X10] :
( ( is_fun_a_bool(X5)
& is_fun_a_bool(X10) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X10)),hAPP_fun_a_bool_nat(finite_card_a,X5)))
=> X5 = X10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_card__seteq) ).
fof(fact_989_le__cube,axiom,
! [X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X15)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_989_le__cube) ).
fof(fact_80_card__seteq,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X10)),hAPP_f696928925ol_nat(finite346522414t_bool,X5)))
=> X5 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_card__seteq) ).
fof(fact_79_card__seteq,axiom,
! [X5,X10] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X10))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X10)),hAPP_f521865025ol_nat(finite1876863882t_bool,X5)))
=> X5 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_card__seteq) ).
fof(fact_85_card__seteq,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X10)),hAPP_f22106695ol_nat(finite_card_nat,X5)))
=> X5 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_card__seteq) ).
fof(fact_86_card__seteq,axiom,
! [X5,X10] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X10)),hAPP_f957591787ol_nat(finite_card_int,X5)))
=> X5 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_card__seteq) ).
fof(fact_893_less__imp__diff__less,axiom,
! [X14,X24,X22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X22))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X24),X14)),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_893_less__imp__diff__less) ).
fof(fact_848_diff__add__assoc2,axiom,
! [X23,X22,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X23)),X22) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X24),X22)),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_848_diff__add__assoc2) ).
fof(fact_847_add__diff__assoc2,axiom,
! [X23,X22,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X24),X22)),X23) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X23)),X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_847_add__diff__assoc2) ).
fof(fact_951_add__gr__0,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X25),X17)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X25))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_951_add__gr__0) ).
fof(fact_1073_self__quotient__aux1,axiom,
! [X144,X143,X124] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X124))
=> ( X124 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X144),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X124),X143))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X144),X124))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X143)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1073_self__quotient__aux1) ).
fof(fact_1055_zless__imp__add1__zle,axiom,
! [X135,X98] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X135),X98))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X135),one_one_int)),X98)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1055_zless__imp__add1__zle) ).
fof(fact_373_insert__Collect,axiom,
! [X8,X13] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),collect_a(X13)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8))),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_insert__Collect) ).
fof(fact_1074_self__quotient__aux2,axiom,
! [X144,X143,X124] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X124))
=> ( X124 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X144),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X124),X143))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X144))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X143),one_one_int)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1074_self__quotient__aux2) ).
fof(fact_741_card__Diff__singleton,axiom,
! [X11,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,X5)),one_one_nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_741_card__Diff__singleton) ).
fof(fact_742_card__Diff__singleton,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,X5)),one_one_nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_card__Diff__singleton) ).
fof(fact_740_card__Diff__singleton,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,X5)),one_one_nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_740_card__Diff__singleton) ).
fof(fact_743_card__Diff__singleton,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,X5)),one_one_nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_743_card__Diff__singleton) ).
fof(fact_705_DiffE,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)))
=> ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_705_DiffE) ).
fof(fact_704_DiffE,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10)))
=> ~ ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X5))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_704_DiffE) ).
fof(fact_707_DiffE,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10)))
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_707_DiffE) ).
fof(fact_706_DiffE,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10)))
=> ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_706_DiffE) ).
fof(fact_60_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_card__image__le) ).
fof(fact_70_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_card__image__le) ).
fof(fact_65_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(X9,X5))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_card__image__le) ).
fof(fact_64_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(X9,X5))),hAPP_f55526627ol_nat(finite1340463720e_bool,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_card__image__le) ).
fof(fact_63_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(X9,X5))),hAPP_f696928925ol_nat(finite346522414t_bool,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_card__image__le) ).
fof(fact_62_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(X9,X5))),hAPP_f521865025ol_nat(finite1876863882t_bool,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_card__image__le) ).
fof(fact_61_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(X9,X5))),hAPP_fun_a_bool_nat(finite_card_a,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_card__image__le) ).
fof(fact_54_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_card__image__le) ).
fof(fact_59_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X9,X5))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_card__image__le) ).
fof(fact_58_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X9,X5))),hAPP_f55526627ol_nat(finite1340463720e_bool,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_card__image__le) ).
fof(fact_57_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X9,X5))),hAPP_f696928925ol_nat(finite346522414t_bool,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_card__image__le) ).
fof(fact_56_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(X9,X5))),hAPP_f521865025ol_nat(finite1876863882t_bool,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_card__image__le) ).
fof(fact_55_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X9,X5))),hAPP_fun_a_bool_nat(finite_card_a,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_card__image__le) ).
fof(fact_51_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X9,X5))),hAPP_f696928925ol_nat(finite346522414t_bool,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_card__image__le) ).
fof(fact_50_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(X9,X5))),hAPP_f521865025ol_nat(finite1876863882t_bool,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_card__image__le) ).
fof(fact_52_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X9,X5))),hAPP_f55526627ol_nat(finite1340463720e_bool,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_card__image__le) ).
fof(fact_53_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X9,X5))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_card__image__le) ).
fof(fact_69_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_card__image__le) ).
fof(fact_49_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X9,X5))),hAPP_fun_a_bool_nat(finite_card_a,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_card__image__le) ).
fof(fact_67_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_card__image__le) ).
fof(fact_68_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(X9,X5))),hAPP_f957591787ol_nat(finite_card_int,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_card__image__le) ).
fof(fact_48_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_card__image__le) ).
fof(fact_66_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X9,X5))),hAPP_fun_a_bool_nat(finite_card_a,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_card__image__le) ).
fof(fact_387_insert__iff,axiom,
! [X8,X31,X5] :
( ( is_pname(X8)
& is_pname(X31) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X31),X5)))
<=> ( X8 = X31
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_insert__iff) ).
fof(fact_298_insertE,axiom,
! [X8,X31,X5] :
( ( is_pname(X8)
& is_pname(X31) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X31),X5)))
=> ( X8 != X31
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_insertE) ).
fof(fact_384_insert__iff,axiom,
! [X8,X31,X5] :
( ( is_a(X8)
& is_a(X31) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X31),X5)))
<=> ( X8 = X31
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_insert__iff) ).
fof(fact_295_insertE,axiom,
! [X8,X31,X5] :
( ( is_a(X8)
& is_a(X31) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X31),X5)))
=> ( X8 != X31
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_insertE) ).
fof(fact_1002_nat__0__less__mult__iff,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X25),X17)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X25))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1002_nat__0__less__mult__iff) ).
fof(fact_1128_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [X19,X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X18))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X19))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X18),X19))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1128_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(fact_1083_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X19,X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X18))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X19))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X18),X19))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1083_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_1085_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [X19,X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X18))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X19))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X18),X19))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1085_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_1029_zadd__zmult__distrib,axiom,
! [X136,X137,X135] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X136),X137)),X135) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X136),X135)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X137),X135)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1029_zadd__zmult__distrib) ).
fof(fact_1025_zdiff__zmult__distrib,axiom,
! [X136,X137,X135] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X136),X137)),X135) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X136),X135)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X137),X135)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1025_zdiff__zmult__distrib) ).
fof(fact_984_add__mult__distrib,axiom,
! [X15,X14,X22] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X14)),X22) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_984_add__mult__distrib) ).
fof(fact_991_diff__mult__distrib,axiom,
! [X15,X14,X22] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14)),X22) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_991_diff__mult__distrib) ).
fof(fact_489_less__eq__nat_Osimps_I2_J,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X25)),X17))
<=> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X25)),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_less__eq__nat_Osimps_I2_J) ).
fof(fact_386_insert__iff,axiom,
! [X8,X31,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X31),X5)))
<=> ( X8 = X31
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_insert__iff) ).
fof(fact_297_insertE,axiom,
! [X8,X31,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X31),X5)))
=> ( X8 != X31
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_insertE) ).
fof(fact_385_insert__iff,axiom,
! [X8,X31,X5] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X31),X5)))
<=> ( X8 = X31
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_insert__iff) ).
fof(fact_296_insertE,axiom,
! [X8,X31,X5] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X31),X5)))
=> ( X8 != X31
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_insertE) ).
fof(fact_1014_mult__eq__if,axiom,
! [X14,X15] :
( ( X15 = zero_zero_nat
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X14) = zero_zero_nat )
& ( X15 != zero_zero_nat
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X14) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),one_one_nat)),X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1014_mult__eq__if) ).
fof(fact_717_DiffD1,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_717_DiffD1) ).
fof(fact_716_DiffD1,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10)))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_716_DiffD1) ).
fof(fact_719_DiffD1,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10)))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_719_DiffD1) ).
fof(fact_718_DiffD1,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10)))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_718_DiffD1) ).
fof(fact_727_set__diff__eq,axiom,
! [X5,X10] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X5)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X10)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_727_set__diff__eq) ).
fof(fact_726_set__diff__eq,axiom,
! [X5,X10] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X10)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_726_set__diff__eq) ).
fof(fact_1056_zless__add1__eq,axiom,
! [X139,X56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X139),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X56),one_one_int)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X139),X56))
| X139 = X56 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1056_zless__add1__eq) ).
fof(fact_1137_transfer__nat__int__set__relations_I2_J,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X11)),image_nat_int(semiri1621563631at_int,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1137_transfer__nat__int__set__relations_I2_J) ).
fof(fact_1133_transfer__nat__int__set__relations_I4_J,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X5),X10))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X5)),image_nat_int(semiri1621563631at_int,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1133_transfer__nat__int__set__relations_I4_J) ).
fof(fact_1134_transfer__nat__int__set__relations_I5_J,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X5)),image_nat_int(semiri1621563631at_int,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1134_transfer__nat__int__set__relations_I5_J) ).
fof(fact_875_Suc__less__SucD,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X15)),hAPP_nat_nat(suc,X14)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_875_Suc__less__SucD) ).
fof(fact_867_Suc__less__eq,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X25)),hAPP_nat_nat(suc,X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_867_Suc__less__eq) ).
fof(fact_1109_transfer__int__nat__relations_I2_J,axiom,
! [X11,X39] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X11)),hAPP_nat_int(semiri1621563631at_int,X39)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X11),X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1109_transfer__int__nat__relations_I2_J) ).
fof(fact_1101_zless__int,axiom,
! [X25,X17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X25)),hAPP_nat_int(semiri1621563631at_int,X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1101_zless__int) ).
fof(fact_167_Suc__le__mono,axiom,
! [X17,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X17)),hAPP_nat_nat(suc,X25)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_Suc__le__mono) ).
fof(fact_1110_transfer__int__nat__relations_I3_J,axiom,
! [X11,X39] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X11)),hAPP_nat_int(semiri1621563631at_int,X39)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1110_transfer__int__nat__relations_I3_J) ).
fof(fact_1102_zle__int,axiom,
! [X25,X17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X25)),hAPP_nat_int(semiri1621563631at_int,X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1102_zle__int) ).
fof(fact_952_zero__less__diff,axiom,
! [X17,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X17),X25)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_952_zero__less__diff) ).
fof(fact_1048_zle__diff1__eq,axiom,
! [X139,X56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X139),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X56),one_one_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X139),X56)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1048_zle__diff1__eq) ).
fof(fact_1053_zle__add1__eq__le,axiom,
! [X139,X56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X139),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X56),one_one_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X139),X56)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1053_zle__add1__eq__le) ).
fof(fact_846_diff__add__assoc,axiom,
! [X23,X22,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X24)),X22) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X24),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_846_diff__add__assoc) ).
fof(fact_842_add__diff__assoc,axiom,
! [X23,X22,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X24),X22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X24)),X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_842_add__diff__assoc) ).
fof(fact_838_diff__diff__right,axiom,
! [X23,X22,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X23),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X24),X22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X22)),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_838_diff__diff__right) ).
fof(fact_908_diff__less__Suc,axiom,
! [X15,X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14)),hAPP_nat_nat(suc,X15))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_908_diff__less__Suc) ).
fof(fact_898_less__add__Suc1,axiom,
! [X23,X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X15)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_898_less__add__Suc1) ).
fof(fact_899_less__add__Suc2,axiom,
! [X23,X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X23)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_899_less__add__Suc2) ).
fof(fact_872_less__trans__Suc,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X24))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X24),X22))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X23)),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_872_less__trans__Suc) ).
fof(fact_968_add__eq__if,axiom,
! [X14,X15] :
( ( X15 = zero_zero_nat
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X14) = X14 )
& ( X15 != zero_zero_nat
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X14) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),one_one_nat)),X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_968_add__eq__if) ).
fof(fact_920_Suc__lessE,axiom,
! [X23,X22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X23)),X22))
=> ~ ! [X127] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X127))
=> X22 != hAPP_nat_nat(suc,X127) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_920_Suc__lessE) ).
fof(fact_113_finite__Collect__conjI,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X13)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X12))) )
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X13),X12)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_finite__Collect__conjI) ).
fof(fact_112_finite__Collect__conjI,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X13)))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X12))) )
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X13),X12)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_finite__Collect__conjI) ).
fof(fact_114_finite__Collect__conjI,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X13)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X12))) )
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X13),X12)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_finite__Collect__conjI) ).
fof(fact_115_finite__Collect__conjI,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X13)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X12))) )
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X13),X12)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_finite__Collect__conjI) ).
fof(fact_116_finite__Collect__conjI,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X13)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X12))) )
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X13),X12)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_finite__Collect__conjI) ).
fof(fact_111_finite__Collect__conjI,axiom,
! [X12,X13] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X13)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X12))) )
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X13),X12)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_finite__Collect__conjI) ).
fof(fact_660_subset__singletonD,axiom,
! [X5,X11] :
( is_fun_a_bool(X5)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)))
=> ( X5 = bot_bot_fun_a_bool
| X5 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_subset__singletonD) ).
fof(fact_78_card__mono,axiom,
! [X5,X10] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X5)),hAPP_f957591787ol_nat(finite_card_int,X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_card__mono) ).
fof(fact_77_card__mono,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X5)),hAPP_f22106695ol_nat(finite_card_nat,X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_card__mono) ).
fof(fact_74_card__mono,axiom,
! [X5,X10] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_card__mono) ).
fof(fact_73_card__mono,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)),hAPP_f55526627ol_nat(finite1340463720e_bool,X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_card__mono) ).
fof(fact_72_card__mono,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X5)),hAPP_f696928925ol_nat(finite346522414t_bool,X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_card__mono) ).
fof(fact_71_card__mono,axiom,
! [X5,X10] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X10))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X5)),hAPP_f521865025ol_nat(finite1876863882t_bool,X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_card__mono) ).
fof(fact_76_card__mono,axiom,
! [X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X5)),hAPP_fun_a_bool_nat(finite_card_a,X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_card__mono) ).
fof(fact_75_card__mono,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X5)),hAPP_f921600141ol_nat(finite_card_pname,X10))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_card__mono) ).
fof(fact_547_insert__Diff,axiom,
! [X8,X5] :
( is_fun_pname_bool(X5)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),bot_bo844097828e_bool))) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_insert__Diff) ).
fof(fact_544_insert__Diff,axiom,
! [X8,X5] :
( is_fun_a_bool(X5)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5))
=> hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool))) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_insert__Diff) ).
fof(fact_661_subset__singletonD,axiom,
! [X5,X11] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)))
=> ( X5 = bot_bot_fun_nat_bool
| X5 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_subset__singletonD) ).
fof(fact_662_subset__singletonD,axiom,
! [X5,X11] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)))
=> ( X5 = bot_bot_fun_int_bool
| X5 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_subset__singletonD) ).
fof(fact_948_less__Suc__eq__0__disj,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),hAPP_nat_nat(suc,X17)))
<=> ( X25 = zero_zero_nat
| ? [X127] :
( X25 = hAPP_nat_nat(suc,X127)
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X127),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_948_less__Suc__eq__0__disj) ).
fof(fact_545_insert__Diff,axiom,
! [X8,X5] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X5))
=> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool))) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_insert__Diff) ).
fof(fact_546_insert__Diff,axiom,
! [X8,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5))
=> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool))) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_insert__Diff) ).
fof(fact_596_doubleton__eq__iff,axiom,
! [X8,X31,X32,X73] :
( ( is_a(X8)
& is_a(X31)
& is_a(X32)
& is_a(X73) )
=> ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X31),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X32),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X73),bot_bot_fun_a_bool))
<=> ( ( X8 = X32
& X31 = X73 )
| ( X8 = X73
& X31 = X32 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_doubleton__eq__iff) ).
fof(fact_587_Diff__subset,axiom,
! [X5,X10] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_Diff__subset) ).
fof(fact_586_Diff__subset,axiom,
! [X5,X10] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10)),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_Diff__subset) ).
fof(fact_588_Diff__subset,axiom,
! [X5,X10] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10)),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_Diff__subset) ).
fof(fact_179_diff__le__self,axiom,
! [X15,X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14)),X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_diff__le__self) ).
fof(fact_1027_zadd__zmult__distrib2,axiom,
! [X135,X136,X137] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X135),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X136),X137)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X135),X136)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X135),X137)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1027_zadd__zmult__distrib2) ).
fof(fact_1026_zdiff__zmult__distrib2,axiom,
! [X135,X136,X137] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X135),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X136),X137)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X135),X136)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X135),X137)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1026_zdiff__zmult__distrib2) ).
fof(fact_985_add__mult__distrib2,axiom,
! [X22,X15,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X14)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_985_add__mult__distrib2) ).
fof(fact_992_diff__mult__distrib2,axiom,
! [X22,X15,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X22),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_992_diff__mult__distrib2) ).
fof(fact_131_diff__commute,axiom,
! [X23,X24,X22] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X23),X24)),X22) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X23),X22)),X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_diff__commute) ).
fof(fact_478_subsetI,axiom,
! [X10,X5] :
( ! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X10)) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_subsetI) ).
fof(fact_477_subsetI,axiom,
! [X10,X5] :
( ! [X30] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X5))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X10)) )
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_subsetI) ).
fof(fact_480_subsetI,axiom,
! [X10,X5] :
( ! [X30] :
( is_pname(X30)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X10)) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_subsetI) ).
fof(fact_479_subsetI,axiom,
! [X10,X5] :
( ! [X30] :
( is_a(X30)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X10)) ) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_subsetI) ).
fof(fact_175_eq__diff__iff,axiom,
! [X17,X16,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X25))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X17))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X25),X16) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X17),X16)
<=> X25 = X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_eq__diff__iff) ).
fof(fact_560_Diff__insert,axiom,
! [X5,X8,X10] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X10)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_Diff__insert) ).
fof(fact_559_Diff__insert,axiom,
! [X5,X8,X10] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X10)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_Diff__insert) ).
fof(fact_558_Diff__insert,axiom,
! [X5,X8,X10] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X10)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_Diff__insert) ).
fof(fact_582_double__diff,axiom,
! [X67,X5,X10] :
( is_fun_a_bool(X5)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X67))
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X10),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X67),X5)) = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_double__diff) ).
fof(fact_976_nat__induct,axiom,
! [X17,X13] :
( hBOOL(hAPP_nat_bool(X13,zero_zero_nat))
=> ( ! [X29] :
( hBOOL(hAPP_nat_bool(X13,X29))
=> hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(suc,X29))) )
=> hBOOL(hAPP_nat_bool(X13,X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_976_nat__induct) ).
fof(fact_670_card__Diff__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),X5))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,X5)),hAPP_f957591787ol_nat(finite_card_int,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_card__Diff__subset) ).
fof(fact_671_card__Diff__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,X5)),hAPP_f22106695ol_nat(finite_card_nat,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_card__Diff__subset) ).
fof(fact_672_card__Diff__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,X5)),hAPP_fun_a_bool_nat(finite_card_a,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_card__Diff__subset) ).
fof(fact_673_card__Diff__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,X5)),hAPP_f921600141ol_nat(finite_card_pname,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_card__Diff__subset) ).
fof(fact_602_singleton__iff,axiom,
! [X31,X8] :
( ( is_pname(X31)
& is_pname(X8) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),bot_bo844097828e_bool)))
<=> X31 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_singleton__iff) ).
fof(fact_595_singletonE,axiom,
! [X31,X8] :
( ( is_pname(X31)
& is_pname(X8) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),bot_bo844097828e_bool)))
=> X31 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_singletonE) ).
fof(fact_599_singleton__iff,axiom,
! [X31,X8] :
( ( is_a(X31)
& is_a(X8) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool)))
<=> X31 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_singleton__iff) ).
fof(fact_592_singletonE,axiom,
! [X31,X8] :
( ( is_a(X31)
& is_a(X8) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool)))
=> X31 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_singletonE) ).
fof(fact_433_imageI,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X9,X11)),image_nat_int(X9,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_imageI) ).
fof(fact_473_image__mono,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X9,X5)),image_nat_int(X9,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_image__mono) ).
fof(fact_474_image__mono,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X9,X5)),image_pname_a(X9,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_image__mono) ).
fof(fact_434_imageI,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X9,X11)),image_pname_a(X9,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_imageI) ).
fof(fact_448_le__funE,axiom,
! [X11,X9,X69] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),X69))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X9,X11)),hAPP_nat_bool(X69,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_le__funE) ).
fof(fact_445_le__funD,axiom,
! [X11,X9,X69] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),X69))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X9,X11)),hAPP_nat_bool(X69,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_le__funD) ).
fof(fact_447_le__funE,axiom,
! [X11,X9,X69] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),X69))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X9,X11)),hAPP_int_bool(X69,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_le__funE) ).
fof(fact_444_le__funD,axiom,
! [X11,X9,X69] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X9),X69))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X9,X11)),hAPP_int_bool(X69,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_le__funD) ).
fof(fact_449_le__funE,axiom,
! [X11,X9,X69] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),X69))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X9,X11)),hAPP_a_bool(X69,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_le__funE) ).
fof(fact_446_le__funD,axiom,
! [X11,X9,X69] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),X69))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X9,X11)),hAPP_a_bool(X69,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_le__funD) ).
fof(fact_773_folding__one__idem_Osubset__idem,axiom,
! [X10,X5,X9,X7] :
( is_fun_pname_bool(X10)
=> ( hBOOL(finite89670078_pname(X9,X7))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( X10 != bot_bo844097828e_bool
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5))
=> hAPP_pname_pname(hAPP_p1170154830_pname(X9,hAPP_f1297739591_pname(X7,X10)),hAPP_f1297739591_pname(X7,X5)) = hAPP_f1297739591_pname(X7,X5) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_773_folding__one__idem_Osubset__idem) ).
fof(fact_774_folding__one__idem_Osubset__idem,axiom,
! [X10,X5,X9,X7] :
( is_fun_a_bool(X10)
=> ( hBOOL(finite1819937229idem_a(X9,X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( X10 != bot_bot_fun_a_bool
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5))
=> hAPP_a_a(hAPP_a_fun_a_a(X9,hAPP_fun_a_bool_a(X7,X10)),hAPP_fun_a_bool_a(X7,X5)) = hAPP_fun_a_bool_a(X7,X5) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_774_folding__one__idem_Osubset__idem) ).
fof(fact_580_double__diff,axiom,
! [X67,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),X67))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X10),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X67),X5)) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_double__diff) ).
fof(fact_581_double__diff,axiom,
! [X67,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X67))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X10),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X67),X5)) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_double__diff) ).
fof(fact_772_folding__one__idem_Osubset__idem,axiom,
! [X10,X5,X9,X7] :
( hBOOL(finite795500164em_nat(X9,X7))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( X10 != bot_bot_fun_nat_bool
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(X9,hAPP_f22106695ol_nat(X7,X10)),hAPP_f22106695ol_nat(X7,X5)) = hAPP_f22106695ol_nat(X7,X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_772_folding__one__idem_Osubset__idem) ).
fof(fact_771_folding__one__idem_Osubset__idem,axiom,
! [X10,X5,X9,X7] :
( hBOOL(finite1432773856em_int(X9,X7))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( X10 != bot_bot_fun_int_bool
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),X5))
=> hAPP_int_int(hAPP_int_fun_int_int(X9,hAPP_f1594865479ol_int(X7,X10)),hAPP_f1594865479ol_int(X7,X5)) = hAPP_f1594865479ol_int(X7,X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_771_folding__one__idem_Osubset__idem) ).
fof(fact_874_Suc__lessD,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X15)),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_874_Suc__lessD) ).
fof(fact_907_Suc__le__lessD,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X15)),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_907_Suc__le__lessD) ).
fof(fact_903_Suc__le__eq,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X25)),X17))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_903_Suc__le__eq) ).
fof(fact_901_less__eq__Suc__le,axiom,
! [X17,X25] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),X25))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X17)),X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_901_less__eq__Suc__le) ).
fof(fact_164_Suc__leD,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X15)),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_Suc__leD) ).
fof(fact_395_insertI2,axiom,
! [X31,X8,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X10))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X31),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_insertI2) ).
fof(fact_463_subset__insertI2,axiom,
! [X31,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X31),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_subset__insertI2) ).
fof(fact_394_insertI2,axiom,
! [X31,X8,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X10))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X31),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_insertI2) ).
fof(fact_462_subset__insertI2,axiom,
! [X31,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X31),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_subset__insertI2) ).
fof(fact_396_insertI2,axiom,
! [X31,X8,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X10))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X31),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_insertI2) ).
fof(fact_461_subset__insertI2,axiom,
! [X31,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X31),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_subset__insertI2) ).
fof(fact_393_insertI2,axiom,
! [X31,X8,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X31),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_insertI2) ).
fof(fact_885_termination__basic__simps_I1_J,axiom,
! [X98,X18,X19] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X18),X19))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X18),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X19),X98))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_885_termination__basic__simps_I1_J) ).
fof(fact_879_trans__less__add1,axiom,
! [X15,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X24))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X15))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_879_trans__less__add1) ).
fof(fact_886_termination__basic__simps_I2_J,axiom,
! [X19,X18,X98] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X18),X98))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X18),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X19),X98))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_886_termination__basic__simps_I2_J) ).
fof(fact_880_trans__less__add2,axiom,
! [X15,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X24))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_880_trans__less__add2) ).
fof(fact_854_termination__basic__simps_I3_J,axiom,
! [X98,X18,X19] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X18),X19))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X18),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X19),X98))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_854_termination__basic__simps_I3_J) ).
fof(fact_826_trans__le__add1,axiom,
! [X15,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X24))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X15))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_826_trans__le__add1) ).
fof(fact_853_termination__basic__simps_I4_J,axiom,
! [X19,X18,X98] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X18),X98))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X18),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X19),X98))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_853_termination__basic__simps_I4_J) ).
fof(fact_827_trans__le__add2,axiom,
! [X15,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X24))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_827_trans__le__add2) ).
fof(fact_570_finite__Diff2,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_finite__Diff2) ).
fof(fact_569_finite__Diff2,axiom,
! [X5,X10] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10)))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_finite__Diff2) ).
fof(fact_571_finite__Diff2,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_finite__Diff2) ).
fof(fact_601_singleton__iff,axiom,
! [X31,X8] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool)))
<=> X31 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_singleton__iff) ).
fof(fact_594_singletonE,axiom,
! [X31,X8] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool)))
=> X31 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_singletonE) ).
fof(fact_600_singleton__iff,axiom,
! [X31,X8] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X31),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool)))
<=> X31 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_singleton__iff) ).
fof(fact_593_singletonE,axiom,
! [X31,X8] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X31),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool)))
=> X31 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_singletonE) ).
fof(fact_573_insert__Diff1,axiom,
! [X5,X11,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X10))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)),X10) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_insert__Diff1) ).
fof(fact_574_insert__Diff1,axiom,
! [X5,X11,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)),X10) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_insert__Diff1) ).
fof(fact_575_insert__Diff1,axiom,
! [X5,X11,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)),X10) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_insert__Diff1) ).
fof(fact_572_insert__Diff1,axiom,
! [X5,X11,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10))
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)),X10) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_insert__Diff1) ).
fof(fact_598_doubleton__eq__iff,axiom,
! [X8,X31,X32,X73] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X31),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X32),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X73),bot_bot_fun_int_bool))
<=> ( ( X8 = X32
& X31 = X73 )
| ( X8 = X73
& X31 = X32 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_doubleton__eq__iff) ).
fof(fact_597_doubleton__eq__iff,axiom,
! [X8,X31,X32,X73] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X31),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X32),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X73),bot_bot_fun_nat_bool))
<=> ( ( X8 = X32
& X31 = X73 )
| ( X8 = X73
& X31 = X32 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_doubleton__eq__iff) ).
fof(fact_1170_numeral__1__eq__Suc__0,axiom,
number_number_of_nat(bit1(pls)) = hAPP_nat_nat(suc,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1170_numeral__1__eq__Suc__0) ).
fof(fact_856_Suc__mono,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X15)),hAPP_nat_nat(suc,X14))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_856_Suc__mono) ).
fof(fact_1123_zless__iff__Suc__zadd,axiom,
! [X139,X56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X139),X56))
<=> ? [X29] : X56 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X139),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X29))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1123_zless__iff__Suc__zadd) ).
fof(fact_1174_nat__numeral__1__eq__1,axiom,
number_number_of_nat(bit1(pls)) = one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1174_nat__numeral__1__eq__1) ).
fof(fact_1173_Numeral1__eq1__nat,axiom,
one_one_nat = number_number_of_nat(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1173_Numeral1__eq1__nat) ).
fof(fact_388_insert__code,axiom,
! [X39,X5,X11] :
( ( is_a(X39)
& is_a(X11) )
=> ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X39),X5),X11))
<=> ( X39 = X11
| hBOOL(hAPP_a_bool(X5,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_insert__code) ).
fof(fact_418_set__rev__mp,axiom,
! [X10,X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_set__rev__mp) ).
fof(fact_422_set__mp,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_set__mp) ).
fof(fact_414_in__mono,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_in__mono) ).
fof(fact_288_subsetD,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_subsetD) ).
fof(fact_426_subset__trans,axiom,
! [X67,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X67))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X67)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_subset__trans) ).
fof(fact_349_order__trans,axiom,
! [X56,X11,X39] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X39))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X39),X56))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X56)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_order__trans) ).
fof(fact_359_xt1_I6_J,axiom,
! [X56,X39,X11] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X39),X11))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X56),X39))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X56),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_xt1_I6_J) ).
fof(fact_417_set__rev__mp,axiom,
! [X10,X11,X5] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_set__rev__mp) ).
fof(fact_421_set__mp,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_set__mp) ).
fof(fact_413_in__mono,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_in__mono) ).
fof(fact_287_subsetD,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X5))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_subsetD) ).
fof(fact_425_subset__trans,axiom,
! [X67,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),X67))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X67)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_subset__trans) ).
fof(fact_348_order__trans,axiom,
! [X56,X11,X39] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X11),X39))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X39),X56))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X11),X56)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_order__trans) ).
fof(fact_358_xt1_I6_J,axiom,
! [X56,X39,X11] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X39),X11))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X56),X39))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X56),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_xt1_I6_J) ).
fof(fact_420_set__rev__mp,axiom,
! [X10,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_set__rev__mp) ).
fof(fact_424_set__mp,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_set__mp) ).
fof(fact_416_in__mono,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_in__mono) ).
fof(fact_290_subsetD,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_subsetD) ).
fof(fact_427_subset__trans,axiom,
! [X67,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X67))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X67)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_subset__trans) ).
fof(fact_352_order__trans,axiom,
! [X56,X11,X39] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X39))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X39),X56))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X56)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_order__trans) ).
fof(fact_362_xt1_I6_J,axiom,
! [X56,X39,X11] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X39),X11))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X56),X39))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X56),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_xt1_I6_J) ).
fof(fact_419_set__rev__mp,axiom,
! [X10,X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_set__rev__mp) ).
fof(fact_423_set__mp,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_set__mp) ).
fof(fact_415_in__mono,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_in__mono) ).
fof(fact_289_subsetD,axiom,
! [X32,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_subsetD) ).
fof(fact_351_order__trans,axiom,
! [X57,X58,X59] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X58),X59))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X59),X57))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X58),X57)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_order__trans) ).
fof(fact_127_le__trans,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X24))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X24),X22))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_le__trans) ).
fof(fact_361_xt1_I6_J,axiom,
! [X62,X63,X64] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X63),X64))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X62),X63))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X62),X64)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_xt1_I6_J) ).
fof(fact_1046_zle__trans,axiom,
! [X22,X23,X24] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X23),X24))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X24),X22))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X23),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1046_zle__trans) ).
fof(fact_350_order__trans,axiom,
! [X57,X58,X59] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X58),X59))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X59),X57))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X58),X57)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_order__trans) ).
fof(fact_360_xt1_I6_J,axiom,
! [X62,X63,X64] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X63),X64))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X62),X63))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X62),X64)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_xt1_I6_J) ).
fof(fact_906_le__less__Suc__eq,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),hAPP_nat_nat(suc,X25)))
<=> X17 = X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_906_le__less__Suc__eq) ).
fof(fact_883_less__add__eq__less,axiom,
! [X15,X14,X22,X26] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X26))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X26) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X14)
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_883_less__add__eq__less) ).
fof(fact_488_diff__eq__diff__less__eq,axiom,
! [X8,X31,X32,X73] :
( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X8),X31) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X32),X73)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X8),X31))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X32),X73)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_diff__eq__diff__less__eq) ).
fof(fact_1038_le__imp__0__less,axiom,
! [X98] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X98))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X98))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1038_le__imp__0__less) ).
fof(fact_895_finite__nat__set__iff__bounded,axiom,
! [X72] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X72))
<=> ? [X35] :
! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X72))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X35)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_895_finite__nat__set__iff__bounded) ).
fof(fact_486_finite__nat__set__iff__bounded__le,axiom,
! [X72] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X72))
<=> ? [X35] :
! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X72))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X35)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_finite__nat__set__iff__bounded__le) ).
fof(fact_917_bounded__nat__set__is__finite,axiom,
! [X17,X72] :
( ! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X72))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X17)) )
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X72)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_917_bounded__nat__set__is__finite) ).
fof(fact_1125_zdiff__int,axiom,
! [X14,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15))
=> hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X15)),hAPP_nat_int(semiri1621563631at_int,X14)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1125_zdiff__int) ).
fof(fact_440_insert__compr__raw,axiom,
! [X30,X68] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X30),X68) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X30)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X68))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_insert__compr__raw) ).
fof(fact_372_insert__compr,axiom,
! [X8,X10] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X10) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X8)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_insert__compr) ).
fof(fact_437_insert__compr__raw,axiom,
! [X30,X68] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X30),X68) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X30)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X68))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_insert__compr__raw) ).
fof(fact_369_insert__compr,axiom,
! [X8,X10] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X10) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_insert__compr) ).
fof(fact_300_Suc__le__D,axiom,
! [X14,X34] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X14)),X34))
=> ? [X35] : X34 = hAPP_nat_nat(suc,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_Suc__le__D) ).
fof(fact_871_Suc__lessI,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> ( hAPP_nat_nat(suc,X15) != X14
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X15)),X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_871_Suc__lessI) ).
fof(fact_844_le__add__diff__inverse2,axiom,
! [X14,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14)),X14) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_844_le__add__diff__inverse2) ).
fof(fact_1120_transfer__int__nat__quantifiers_I1_J,axiom,
! [X13] :
( ! [X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X30))
=> hBOOL(hAPP_int_bool(X13,X30)) )
<=> ! [X30] : hBOOL(hAPP_int_bool(X13,hAPP_nat_int(semiri1621563631at_int,X30))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1120_transfer__int__nat__quantifiers_I1_J) ).
fof(fact_141_finite__insert,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X8),X5)))
<=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_finite__insert) ).
fof(fact_140_finite__insert,axiom,
! [X8,X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X8),X5)))
<=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_finite__insert) ).
fof(fact_142_finite__insert,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X8),X5)))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_finite__insert) ).
fof(fact_143_finite__insert,axiom,
! [X8,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X8),X5)))
<=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_finite__insert) ).
fof(fact_145_finite__insert,axiom,
! [X8,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X5)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_finite__insert) ).
fof(fact_146_finite__insert,axiom,
! [X8,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X5)))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_finite__insert) ).
fof(fact_144_finite__insert,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X5)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_finite__insert) ).
fof(fact_147_finite__insert,axiom,
! [X8,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X5)))
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_finite__insert) ).
fof(fact_836_diff__cancel,axiom,
! [X22,X15,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X22),X14)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_836_diff__cancel) ).
fof(fact_837_diff__cancel2,axiom,
! [X15,X22,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X22)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_837_diff__cancel2) ).
fof(fact_1023_zmult__assoc,axiom,
! [X136,X137,X138] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X136),X137)),X138) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X136),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X137),X138)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1023_zmult__assoc) ).
fof(fact_1041_zadd__assoc,axiom,
! [X136,X137,X138] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X136),X137)),X138) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X136),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X137),X138)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1041_zadd__assoc) ).
fof(fact_786_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X86,X87,X88] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X86),X87)),X88) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X86),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X87),X88)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_786_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_1017_nat__mult__assoc,axiom,
! [X15,X14,X22] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X14)),X22) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1017_nat__mult__assoc) ).
fof(fact_800_nat__add__assoc,axiom,
! [X15,X14,X22] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X14)),X22) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_800_nat__add__assoc) ).
fof(fact_787_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X86,X87,X88] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X86),X87)),X88) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X86),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X87),X88)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_787_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_835_diff__diff__left,axiom,
! [X23,X24,X22] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X23),X24)),X22) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X23),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_835_diff__diff__left) ).
fof(fact_905_Suc__leI,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X15)),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_905_Suc__leI) ).
fof(fact_119_Suc__diff__le,axiom,
! [X14,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X15)),X14) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_Suc__diff__le) ).
fof(fact_554_insert__Diff__single,axiom,
! [X8,X5] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool))) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_insert__Diff__single) ).
fof(fact_553_insert__Diff__single,axiom,
! [X8,X5] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool))) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_insert__Diff__single) ).
fof(fact_552_insert__Diff__single,axiom,
! [X8,X5] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool))) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_insert__Diff__single) ).
fof(fact_168_le__Suc__eq,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),hAPP_nat_nat(suc,X17)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17))
| X25 = hAPP_nat_nat(suc,X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_le__Suc__eq) ).
fof(fact_192_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X10),image_26036933t_bool(X9,X5)))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_finite__surj) ).
fof(fact_198_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X10),image_892525857t_bool(X9,X5)))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_finite__surj) ).
fof(fact_186_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X10),image_2129980159t_bool(X9,X5)))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_finite__surj) ).
fof(fact_191_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X10),image_1556378401t_bool(X9,X5)))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_finite__surj) ).
fof(fact_197_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X10),image_275383677t_bool(X9,X5)))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_finite__surj) ).
fof(fact_185_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X10),image_1512837979t_bool(X9,X5)))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_finite__surj) ).
fof(fact_193_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X10),image_1655916159e_bool(X9,X5)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_finite__surj) ).
fof(fact_199_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X10),image_637364955e_bool(X9,X5)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_finite__surj) ).
fof(fact_187_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X10),image_47868345e_bool(X9,X5)))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_finite__surj) ).
fof(fact_194_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X10),image_nat_fun_a_bool(X9,X5)))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_finite__surj) ).
fof(fact_200_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X10),image_int_fun_a_bool(X9,X5)))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_finite__surj) ).
fof(fact_188_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X10),image_112932426a_bool(X9,X5)))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_finite__surj) ).
fof(fact_209_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),image_496248727ol_nat(X9,X5)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_finite__surj) ).
fof(fact_208_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),image_1431733819ol_nat(X9,X5)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_finite__surj) ).
fof(fact_210_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),image_1551609309ol_nat(X9,X5)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_finite__surj) ).
fof(fact_211_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),image_fun_a_bool_nat(X9,X5)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_finite__surj) ).
fof(fact_207_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),image_a_nat(X9,X5)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_finite__surj) ).
fof(fact_214_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),image_1133522419ol_int(X9,X5)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_finite__surj) ).
fof(fact_213_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),image_2069007511ol_int(X9,X5)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_finite__surj) ).
fof(fact_215_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),image_41399353ol_int(X9,X5)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_finite__surj) ).
fof(fact_216_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),image_fun_a_bool_int(X9,X5)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_finite__surj) ).
fof(fact_218_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),image_nat_int(X9,X5)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_finite__surj) ).
fof(fact_212_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),image_a_int(X9,X5)))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_finite__surj) ).
fof(fact_204_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_1921560913_pname(X9,X5)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_finite__surj) ).
fof(fact_203_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_62782965_pname(X9,X5)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_finite__surj) ).
fof(fact_205_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_1283814551_pname(X9,X5)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_finite__surj) ).
fof(fact_206_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_1854862208_pname(X9,X5)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_finite__surj) ).
fof(fact_195_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_nat_pname(X9,X5)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_finite__surj) ).
fof(fact_201_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_int_pname(X9,X5)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_finite__surj) ).
fof(fact_189_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_pname_pname(X9,X5)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_finite__surj) ).
fof(fact_202_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_a_pname(X9,X5)))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_finite__surj) ).
fof(fact_182_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_fun_nat_bool_a(X9,X5)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_finite__surj) ).
fof(fact_181_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_fun_int_bool_a(X9,X5)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_finite__surj) ).
fof(fact_183_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_876012084bool_a(X9,X5)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_finite__surj) ).
fof(fact_184_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_fun_a_bool_a(X9,X5)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_finite__surj) ).
fof(fact_190_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_nat_a(X9,X5)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_finite__surj) ).
fof(fact_196_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_int_a(X9,X5)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_finite__surj) ).
fof(fact_217_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_pname_a(X9,X5)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_finite__surj) ).
fof(fact_180_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),image_a_a(X9,X5)))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_finite__surj) ).
fof(fact_282_image__eqI,axiom,
! [X5,X31,X9,X11] :
( X31 = hAPP_nat_int(X9,X11)
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X31),image_nat_int(X9,X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_image__eqI) ).
fof(fact_435_rev__image__eqI,axiom,
! [X31,X9,X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( X31 = hAPP_nat_int(X9,X11)
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X31),image_nat_int(X9,X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_rev__image__eqI) ).
fof(fact_283_image__eqI,axiom,
! [X5,X31,X9,X11] :
( X31 = hAPP_pname_a(X9,X11)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),image_pname_a(X9,X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_image__eqI) ).
fof(fact_436_rev__image__eqI,axiom,
! [X31,X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( X31 = hAPP_pname_a(X9,X11)
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),image_pname_a(X9,X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_rev__image__eqI) ).
fof(fact_866_less__Suc__eq,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),hAPP_nat_nat(suc,X17)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17))
| X25 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_866_less__Suc__eq) ).
fof(fact_902_less__Suc__eq__le,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),hAPP_nat_nat(suc,X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_902_less__Suc__eq__le) ).
fof(fact_1032_odd__nonzero,axiom,
! [X98] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X98)),X98) != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1032_odd__nonzero) ).
fof(fact_983_Suc__mult__cancel1,axiom,
! [X16,X25,X17] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X16)),X25) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X16)),X17)
<=> X25 = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_983_Suc__mult__cancel1) ).
fof(fact_919_lessE,axiom,
! [X23,X22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X22))
=> ( X22 != hAPP_nat_nat(suc,X23)
=> ~ ! [X127] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X127))
=> X22 != hAPP_nat_nat(suc,X127) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_919_lessE) ).
fof(fact_1121_int__le__0__conv,axiom,
! [X17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X17)),zero_zero_int))
<=> X17 = zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1121_int__le__0__conv) ).
fof(fact_1119_transfer__int__nat__quantifiers_I2_J,axiom,
! [X13] :
( ? [X30] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X30))
& hBOOL(hAPP_int_bool(X13,X30)) )
<=> ? [X30] : hBOOL(hAPP_int_bool(X13,hAPP_nat_int(semiri1621563631at_int,X30))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1119_transfer__int__nat__quantifiers_I2_J) ).
fof(fact_916_less__imp__Suc__add,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> ? [X119] : X14 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X119)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_916_less__imp__Suc__add) ).
fof(fact_900_less__iff__Suc__add,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17))
<=> ? [X119] : X17 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X25),X119)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_900_less__iff__Suc__add) ).
fof(fact_406_set__eq__subset,axiom,
! [X5,X10] :
( ( is_fun_a_bool(X5)
& is_fun_a_bool(X10) )
=> ( X5 = X10
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_set__eq__subset) ).
fof(fact_357_xt1_I5_J,axiom,
! [X39,X11] :
( ( is_fun_a_bool(X39)
& is_fun_a_bool(X11) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X39),X11))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X39))
=> X11 = X39 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_xt1_I5_J) ).
fof(fact_347_order__antisym,axiom,
! [X11,X39] :
( ( is_fun_a_bool(X11)
& is_fun_a_bool(X39) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X39))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X39),X11))
=> X11 = X39 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_order__antisym) ).
fof(fact_322_order__antisym__conv,axiom,
! [X39,X11] :
( ( is_fun_a_bool(X39)
& is_fun_a_bool(X11) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X39),X11))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X39))
<=> X11 = X39 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_order__antisym__conv) ).
fof(fact_312_order__eq__iff,axiom,
! [X11,X39] :
( ( is_fun_a_bool(X11)
& is_fun_a_bool(X39) )
=> ( X11 = X39
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X39))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X39),X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_order__eq__iff) ).
fof(fact_286_equalityI,axiom,
! [X5,X10] :
( ( is_fun_a_bool(X5)
& is_fun_a_bool(X10) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5))
=> X5 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_equalityI) ).
fof(fact_1126_zero__less__int__conv,axiom,
! [X17] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X17)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1126_zero__less__int__conv) ).
fof(fact_778_folding__one__idem_Oinsert__idem,axiom,
! [X11,X5,X9,X7] :
( is_fun_pname_bool(X5)
=> ( hBOOL(finite89670078_pname(X9,X7))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( X5 != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(X7,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)) = hAPP_pname_pname(hAPP_p1170154830_pname(X9,X11),hAPP_f1297739591_pname(X7,X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_778_folding__one__idem_Oinsert__idem) ).
fof(fact_775_folding__one__idem_Oinsert__idem,axiom,
! [X11,X5,X9,X7] :
( is_fun_a_bool(X5)
=> ( hBOOL(finite1819937229idem_a(X9,X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( X5 != bot_bot_fun_a_bool
=> hAPP_fun_a_bool_a(X7,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)) = hAPP_a_a(hAPP_a_fun_a_a(X9,X11),hAPP_fun_a_bool_a(X7,X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_775_folding__one__idem_Oinsert__idem) ).
fof(fact_469_insert__image,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X9,X11)),image_nat_int(X9,X5)) = image_nat_int(X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_insert__image) ).
fof(fact_470_insert__image,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X9,X11)),image_pname_a(X9,X5)) = image_pname_a(X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_insert__image) ).
fof(fact_777_folding__one__idem_Oinsert__idem,axiom,
! [X11,X5,X9,X7] :
( hBOOL(finite795500164em_nat(X9,X7))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( X5 != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(X7,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X9,X11),hAPP_f22106695ol_nat(X7,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_777_folding__one__idem_Oinsert__idem) ).
fof(fact_776_folding__one__idem_Oinsert__idem,axiom,
! [X11,X5,X9,X7] :
( hBOOL(finite1432773856em_int(X9,X7))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( X5 != bot_bot_fun_int_bool
=> hAPP_f1594865479ol_int(X7,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)) = hAPP_int_int(hAPP_int_fun_int_int(X9,X11),hAPP_f1594865479ol_int(X7,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_776_folding__one__idem_Oinsert__idem) ).
fof(fact_405_set__eq__subset,axiom,
! [X5,X10] :
( X5 = X10
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_set__eq__subset) ).
fof(fact_354_xt1_I5_J,axiom,
! [X39,X11] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X39),X11))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X39))
=> X11 = X39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_xt1_I5_J) ).
fof(fact_344_order__antisym,axiom,
! [X11,X39] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X39))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X39),X11))
=> X11 = X39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_order__antisym) ).
fof(fact_319_order__antisym__conv,axiom,
! [X39,X11] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X39),X11))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X39))
<=> X11 = X39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_order__antisym__conv) ).
fof(fact_309_order__eq__iff,axiom,
! [X11,X39] :
( X11 = X39
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X39))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X39),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_order__eq__iff) ).
fof(fact_285_equalityI,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5))
=> X5 = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_equalityI) ).
fof(fact_404_set__eq__subset,axiom,
! [X5,X10] :
( X5 = X10
<=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_set__eq__subset) ).
fof(fact_353_xt1_I5_J,axiom,
! [X39,X11] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X39),X11))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X11),X39))
=> X11 = X39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_xt1_I5_J) ).
fof(fact_343_order__antisym,axiom,
! [X11,X39] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X11),X39))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X39),X11))
=> X11 = X39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_order__antisym) ).
fof(fact_318_order__antisym__conv,axiom,
! [X39,X11] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X39),X11))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X11),X39))
<=> X11 = X39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_order__antisym__conv) ).
fof(fact_308_order__eq__iff,axiom,
! [X11,X39] :
( X11 = X39
<=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X11),X39))
& hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X39),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_order__eq__iff) ).
fof(fact_284_equalityI,axiom,
! [X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),X5))
=> X5 = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_equalityI) ).
fof(fact_356_xt1_I5_J,axiom,
! [X60,X61] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X60),X61))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X61),X60))
=> X61 = X60 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_xt1_I5_J) ).
fof(fact_346_order__antisym,axiom,
! [X54,X55] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X54),X55))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X55),X54))
=> X54 = X55 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_order__antisym) ).
fof(fact_321_order__antisym__conv,axiom,
! [X39,X11] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X39),X11))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),X39))
<=> X11 = X39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_order__antisym__conv) ).
fof(fact_311_order__eq__iff,axiom,
! [X11,X39] :
( X11 = X39
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),X39))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X39),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_order__eq__iff) ).
fof(fact_126_le__antisym,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15))
=> X15 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_le__antisym) ).
fof(fact_1047_zle__antisym,axiom,
! [X98,X135] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X98),X135))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X135),X98))
=> X98 = X135 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1047_zle__antisym) ).
fof(fact_355_xt1_I5_J,axiom,
! [X60,X61] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X60),X61))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X61),X60))
=> X61 = X60 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_xt1_I5_J) ).
fof(fact_345_order__antisym,axiom,
! [X54,X55] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X54),X55))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X55),X54))
=> X54 = X55 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_order__antisym) ).
fof(fact_320_order__antisym__conv,axiom,
! [X39,X11] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X39),X11))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X39))
<=> X11 = X39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_order__antisym__conv) ).
fof(fact_310_order__eq__iff,axiom,
! [X11,X39] :
( X11 = X39
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X11),X39))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X39),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_order__eq__iff) ).
fof(fact_971_less__imp__add__positive,axiom,
! [X23,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X24))
=> ? [X119] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X119))
& hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X119) = X24 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_971_less__imp__add__positive) ).
fof(fact_870_less__SucI,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_nat_nat(suc,X14))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_870_less__SucI) ).
fof(fact_904_le__imp__less__Suc,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_nat_nat(suc,X14))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_904_le__imp__less__Suc) ).
fof(fact_166_le__SucI,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),hAPP_nat_nat(suc,X14))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_le__SucI) ).
fof(conj_5,hypothesis,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
fof(fact_977_expand__Suc,axiom,
! [X133] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X133)))
=> number_number_of_nat(X133) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,number_number_of_nat(X133)),one_one_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_977_expand__Suc) ).
fof(fact_864_nat__less__cases,axiom,
! [X13,X25,X17] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X13,X17),X25)) )
=> ( ( X25 = X17
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X13,X17),X25)) )
=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),X25))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X13,X17),X25)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X13,X17),X25)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_864_nat__less__cases) ).
fof(fact_959_Suc__pred,axiom,
! [X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X14))
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),hAPP_nat_nat(suc,zero_zero_nat))) = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_959_Suc__pred) ).
fof(fact_747_diff__Suc__eq__diff__pred,axiom,
! [X15,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),hAPP_nat_nat(suc,X14)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),one_one_nat)),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_747_diff__Suc__eq__diff__pred) ).
fof(fact_1105_zle__iff__zadd,axiom,
! [X139,X56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X139),X56))
<=> ? [X29] : X56 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X139),hAPP_nat_int(semiri1621563631at_int,X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1105_zle__iff__zadd) ).
fof(fact_664_nat__case__Suc,axiom,
! [X76,X77,X20] :
( hBOOL(hAPP_nat_bool(nat_case_bool(X76,X77),hAPP_nat_nat(suc,X20)))
<=> hBOOL(hAPP_nat_bool(X77,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_nat__case__Suc) ).
fof(fact_841_le__add__diff__inverse,axiom,
! [X14,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14)) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_841_le__add__diff__inverse) ).
fof(fact_176_diff__diff__cancel,axiom,
! [X23,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X14))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X23)) = X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_diff__diff__cancel) ).
fof(fact_1059_nat__mult__eq__cancel1,axiom,
! [X25,X17,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X16))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X25) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X17)
<=> X25 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1059_nat__mult__eq__cancel1) ).
fof(fact_367_insertI1,axiom,
! [X8,X10] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_insertI1) ).
fof(fact_452_subset__insertI,axiom,
! [X10,X8] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_subset__insertI) ).
fof(fact_366_insertI1,axiom,
! [X8,X10] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_insertI1) ).
fof(fact_451_subset__insertI,axiom,
! [X10,X8] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_subset__insertI) ).
fof(fact_368_insertI1,axiom,
! [X8,X10] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_insertI1) ).
fof(fact_450_subset__insertI,axiom,
! [X10,X8] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_subset__insertI) ).
fof(fact_365_insertI1,axiom,
! [X8,X10] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_insertI1) ).
fof(fact_990_le__square,axiom,
! [X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X15))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_990_le__square) ).
fof(fact_823_le__add1,axiom,
! [X14,X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X15))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_823_le__add1) ).
fof(fact_822_le__add2,axiom,
! [X14,X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X14))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_822_le__add2) ).
fof(fact_845_le__imp__diff__is__add,axiom,
! [X16,X33,X120] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X33),X120))
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X120),X33) = X16
<=> X120 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X16),X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_845_le__imp__diff__is__add) ).
fof(fact_1042_zadd__left__commute,axiom,
! [X18,X19,X98] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X18),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X19),X98)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X19),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X18),X98)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1042_zadd__left__commute) ).
fof(fact_799_nat__add__left__commute,axiom,
! [X18,X19,X98] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X18),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X19),X98)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X19),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X18),X98)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_799_nat__add__left__commute) ).
fof(fact_383_insert__commute,axiom,
! [X11,X39,X5] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X39),X5)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X39),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_insert__commute) ).
fof(fact_41_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X8),X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_finite_OinsertI) ).
fof(fact_40_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X8),X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_finite_OinsertI) ).
fof(fact_42_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X8),X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_finite_OinsertI) ).
fof(fact_43_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X8),X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_finite_OinsertI) ).
fof(fact_495_finite__Diff,axiom,
! [X10,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_finite__Diff) ).
fof(fact_45_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_finite_OinsertI) ).
fof(fact_494_finite__Diff,axiom,
! [X10,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_finite__Diff) ).
fof(fact_46_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_finite_OinsertI) ).
fof(fact_496_finite__Diff,axiom,
! [X10,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_finite__Diff) ).
fof(fact_44_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_finite_OinsertI) ).
fof(fact_47_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_finite_OinsertI) ).
fof(fact_2_finite__Collect__subsets,axiom,
! [X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_finite__Collect__subsets) ).
fof(fact_1_finite__Collect__subsets,axiom,
! [X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5))
=> hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
fof(fact_3_finite__Collect__subsets,axiom,
! [X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_finite__Collect__subsets) ).
fof(fact_4_finite__Collect__subsets,axiom,
! [X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_finite__Collect__subsets) ).
fof(fact_7_finite__Collect__subsets,axiom,
! [X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_finite__Collect__subsets) ).
fof(fact_8_finite__Collect__subsets,axiom,
! [X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_finite__Collect__subsets) ).
fof(fact_6_finite__Collect__subsets,axiom,
! [X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_finite__Collect__subsets) ).
fof(fact_5_finite__Collect__subsets,axiom,
! [X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_finite__Collect__subsets) ).
fof(fact_467_image__insert,axiom,
! [X9,X8,X10] : image_nat_int(X9,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X10)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X9,X8)),image_nat_int(X9,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_image__insert) ).
fof(fact_468_image__insert,axiom,
! [X9,X8,X10] : image_pname_a(X9,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X10)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X9,X8)),image_pname_a(X9,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_image__insert) ).
fof(fact_890_le__neq__implies__less,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> ( X15 != X14
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_890_le__neq__implies__less) ).
fof(fact_888_le__eq__less__or__eq,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17))
| X25 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_888_le__eq__less__or__eq) ).
fof(fact_887_nat__less__le,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17))
& X25 != X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_887_nat__less__le) ).
fof(fact_1050_zless__le,axiom,
! [X56,X139] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X56),X139))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X56),X139))
& X56 != X139 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1050_zless__le) ).
fof(fact_892_termination__basic__simps_I5_J,axiom,
! [X18,X19] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X18),X19))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X18),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_892_termination__basic__simps_I5_J) ).
fof(fact_891_less__or__eq__imp__le,axiom,
! [X15,X14] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
| X15 = X14 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_891_less__or__eq__imp__le) ).
fof(fact_889_less__imp__le__nat,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_889_less__imp__le__nat) ).
fof(fact_1130_tsub__eq,axiom,
! [X19,X18] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X18))
=> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X18),X19) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X18),X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1130_tsub__eq) ).
fof(fact_1166_succ__Pls,axiom,
succ(pls) = bit1(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1166_succ__Pls) ).
fof(fact_1131_zero__less__imp__eq__int,axiom,
! [X22] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X22))
=> ? [X29] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X29))
& X22 = hAPP_nat_int(semiri1621563631at_int,X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1131_zero__less__imp__eq__int) ).
fof(fact_966_Suc__diff__1,axiom,
! [X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X14))
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),one_one_nat)) = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_966_Suc__diff__1) ).
fof(fact_967_Suc__pred_H,axiom,
! [X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X14))
=> X14 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),one_one_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_967_Suc__pred_H) ).
fof(fact_1005_mult__Suc,axiom,
! [X15,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X15)),X14) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1005_mult__Suc) ).
fof(fact_149_finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X5),X10))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_finite__subset) ).
fof(fact_157_rev__finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X10))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X5),X10))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_rev__finite__subset) ).
fof(fact_148_finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X5),X10))
=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X10))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_finite__subset) ).
fof(fact_156_rev__finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X10))
=> ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X5),X10))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_rev__finite__subset) ).
fof(fact_150_finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X5),X10))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_finite__subset) ).
fof(fact_158_rev__finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X10))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X5),X10))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_rev__finite__subset) ).
fof(fact_151_finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X5),X10))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_finite__subset) ).
fof(fact_159_rev__finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X10))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X5),X10))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_rev__finite__subset) ).
fof(fact_154_finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_finite__subset) ).
fof(fact_162_rev__finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_rev__finite__subset) ).
fof(fact_155_finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_finite__subset) ).
fof(fact_163_rev__finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X10))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_rev__finite__subset) ).
fof(fact_153_finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_finite__subset) ).
fof(fact_161_rev__finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_rev__finite__subset) ).
fof(fact_152_finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_finite__subset) ).
fof(fact_160_rev__finite__subset,axiom,
! [X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X10))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_rev__finite__subset) ).
fof(fact_1111_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
! [X18,X19] : hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X18)),hAPP_nat_int(semiri1621563631at_int,X19)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X18),X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1111_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).
fof(fact_1108_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
! [X18,X19] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X18)),hAPP_nat_int(semiri1621563631at_int,X19)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X18),X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1108_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).
fof(fact_1106_zmult__int,axiom,
! [X15,X14] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X15)),hAPP_nat_int(semiri1621563631at_int,X14)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1106_zmult__int) ).
fof(fact_1112_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
! [X18,X19] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X18)),hAPP_nat_int(semiri1621563631at_int,X19)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X18),X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1112_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
fof(fact_1103_zadd__int,axiom,
! [X15,X14] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X15)),hAPP_nat_int(semiri1621563631at_int,X14)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1103_zadd__int) ).
fof(fact_1107_int__mult,axiom,
! [X15,X14] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X14)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X15)),hAPP_nat_int(semiri1621563631at_int,X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1107_int__mult) ).
fof(fact_824_le__iff__add,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17))
<=> ? [X119] : X17 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X25),X119) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_824_le__iff__add) ).
fof(fact_947_less__Suc0,axiom,
! [X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),hAPP_nat_nat(suc,zero_zero_nat)))
<=> X17 = zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_947_less__Suc0) ).
fof(fact_817_diff__add__cancel,axiom,
! [X115,X116] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X115),X116)),X116) = X115,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_817_diff__add__cancel) ).
fof(fact_818_add__diff__cancel,axiom,
! [X117,X118] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X117),X118)),X118) = X117,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_818_add__diff__cancel) ).
fof(fact_834_diff__add__inverse,axiom,
! [X14,X15] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X15)),X14) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_834_diff__add__inverse) ).
fof(fact_833_diff__add__inverse2,axiom,
! [X15,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X14)),X14) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_833_diff__add__inverse2) ).
fof(fact_1036_int__one__le__iff__zero__less,axiom,
! [X56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X56))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X56)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1036_int__one__le__iff__zero__less) ).
fof(fact_974_zero__induct,axiom,
! [X13,X16] :
( hBOOL(hAPP_nat_bool(X13,X16))
=> ( ! [X29] :
( hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(suc,X29)))
=> hBOOL(hAPP_nat_bool(X13,X29)) )
=> hBOOL(hAPP_nat_bool(X13,zero_zero_nat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_974_zero__induct) ).
fof(fact_665_image__constant,axiom,
! [X32,X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> image_nat_int(cOMBK_int_nat(X32),X5) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X32),bot_bot_fun_int_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_image__constant) ).
fof(fact_666_image__constant,axiom,
! [X32,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> image_pname_a(cOMBK_a_pname(X32),X5) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X32),bot_bot_fun_a_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_image__constant) ).
fof(fact_1031_pos__zmult__eq__1__iff,axiom,
! [X17,X25] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X25))
=> ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X25),X17) = one_one_int
<=> ( X25 = one_one_int
& X17 = one_one_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1031_pos__zmult__eq__1__iff) ).
fof(fact_1004_mult__Suc__right,axiom,
! [X15,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),hAPP_nat_nat(suc,X14)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1004_mult__Suc__right) ).
fof(fact_820_add__Suc,axiom,
! [X15,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X15)),X14) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_820_add__Suc) ).
fof(fact_958_diff__Suc,axiom,
! [X25,X17] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X25),hAPP_nat_nat(suc,X17)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X25),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_958_diff__Suc) ).
fof(fact_400_insert__absorb,axiom,
! [X8,X5] :
( is_fun_pname_bool(X5)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5))
=> hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X5) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_insert__absorb) ).
fof(fact_397_insert__absorb,axiom,
! [X8,X5] :
( is_fun_a_bool(X5)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5))
=> hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X5) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_insert__absorb) ).
fof(fact_0_assms_I1_J,axiom,
! [X3,X4] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X4))
=> hBOOL(hAPP_fun_a_bool_bool(p(X4),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
fof(fact_703_assms_I4_J,axiom,
! [X80] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X80),u))
=> hBOOL(wt(the_com(body(X80)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_703_assms_I4_J) ).
fof(fact_1175_one__is__num__one,axiom,
one_one_int = number_number_of_int(bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1175_one__is__num__one) ).
fof(fact_398_insert__absorb,axiom,
! [X8,X5] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X5))
=> hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X5) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_insert__absorb) ).
fof(fact_399_insert__absorb,axiom,
! [X8,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5))
=> hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X5) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_insert__absorb) ).
fof(fact_956_diff__is__0__eq_H,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14) = zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_956_diff__is__0__eq_H) ).
fof(fact_955_diff__is__0__eq,axiom,
! [X25,X17] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X25),X17) = zero_zero_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_955_diff__is__0__eq) ).
fof(fact_1145_zabs__less__one__iff,axiom,
! [X56] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X56)),one_one_int))
<=> X56 = zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1145_zabs__less__one__iff) ).
fof(fact_859_nat__neq__iff,axiom,
! [X25,X17] :
( X25 != X17
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_859_nat__neq__iff) ).
fof(fact_1049_zless__linear,axiom,
! [X18,X19] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X18),X19))
| X18 = X19
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X19),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1049_zless__linear) ).
fof(fact_785_the__elem__def,axiom,
! [X85] : hAPP_f1594865479ol_int(the_elem_int,X85) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,X85),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_785_the__elem__def) ).
fof(fact_784_the__elem__def,axiom,
! [X85] : hAPP_f22106695ol_nat(the_elem_nat,X85) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X85),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_784_the__elem__def) ).
fof(fact_783_the__elem__def,axiom,
! [X85] : hAPP_fun_a_bool_a(the_elem_a,X85) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,X85),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_783_the__elem__def) ).
fof(fact_307_linorder__linear,axiom,
! [X37,X38] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X37),X38))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X38),X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_linorder__linear) ).
fof(fact_129_nat__le__linear,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_nat__le__linear) ).
fof(fact_1045_zle__linear,axiom,
! [X98,X135] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X98),X135))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X135),X98)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1045_zle__linear) ).
fof(fact_306_linorder__linear,axiom,
! [X37,X38] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X37),X38))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X38),X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_linorder__linear) ).
fof(fact_694_finite_Osimps,axiom,
! [X8] :
( is_fun_pname_bool(X8)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X8))
<=> ( X8 = bot_bo844097828e_bool
| ? [X81,X78] :
( is_fun_pname_bool(X81)
& is_pname(X78)
& X8 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X78),X81)
& hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X81)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_finite_Osimps) ).
fof(fact_691_finite_Osimps,axiom,
! [X8] :
( is_fun_a_bool(X8)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X8))
<=> ( X8 = bot_bot_fun_a_bool
| ? [X81,X78] :
( is_fun_a_bool(X81)
& is_a(X78)
& X8 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X78),X81)
& hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X81)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_finite_Osimps) ).
fof(fact_377_mem__def,axiom,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
<=> hBOOL(hAPP_nat_bool(X5,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_mem__def) ).
fof(fact_376_mem__def,axiom,
! [X11,X5] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
<=> hBOOL(hAPP_int_bool(X5,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_mem__def) ).
fof(fact_379_mem__def,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
<=> hBOOL(hAPP_pname_bool(X5,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_mem__def) ).
fof(fact_378_mem__def,axiom,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
<=> hBOOL(hAPP_a_bool(X5,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_mem__def) ).
fof(fact_382_insert__absorb2,axiom,
! [X11,X5] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_insert__absorb2) ).
fof(fact_819_add__Suc__right,axiom,
! [X15,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),hAPP_nat_nat(suc,X14)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_819_add__Suc__right) ).
fof(fact_1143_int__diff__cases,axiom,
! [X98] :
~ ! [X35,X29] : X98 != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X35)),hAPP_nat_int(semiri1621563631at_int,X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1143_int__diff__cases) ).
fof(fact_172_diff__Suc__Suc,axiom,
! [X15,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X15)),hAPP_nat_nat(suc,X14)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_diff__Suc__Suc) ).
fof(fact_821_add__Suc__shift,axiom,
! [X15,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X15)),X14) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),hAPP_nat_nat(suc,X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_821_add__Suc__shift) ).
fof(fact_1146_neg__def,axiom,
! [X153] :
( hBOOL(hAPP_int_bool(nat_neg,X153))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X153),zero_zero_int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1146_neg__def) ).
fof(fact_1114_transfer__nat__int__set__relations_I1_J,axiom,
! [X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
<=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1114_transfer__nat__int__set__relations_I1_J) ).
fof(fact_748_folding__one_Osingleton,axiom,
! [X11,X9,X7] :
( is_a(X11)
=> ( hBOOL(finite_folding_one_a(X9,X7))
=> hAPP_fun_a_bool_a(X7,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_748_folding__one_Osingleton) ).
fof(fact_530_ex__in__conv,axiom,
! [X5] :
( is_fun_pname_bool(X5)
=> ( ? [X30] :
( is_pname(X30)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5)) )
<=> X5 != bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_ex__in__conv) ).
fof(fact_529_ex__in__conv,axiom,
! [X5] :
( is_fun_a_bool(X5)
=> ( ? [X30] :
( is_a(X30)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5)) )
<=> X5 != bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_ex__in__conv) ).
fof(fact_750_folding__one_Osingleton,axiom,
! [X11,X9,X7] :
( hBOOL(finite1626084323ne_int(X9,X7))
=> hAPP_f1594865479ol_int(X7,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_750_folding__one_Osingleton) ).
fof(fact_749_folding__one_Osingleton,axiom,
! [X11,X9,X7] :
( hBOOL(finite988810631ne_nat(X9,X7))
=> hAPP_f22106695ol_nat(X7,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_749_folding__one_Osingleton) ).
fof(fact_693_finite_Osimps,axiom,
! [X8] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X8))
<=> ( X8 = bot_bot_fun_nat_bool
| ? [X81,X78] :
( X8 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X78),X81)
& hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X81)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_finite_Osimps) ).
fof(fact_692_finite_Osimps,axiom,
! [X8] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X8))
<=> ( X8 = bot_bot_fun_int_bool
| ? [X81,X78] :
( X8 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X78),X81)
& hBOOL(hAPP_f448129468l_bool(finite_finite_int,X81)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_finite_Osimps) ).
fof(fact_1142_zero__le__imp__eq__int,axiom,
! [X22] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X22))
=> ? [X29] : X22 = hAPP_nat_int(semiri1621563631at_int,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1142_zero__le__imp__eq__int) ).
fof(fact_1141_nonneg__eq__int,axiom,
! [X98] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X98))
=> ~ ! [X35] : X98 != hAPP_nat_int(semiri1621563631at_int,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1141_nonneg__eq__int) ).
fof(fact_1140_nonneg__int__cases,axiom,
! [X22] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X22))
=> ~ ! [X29] : X22 != hAPP_nat_int(semiri1621563631at_int,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1140_nonneg__int__cases) ).
fof(fact_972_gr0__implies__Suc,axiom,
! [X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X14))
=> ? [X35] : X14 = hAPP_nat_nat(suc,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_972_gr0__implies__Suc) ).
fof(fact_946_gr0__conv__Suc,axiom,
! [X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X17))
<=> ? [X35] : X17 = hAPP_nat_nat(suc,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_946_gr0__conv__Suc) ).
fof(fact_589_singleton__inject,axiom,
! [X8,X31] :
( ( is_a(X8)
& is_a(X31) )
=> ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X31),bot_bot_fun_a_bool)
=> X8 = X31 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_singleton__inject) ).
fof(fact_1150_abs__zmult__eq__1,axiom,
! [X15,X14] :
( abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X15),X14)) = one_one_int
=> abs_abs_int(X15) = one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1150_abs__zmult__eq__1) ).
fof(fact_625_bot__unique,axiom,
! [X8] :
( is_fun_a_bool(X8)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X8),bot_bot_fun_a_bool))
<=> X8 = bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_bot__unique) ).
fof(fact_621_le__bot,axiom,
! [X8] :
( is_fun_a_bool(X8)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X8),bot_bot_fun_a_bool))
=> X8 = bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_le__bot) ).
fof(fact_611_subset__empty,axiom,
! [X5] :
( is_fun_a_bool(X5)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),bot_bot_fun_a_bool))
<=> X5 = bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_subset__empty) ).
fof(fact_863_less__not__refl3,axiom,
! [X121,X122] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X121),X122))
=> X121 != X122 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_863_less__not__refl3) ).
fof(fact_862_less__not__refl2,axiom,
! [X14,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X15))
=> X15 != X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_862_less__not__refl2) ).
fof(fact_20_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
fof(fact_15_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_finite__imageI) ).
fof(fact_10_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_finite__imageI) ).
fof(fact_19_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_finite__imageI) ).
fof(fact_14_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_finite__imageI) ).
fof(fact_9_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_finite__imageI) ).
fof(fact_16_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_finite__imageI) ).
fof(fact_21_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_finite__imageI) ).
fof(fact_11_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_finite__imageI) ).
fof(fact_17_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_finite__imageI) ).
fof(fact_22_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_finite__imageI) ).
fof(fact_12_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite__imageI) ).
fof(fact_32_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_finite__imageI) ).
fof(fact_31_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_finite__imageI) ).
fof(fact_30_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_finite__imageI) ).
fof(fact_29_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_finite__imageI) ).
fof(fact_28_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_finite__imageI) ).
fof(fact_39_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_finite__imageI) ).
fof(fact_37_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_finite__imageI) ).
fof(fact_36_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_finite__imageI) ).
fof(fact_35_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_finite__imageI) ).
fof(fact_34_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X7))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_finite__imageI) ).
fof(fact_33_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_finite__imageI) ).
fof(fact_25_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_finite__imageI) ).
fof(fact_24_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_finite__imageI) ).
fof(fact_26_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_finite__imageI) ).
fof(fact_27_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_finite__imageI) ).
fof(fact_23_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_finite__imageI) ).
fof(fact_13_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_finite__imageI) ).
fof(fact_18_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_finite__imageI) ).
fof(fact_38_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X6,X7))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_finite__imageI) ).
fof(fact_936_gr__implies__not0,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> X14 != zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_936_gr__implies__not0) ).
fof(fact_528_ex__in__conv,axiom,
! [X5] :
( ? [X30] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
<=> X5 != bot_bot_fun_nat_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_ex__in__conv) ).
fof(fact_527_ex__in__conv,axiom,
! [X5] :
( ? [X30] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X5))
<=> X5 != bot_bot_fun_int_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_ex__in__conv) ).
fof(fact_669_diff__eq__diff__eq,axiom,
! [X8,X31,X32,X73] :
( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X8),X31) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X32),X73)
=> ( X8 = X31
<=> X32 = X73 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_diff__eq__diff__eq) ).
fof(fact_855_lessI,axiom,
! [X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),hAPP_nat_nat(suc,X14))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_855_lessI) ).
fof(fact_982_mult__cancel2,axiom,
! [X25,X16,X17] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X25),X16) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X17),X16)
<=> ( X25 = X17
| X16 = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_982_mult__cancel2) ).
fof(fact_1057_nat__mult__eq__cancel__disj,axiom,
! [X16,X25,X17] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X25) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X17)
<=> ( X16 = zero_zero_nat
| X25 = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1057_nat__mult__eq__cancel__disj) ).
fof(fact_981_mult__cancel1,axiom,
! [X16,X25,X17] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X25) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X16),X17)
<=> ( X25 = X17
| X16 = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_981_mult__cancel1) ).
fof(fact_926_diffs0__imp__equal,axiom,
! [X15,X14] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14) = zero_zero_nat
=> ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),X15) = zero_zero_nat
=> X15 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_926_diffs0__imp__equal) ).
fof(fact_796_add__right__imp__eq,axiom,
! [X95,X96,X97] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X95),X96) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X97),X96)
=> X95 = X97 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_796_add__right__imp__eq) ).
fof(fact_790_add__right__cancel,axiom,
! [X31,X8,X32] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X31),X8) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X32),X8)
<=> X31 = X32 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_790_add__right__cancel) ).
fof(fact_802_nat__add__right__cancel,axiom,
! [X25,X16,X17] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X25),X16) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X17),X16)
<=> X25 = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_802_nat__add__right__cancel) ).
fof(fact_797_add__right__imp__eq,axiom,
! [X95,X96,X97] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X95),X96) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X97),X96)
=> X95 = X97 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_797_add__right__imp__eq) ).
fof(fact_791_add__right__cancel,axiom,
! [X31,X8,X32] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X31),X8) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X32),X8)
<=> X31 = X32 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_791_add__right__cancel) ).
fof(fact_794_add__imp__eq,axiom,
! [X92,X93,X94] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X92),X93) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X92),X94)
=> X93 = X94 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_794_add__imp__eq) ).
fof(fact_792_add__left__imp__eq,axiom,
! [X89,X90,X91] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X89),X90) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X89),X91)
=> X90 = X91 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_792_add__left__imp__eq) ).
fof(fact_788_add__left__cancel,axiom,
! [X8,X31,X32] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X8),X31) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X8),X32)
<=> X31 = X32 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_788_add__left__cancel) ).
fof(fact_801_nat__add__left__cancel,axiom,
! [X16,X25,X17] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X16),X25) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X16),X17)
<=> X25 = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_801_nat__add__left__cancel) ).
fof(fact_795_add__imp__eq,axiom,
! [X92,X93,X94] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X92),X93) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X92),X94)
=> X93 = X94 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_795_add__imp__eq) ).
fof(fact_793_add__left__imp__eq,axiom,
! [X89,X90,X91] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X89),X90) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X89),X91)
=> X90 = X91 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_793_add__left__imp__eq) ).
fof(fact_789_add__left__cancel,axiom,
! [X8,X31,X32] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X8),X31) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X8),X32)
<=> X31 = X32 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_789_add__left__cancel) ).
fof(fact_924_le__0__eq,axiom,
! [X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X17),zero_zero_nat))
<=> X17 = zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_924_le__0__eq) ).
fof(fact_624_bot__unique,axiom,
! [X8] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X8),bot_bot_nat))
<=> X8 = bot_bot_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_bot__unique) ).
fof(fact_620_le__bot,axiom,
! [X74] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X74),bot_bot_nat))
=> X74 = bot_bot_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_le__bot) ).
fof(fact_622_bot__unique,axiom,
! [X8] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X8),bot_bot_fun_nat_bool))
<=> X8 = bot_bot_fun_nat_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_bot__unique) ).
fof(fact_618_le__bot,axiom,
! [X8] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X8),bot_bot_fun_nat_bool))
=> X8 = bot_bot_fun_nat_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_le__bot) ).
fof(fact_609_subset__empty,axiom,
! [X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),bot_bot_fun_nat_bool))
<=> X5 = bot_bot_fun_nat_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_subset__empty) ).
fof(fact_623_bot__unique,axiom,
! [X8] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X8),bot_bot_fun_int_bool))
<=> X8 = bot_bot_fun_int_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_bot__unique) ).
fof(fact_619_le__bot,axiom,
! [X8] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X8),bot_bot_fun_int_bool))
=> X8 = bot_bot_fun_int_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_le__bot) ).
fof(fact_610_subset__empty,axiom,
! [X5] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),bot_bot_fun_int_bool))
<=> X5 = bot_bot_fun_int_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_subset__empty) ).
fof(fact_923_zero__less__Suc,axiom,
! [X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X14))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_923_zero__less__Suc) ).
fof(fact_1118_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
! [X98] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X98))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1118_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
fof(fact_1096_zero__zle__int,axiom,
! [X14] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X14))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1096_zero__zle__int) ).
fof(fact_591_singleton__inject,axiom,
! [X8,X31] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X31),bot_bot_fun_int_bool)
=> X8 = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_591_singleton__inject) ).
fof(fact_590_singleton__inject,axiom,
! [X8,X31] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X31),bot_bot_fun_nat_bool)
=> X8 = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_singleton__inject) ).
fof(fact_938_neq0__conv,axiom,
! [X17] :
( X17 != zero_zero_nat
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_938_neq0__conv) ).
fof(fact_954_diff__add__0,axiom,
! [X14,X15] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X15)) = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_954_diff__add__0) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
! [X159,X160,X161] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X159,X160),X161) = hAPP_bool_bool(hAPP_f1748468828l_bool(X159,X161),hAPP_f54304608l_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
! [X159,X160,X161] : hAPP_f448129468l_bool(cOMBS_1912792529l_bool(X159,X160),X161) = hAPP_bool_bool(hAPP_f1721100032l_bool(X159,X161),hAPP_f448129468l_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O,axiom,
! [X159,X160,X161] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X159,X160),X161) = hAPP_bool_bool(hAPP_f1476298914l_bool(X159,X161),hAPP_f1664156314l_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_,axiom,
! [X159,X160,X161] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X159,X160),X161) = hAPP_bool_bool(hAPP_f198738859l_bool(X159,X161),hAPP_fun_a_bool_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_) ).
fof(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [X159,X160,X161] : hAPP_nat_bool(cOMBS_nat_bool_bool(X159,X160),X161) = hAPP_bool_bool(hAPP_n1006566506l_bool(X159,X161),hAPP_nat_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
fof(help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [X159,X160,X161] : hAPP_int_bool(cOMBS_int_bool_bool(X159,X160),X161) = hAPP_bool_bool(hAPP_i68813070l_bool(X159,X161),hAPP_int_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [X159,X160,X161] : hAPP_pname_bool(cOMBS_568398431l_bool(X159,X160),X161) = hAPP_bool_bool(hAPP_p393069232l_bool(X159,X161),hAPP_pname_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
fof(help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [X159,X160,X161] : hAPP_a_bool(cOMBS_a_bool_bool(X159,X160),X161) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X159,X161),hAPP_a_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
fof(fact_1193_rel__simps_I2_J,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1193_rel__simps_I2_J) ).
fof(fact_950_add__is__1,axiom,
! [X25,X17] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X25),X17) = hAPP_nat_nat(suc,zero_zero_nat)
<=> ( ( X25 = hAPP_nat_nat(suc,zero_zero_nat)
& X17 = zero_zero_nat )
| ( X25 = zero_zero_nat
& X17 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_950_add__is__1) ).
fof(fact_949_one__is__add,axiom,
! [X25,X17] :
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X25),X17)
<=> ( ( X25 = hAPP_nat_nat(suc,zero_zero_nat)
& X17 = zero_zero_nat )
| ( X25 = zero_zero_nat
& X17 = hAPP_nat_nat(suc,zero_zero_nat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_949_one__is__add) ).
fof(fact_1124_int__Suc,axiom,
! [X15] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X15)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1124_int__Suc) ).
fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool__007,axiom,
! [X159,X160,X161] : hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(X159),X160),X161) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool__007) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__008,axiom,
! [X159,X160,X161] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(X159),X160),X161) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__008) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H,axiom,
! [X159,X160,X161] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X159),X160),X161) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__H,axiom,
! [X159,X160,X161] : hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(X159),X160),X161) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__H) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom,
! [X159,X160,X161] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X159),X160),X161) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool,axiom,
! [X159,X160,X161] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X159),X160),X161) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
! [X159,X160,X161] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X159),X160),X161) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
! [X159,X160,X161] : hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(X159),X160),X161) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
! [X159,X160,X161] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X159),X160),X161) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO,axiom,
! [X159,X160,X161] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X159),X160),X161) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Int__Oint_000tc__HOL__Obool_U,axiom,
! [X159,X160,X161] : hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(X159),X160),X161) = hAPP_int_bool(hAPP_n1082236369t_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Int__Oint_000tc__HOL__Obool_U) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__,axiom,
! [X159,X160,X161] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(X159),X160),X161) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,axiom,
! [X159,X160,X161] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(X159),X160),X161) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_,axiom,
! [X159,X160,X161] : hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(X159),X160),X161) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
! [X159,X160,X161] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X159),X160),X161) = hAPP_nat_bool(hAPP_n1699378549t_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [X159,X160,X161] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X159),X160),X161) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__,axiom,
! [X159,X160,X161] : hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(X159),X160),X161) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__) ).
fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,axiom,
! [X159,X160,X161] : hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(X159),X160),X161) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).
fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [X159,X160,X161] : hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(X159),X160),X161) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000t__a_000tc__HOL__Obool_U,axiom,
! [X159,X160,X161] : hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(X159),X160),X161) = hAPP_a_bool(hAPP_int_fun_a_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000t__a_000tc__HOL__Obool_U) ).
fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U,axiom,
! [X159,X160,X161] : hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(X159),X160),X161) = hAPP_int_bool(hAPP_i1948725293t_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U) ).
fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_,axiom,
! [X159,X160,X161] : hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(X159),X160),X161) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom,
! [X159,X160,X161] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X159),X160),X161) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U,axiom,
! [X159,X160,X161] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X159),X160),X161) = hAPP_pname_bool(hAPP_p61793385e_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U,axiom,
! [X159,X160,X161] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X159),X160),X161) = hAPP_a_bool(hAPP_p1534023578a_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) ).
fof(help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a,axiom,
! [X159,X160,X161] : hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(X159),X160),X161) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a) ).
fof(help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo,axiom,
! [X159,X160,X161] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X159),X160),X161) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).
fof(help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U,axiom,
! [X159,X160,X161] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X159),X160),X161) = hAPP_a_bool(hAPP_a_fun_a_bool(X159,X161),X160),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).
fof(fact_696_the__elem__eq,axiom,
! [X11] :
( is_a(X11)
=> hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_the__elem__eq) ).
fof(fact_997_mult__eq__1__iff,axiom,
! [X25,X17] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X25),X17) = hAPP_nat_nat(suc,zero_zero_nat)
<=> ( X25 = hAPP_nat_nat(suc,zero_zero_nat)
& X17 = hAPP_nat_nat(suc,zero_zero_nat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_997_mult__eq__1__iff) ).
fof(fact_746_diff__Suc__1,axiom,
! [X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X14)),one_one_nat) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_746_diff__Suc__1) ).
fof(fact_698_the__elem__eq,axiom,
! [X11] : hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698_the__elem__eq) ).
fof(fact_697_the__elem__eq,axiom,
! [X11] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_the__elem__eq) ).
fof(help_fimplies_1_1_U,axiom,
! [X160,X159] :
( hBOOL(X159)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X159),X160)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011,axiom,
! [X159,X160,X161] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X159,X160),X161) = hAPP_b589554111l_bool(X159,hAPP_f1664156314l_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010,axiom,
! [X159,X160,X161] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X159,X160),X161) = hAPP_b589554111l_bool(X159,hAPP_f54304608l_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009,axiom,
! [X159,X160,X161] : hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(X159,X160),X161) = hAPP_b589554111l_bool(X159,hAPP_f448129468l_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__013,axiom,
! [X159,X160,X161] : hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(X159,X160),X161) = hAPP_f284875647l_bool(X159,hAPP_n1082236369t_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__013) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
! [X159,X160,X161] : hAPP_i1718399025l_bool(cOMBB_516767136ol_int(X159,X160),X161) = hAPP_f103356543l_bool(X159,hAPP_i418383825t_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006,axiom,
! [X159,X160,X161] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X159,X160),X161) = hAPP_b589554111l_bool(X159,hAPP_fun_a_bool_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_005,axiom,
! [X159,X160,X161] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X159,X160),X161) = hAPP_b589554111l_bool(X159,hAPP_pname_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_005) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_004,axiom,
! [X159,X160,X161] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X159,X160),X161) = hAPP_b589554111l_bool(X159,hAPP_nat_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_004) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_003,axiom,
! [X159,X160,X161] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X159,X160),X161) = hAPP_b589554111l_bool(X159,hAPP_int_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_003) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
! [X159,X160,X161] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X159,X160),X161) = hAPP_b589554111l_bool(X159,hAPP_a_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
fof(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_,axiom,
! [X159,X160,X161] : hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(X159,X160),X161) = hAPP_i1948725293t_bool(X159,hAPP_nat_int(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
! [X159,X160,X161] : hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(X159,X160),X161) = hAPP_f284875647l_bool(X159,hAPP_i1948725293t_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO,axiom,
! [X159,X160,X161] : hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(X159,X160),X161) = hAPP_n215258509l_bool(X159,hAPP_nat_nat(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__014,axiom,
! [X159,X160,X161] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(X159,X160),X161) = hAPP_f103356543l_bool(X159,hAPP_n1699378549t_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__014) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [X159,X160,X161] : hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(X159,X160),X161) = hAPP_n1699378549t_bool(X159,hAPP_nat_nat(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_015,axiom,
! [X159,X160,X161] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(X159,X160),X161) = hAPP_f434788991l_bool(X159,hAPP_n1025906991e_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_015) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___012,axiom,
! [X159,X160,X161] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(X159,X160),X161) = hAPP_f1631501043l_bool(X159,hAPP_nat_fun_a_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___012) ).
fof(help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
! [X159,X160,X161] : hAPP_nat_bool(cOMBB_int_bool_nat(X159,X160),X161) = hAPP_int_bool(X159,hAPP_nat_int(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
! [X159,X160,X161] : hAPP_nat_bool(cOMBB_955900739ol_nat(X159,X160),X161) = hAPP_f54304608l_bool(X159,hAPP_n1699378549t_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
! [X159,X160,X161] : hAPP_nat_bool(cOMBB_bool_bool_nat(X159,X160),X161) = hAPP_bool_bool(X159,hAPP_nat_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
! [X159,X160,X161] : hAPP_i1587699435l_bool(cOMBB_607112096ol_int(X159,X160),X161) = hAPP_f434788991l_bool(X159,hAPP_i7355787e_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__,axiom,
! [X159,X160,X161] : hAPP_i888906320l_bool(cOMBB_313729068ol_int(X159,X160),X161) = hAPP_f1631501043l_bool(X159,hAPP_int_fun_a_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).
fof(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Int__Oint,axiom,
! [X159,X160,X161] : hAPP_int_fun_a_bool(cOMBB_375279840ol_int(X159,X160),X161) = hAPP_a_fun_a_bool(X159,hAPP_int_a(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Int__Oint) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
! [X159,X160,X161] : hAPP_int_bool(cOMBB_1418110531ol_int(X159,X160),X161) = hAPP_f448129468l_bool(X159,hAPP_i1948725293t_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Int__Oint_U,axiom,
! [X159,X160,X161] : hAPP_int_bool(cOMBB_bool_bool_int(X159,X160),X161) = hAPP_bool_bool(X159,hAPP_int_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Int__Oint_U) ).
fof(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna,axiom,
! [X159,X160,X161] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X159,X160),X161) = hAPP_a_fun_a_bool(X159,hAPP_pname_a(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U,axiom,
! [X159,X160,X161] : hAPP_pname_bool(cOMBB_647938656_pname(X159,X160),X161) = hAPP_bool_bool(X159,hAPP_pname_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__,axiom,
! [X159,X160,X161] : hAPP_a_bool(cOMBB_1273333599bool_a(X159,X160),X161) = hAPP_fun_a_bool_bool(X159,hAPP_a_fun_a_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U,axiom,
! [X159,X160,X161] : hAPP_a_bool(cOMBB_bool_bool_a(X159,X160),X161) = hAPP_bool_bool(X159,hAPP_a_bool(X160,X161)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X18),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
fof(fact_408_equalityD1,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_equalityD1) ).
fof(fact_314_order__eq__refl,axiom,
! [X11,X39] :
( X11 = X39
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_order__eq__refl) ).
fof(fact_411_equalityD2,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_equalityD2) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X18),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T) ).
fof(fact_407_equalityD1,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_equalityD1) ).
fof(fact_313_order__eq__refl,axiom,
! [X11,X39] :
( X11 = X39
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X11),X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_order__eq__refl) ).
fof(fact_410_equalityD2,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_equalityD2) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X18),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
fof(help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X18),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
fof(fact_409_equalityD1,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_equalityD1) ).
fof(fact_317_order__eq__refl,axiom,
! [X11,X39] :
( X11 = X39
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_order__eq__refl) ).
fof(fact_412_equalityD2,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_equalityD2) ).
fof(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X18),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
fof(fact_316_order__eq__refl,axiom,
! [X40,X41] :
( X40 = X41
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X40),X41)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_order__eq__refl) ).
fof(fact_128_eq__imp__le,axiom,
! [X15,X14] :
( X15 = X14
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_eq__imp__le) ).
fof(help_fequal_2_1_fequal_000tc__Int__Oint_T,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X18),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Int__Oint_T) ).
fof(fact_315_order__eq__refl,axiom,
! [X40,X41] :
( X40 = X41
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X40),X41)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_order__eq__refl) ).
fof(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X18),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).
fof(help_fequal_2_1_fequal_000t__a_T,axiom,
! [X18,X19] :
( X18 != X19
| hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X18),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).
fof(fact_663_nat__case__Suc,axiom,
! [X76,X77,X20] : hAPP_nat_nat(nat_case_nat(X76,X77),hAPP_nat_nat(suc,X20)) = hAPP_nat_nat(X77,X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_nat__case__Suc) ).
fof(fact_402_subset__refl,axiom,
! [X5] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_subset__refl) ).
fof(fact_302_order__refl,axiom,
! [X11] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_order__refl) ).
fof(fact_401_subset__refl,axiom,
! [X5] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_subset__refl) ).
fof(fact_301_order__refl,axiom,
! [X11] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X11),X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_order__refl) ).
fof(fact_403_subset__refl,axiom,
! [X5] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_subset__refl) ).
fof(fact_305_order__refl,axiom,
! [X11] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_order__refl) ).
fof(fact_304_order__refl,axiom,
! [X36] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X36),X36)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_order__refl) ).
fof(fact_130_le__refl,axiom,
! [X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_le__refl) ).
fof(fact_1044_zle__refl,axiom,
! [X135] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X135),X135)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1044_zle__refl) ).
fof(fact_303_order__refl,axiom,
! [X36] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X36),X36)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_order__refl) ).
fof(fact_1021_zmult__commute,axiom,
! [X98,X135] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X98),X135) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X135),X98),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1021_zmult__commute) ).
fof(fact_1043_zadd__commute,axiom,
! [X98,X135] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X98),X135) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X135),X98),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1043_zadd__commute) ).
fof(fact_1016_nat__mult__commute,axiom,
! [X15,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X14) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1016_nat__mult__commute) ).
fof(fact_798_nat__add__commute,axiom,
! [X15,X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X14) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_798_nat__add__commute) ).
fof(fact_935_gr0I,axiom,
! [X14] :
( X14 != zero_zero_nat
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_935_gr0I) ).
fof(fact_636_singleton__conv,axiom,
! [X8] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_singleton__conv) ).
fof(fact_626_bot__least,axiom,
! [X8] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_bot__least) ).
fof(fact_501_empty__subsetI,axiom,
! [X5] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_empty__subsetI) ).
fof(fact_627_bot__least,axiom,
! [X8] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_bot__least) ).
fof(fact_502_empty__subsetI,axiom,
! [X5] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_empty__subsetI) ).
fof(fact_629_bot__least,axiom,
! [X8] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_bot__least) ).
fof(fact_503_empty__subsetI,axiom,
! [X5] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_empty__subsetI) ).
fof(fact_925_less__eq__nat_Osimps_I1_J,axiom,
! [X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_925_less__eq__nat_Osimps_I1_J) ).
fof(fact_922_le0,axiom,
! [X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_922_le0) ).
fof(fact_628_bot__least,axiom,
! [X75] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),X75)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_bot__least) ).
fof(fact_668_image__constant__conv,axiom,
! [X32,X5] :
( is_fun_pname_bool(X5)
=> ( ( X5 = bot_bo844097828e_bool
=> image_pname_a(cOMBK_a_pname(X32),X5) = bot_bot_fun_a_bool )
& ( X5 != bot_bo844097828e_bool
=> image_pname_a(cOMBK_a_pname(X32),X5) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X32),bot_bot_fun_a_bool) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_image__constant__conv) ).
fof(fact_1007_mult__eq__self__implies__10,axiom,
! [X15,X14] :
( X15 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),X14)
=> ( X14 = one_one_nat
| X15 = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1007_mult__eq__self__implies__10) ).
fof(fact_639_singleton__conv2,axiom,
! [X8] : collect_a(hAPP_a_fun_a_bool(fequal_a,X8)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_singleton__conv2) ).
fof(fact_980_mult__is__0,axiom,
! [X25,X17] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X25),X17) = zero_zero_nat
<=> ( X25 = zero_zero_nat
| X17 = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_980_mult__is__0) ).
fof(fact_931_add__eq__self__zero,axiom,
! [X15,X14] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X14) = X15
=> X14 = zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_931_add__eq__self__zero) ).
fof(fact_932_add__is__0,axiom,
! [X25,X17] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X25),X17) = zero_zero_nat
<=> ( X25 = zero_zero_nat
& X17 = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_932_add__is__0) ).
fof(fact_993_nat__mult__eq__1__iff,axiom,
! [X25,X17] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X25),X17) = one_one_nat
<=> ( X25 = one_one_nat
& X17 = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_993_nat__mult__eq__1__iff) ).
fof(fact_995_nat__1__eq__mult__iff,axiom,
! [X25,X17] :
( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X25),X17)
<=> ( X25 = one_one_nat
& X17 = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_995_nat__1__eq__mult__iff) ).
fof(fact_605_insert__not__empty,axiom,
! [X8,X5] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X5) != bot_bot_fun_int_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_insert__not__empty) ).
fof(fact_604_insert__not__empty,axiom,
! [X8,X5] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X5) != bot_bot_fun_nat_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_insert__not__empty) ).
fof(fact_603_insert__not__empty,axiom,
! [X8,X5] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X5) != bot_bot_fun_a_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_insert__not__empty) ).
fof(fact_607_empty__not__insert,axiom,
! [X8,X5] : bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_empty__not__insert) ).
fof(fact_608_empty__not__insert,axiom,
! [X8,X5] : bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_empty__not__insert) ).
fof(fact_606_empty__not__insert,axiom,
! [X8,X5] : bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_empty__not__insert) ).
fof(fact_667_image__constant__conv,axiom,
! [X32,X5] :
( ( X5 = bot_bot_fun_nat_bool
=> image_nat_int(cOMBK_int_nat(X32),X5) = bot_bot_fun_int_bool )
& ( X5 != bot_bot_fun_nat_bool
=> image_nat_int(cOMBK_int_nat(X32),X5) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X32),bot_bot_fun_int_bool) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_image__constant__conv) ).
fof(fact_850_Suc__eq__plus1,axiom,
! [X14] : hAPP_nat_nat(suc,X14) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_850_Suc__eq__plus1) ).
fof(fact_1113_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
! [X5] : hAPP_f22106695ol_nat(finite_card_nat,X5) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1113_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).
fof(fact_913_less__eq__Suc__le__raw,axiom,
! [X30] : hAPP_n1699378549t_bool(ord_less_nat,X30) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X30)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_913_less__eq__Suc__le__raw) ).
fof(help_If_1_1_If_000tc__Nat__Onat_T,axiom,
! [X18,X19] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X18),X19) = X18,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__Nat__Onat_T) ).
fof(help_If_2_1_If_000tc__Nat__Onat_T,axiom,
! [X18,X19] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X18),X19) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Nat__Onat_T) ).
fof(fact_849_Suc__eq__plus1__left,axiom,
! [X14] : hAPP_nat_nat(suc,X14) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_849_Suc__eq__plus1__left) ).
fof(fact_541_bot__fun__def,axiom,
! [X30] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X30))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_bot__fun__def) ).
fof(fact_535_bot__apply,axiom,
! [X11] :
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X11))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_bot__apply) ).
fof(fact_542_bot__fun__def,axiom,
! [X30] :
( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X30))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_bot__fun__def) ).
fof(fact_536_bot__apply,axiom,
! [X11] :
( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X11))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_bot__apply) ).
fof(fact_543_bot__fun__def,axiom,
! [X30] :
( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X30))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_bot__fun__def) ).
fof(fact_537_bot__apply,axiom,
! [X11] :
( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X11))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_bot__apply) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool,hypothesis,
! [X1,X2] :
( ( is_fun1661590463l_bool(X1)
& is_fun_pname_bool(X2) )
=> is_bool(hAPP_f1664156314l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool,hypothesis,
! [X1,X2] :
( ( is_fun949378684l_bool(X1)
& is_fun_a_bool(X2) )
=> is_bool(hAPP_fun_a_bool_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool,axiom,
! [X1,X2] :
( ( is_fun_pname_bool(X1)
& is_pname(X2) )
=> is_bool(hAPP_pname_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) ).
fof(gsy_c_hAPP_000t__a_000tc__HOL__Obool,axiom,
! [X1,X2] :
( ( is_fun_a_bool(X1)
& is_a(X2) )
=> is_bool(hAPP_a_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__HOL__Obool) ).
fof(fact_516_Diff__empty,axiom,
! [X5] :
( is_fun_a_bool(X5)
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),bot_bot_fun_a_bool) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_Diff__empty) ).
fof(fact_1139_transfer__int__nat__relations_I1_J,axiom,
! [X11,X39] :
( hAPP_nat_int(semiri1621563631at_int,X11) = hAPP_nat_int(semiri1621563631at_int,X39)
<=> X11 = X39 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1139_transfer__int__nat__relations_I1_J) ).
fof(fact_1132_int__int__eq,axiom,
! [X25,X17] :
( hAPP_nat_int(semiri1621563631at_int,X25) = hAPP_nat_int(semiri1621563631at_int,X17)
<=> X25 = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1132_int__int__eq) ).
fof(fact_123_nat_Oinject,axiom,
! [X20,X21] :
( hAPP_nat_nat(suc,X20) = hAPP_nat_nat(suc,X21)
<=> X20 = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_nat_Oinject) ).
fof(fact_122_Suc__inject,axiom,
! [X18,X19] :
( hAPP_nat_nat(suc,X18) = hAPP_nat_nat(suc,X19)
=> X18 = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Suc__inject) ).
fof(fact_1136_transfer__nat__int__set__relations_I3_J,axiom,
! [X5,X10] :
( X5 = X10
<=> image_nat_int(semiri1621563631at_int,X5) = image_nat_int(semiri1621563631at_int,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1136_transfer__nat__int__set__relations_I3_J) ).
fof(fact_1152_abs__int__eq,axiom,
! [X15] : abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X15)) = hAPP_nat_int(semiri1621563631at_int,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1152_abs__int__eq) ).
fof(fact_1149_not__neg__0,axiom,
~ hBOOL(hAPP_int_bool(nat_neg,zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1149_not__neg__0) ).
fof(fact_1148_not__neg__1,axiom,
~ hBOOL(hAPP_int_bool(nat_neg,one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1148_not__neg__1) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_pname(hAPP_f1297739591_pname(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname,axiom,
! [X1,X2] :
( is_pname(X2)
=> is_pname(hAPP_pname_pname(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname) ).
fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_a(hAPP_fun_a_bool_a(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000t__a,hypothesis,
! [X1,X2] :
( is_pname(X2)
=> is_a(hAPP_pname_a(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000t__a) ).
fof(gsy_c_hAPP_000t__a_000t__a,axiom,
! [X1,X2] :
( is_a(X2)
=> is_a(hAPP_a_a(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000t__a) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_002,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun1661590463l_bool(hAPP_f559147733l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_002) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun1661590463l_bool(hAPP_f434788991l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,hypothesis,
! [X1,X2] :
( is_pname(X2)
=> is_fun1661590463l_bool(hAPP_p338031245l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
fof(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun1661590463l_bool(image_47868345e_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_) ).
fof(gsy_c_Set_Oimage_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun1661590463l_bool(image_819518260e_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun1661590463l_bool(cOMBS_350070575l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_bool(hAPP_f1935102916l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_bool(hAPP_f621171935l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
! [X1,X2] :
( is_bool(X2)
=> is_bool(hAPP_bool_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___001,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun949378684l_bool(hAPP_f2117159681l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___001) ).
fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL,hypothesis,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun949378684l_bool(hAPP_f1631501043l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL) ).
fof(gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J,hypothesis,
! [X1,X2] :
( is_a(X2)
=> is_fun949378684l_bool(hAPP_a85458249l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J) ).
fof(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun949378684l_bool(image_112932426a_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(gsy_c_Set_Oimage_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun949378684l_bool(image_a_fun_a_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun949378684l_bool(cOMBS_1035972772l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_pname_bool(hAPP_f759274231e_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [X1,X2] :
( is_pname(X2)
=> is_fun_pname_bool(hAPP_p61793385e_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [X1,X2] :
( is_a(X2)
=> is_fun_pname_bool(hAPP_a93125764e_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun_pname_bool(image_1283814551_pname(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam) ).
fof(gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun_pname_bool(image_1854862208_pname(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
fof(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_pname_bool(image_pname_pname(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname) ).
fof(gsy_c_Set_Oimage_000t__a_000tc__Com__Opname,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_pname_bool(image_a_pname(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__Com__Opname) ).
fof(gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_pname_bool(cOMBS_568398431l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool) ).
fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_pname_bool(cOMBB_647938656_pname(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname) ).
fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J,hypothesis,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_a_bool(hAPP_f2050579477a_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1,X2] :
( is_pname(X2)
=> is_fun_a_bool(hAPP_p1534023578a_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1,X2] :
( is_a(X2)
=> is_fun_a_bool(hAPP_a_fun_a_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun_a_bool(image_876012084bool_a(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a) ).
fof(gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun_a_bool(image_fun_a_bool_a(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a) ).
fof(gsy_c_Set_Oimage_000tc__Com__Opname_000t__a,hypothesis,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_a_bool(image_pname_a(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000t__a) ).
fof(gsy_c_Set_Oimage_000t__a_000t__a,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_a_bool(image_a_a(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000t__a_000t__a) ).
fof(gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_a_bool(cOMBS_a_bool_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool) ).
fof(gsy_c_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__a,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X1)
=> is_fun_a_bool(cOMBB_1273333599bool_a(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__a) ).
fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_a_bool(cOMBB_bool_bool_a(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a) ).
fof(fact_927_diff__self__eq__0,axiom,
! [X15] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X15) = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_927_diff__self__eq__0) ).
fof(fact_512_Diff__cancel,axiom,
! [X5] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X5) = bot_bot_fun_int_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_Diff__cancel) ).
fof(fact_511_Diff__cancel,axiom,
! [X5] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X5) = bot_bot_fun_nat_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_Diff__cancel) ).
fof(fact_513_Diff__cancel,axiom,
! [X5] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X5) = bot_bot_fun_a_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_Diff__cancel) ).
fof(fact_1020_zmult__1__right,axiom,
! [X98] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X98),one_one_int) = X98,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1020_zmult__1__right) ).
fof(fact_1186_add__Pls__right,axiom,
! [X22] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X22),pls) = X22,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1186_add__Pls__right) ).
fof(fact_1033_zadd__0__right,axiom,
! [X98] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X98),zero_zero_int) = X98,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1033_zadd__0__right) ).
fof(fact_1184_diff__bin__simps_I1_J,axiom,
! [X22] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X22),pls) = X22,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1184_diff__bin__simps_I1_J) ).
fof(fact_994_nat__mult__1__right,axiom,
! [X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X14),one_one_nat) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_994_nat__mult__1__right) ).
fof(fact_933_Nat_Oadd__0__right,axiom,
! [X15] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),zero_zero_nat) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_933_Nat_Oadd__0__right) ).
fof(fact_928_minus__nat_Odiff__0,axiom,
! [X15] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),zero_zero_nat) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_928_minus__nat_Odiff__0) ).
fof(fact_515_Diff__empty,axiom,
! [X5] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),bot_bot_fun_int_bool) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_Diff__empty) ).
fof(fact_514_Diff__empty,axiom,
! [X5] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),bot_bot_fun_nat_bool) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_Diff__empty) ).
fof(fact_979_mult__0__right,axiom,
! [X15] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X15),zero_zero_nat) = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_979_mult__0__right) ).
fof(fact_1019_zmult__1,axiom,
! [X98] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X98) = X98,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1019_zmult__1) ).
fof(fact_1185_add__Pls,axiom,
! [X22] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X22) = X22,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1185_add__Pls) ).
fof(fact_1034_zadd__0,axiom,
! [X98] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),X98) = X98,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1034_zadd__0) ).
fof(fact_996_nat__mult__1,axiom,
! [X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),X14) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_996_nat__mult__1) ).
fof(fact_934_plus__nat_Oadd__0,axiom,
! [X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X14) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_934_plus__nat_Oadd__0) ).
fof(fact_1187_mult__Pls,axiom,
! [X135] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),X135) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1187_mult__Pls) ).
fof(fact_978_mult__0,axiom,
! [X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),X14) = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_978_mult__0) ).
fof(fact_929_diff__0__eq__0,axiom,
! [X14] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),X14) = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_929_diff__0__eq__0) ).
fof(fact_525_empty__Diff,axiom,
! [X5] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),X5) = bot_bot_fun_int_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_empty__Diff) ).
fof(fact_524_empty__Diff,axiom,
! [X5] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),X5) = bot_bot_fun_nat_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_empty__Diff) ).
fof(fact_526_empty__Diff,axiom,
! [X5] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),X5) = bot_bot_fun_a_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_empty__Diff) ).
fof(help_fNot_2_1_U,axiom,
! [X159] :
( hBOOL(X159)
| hBOOL(hAPP_bool_bool(fNot,X159)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
fof(fact_613_image__is__empty,axiom,
! [X9,X5] :
( is_fun_pname_bool(X5)
=> ( image_pname_a(X9,X5) = bot_bot_fun_a_bool
<=> X5 = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_image__is__empty) ).
fof(fact_617_empty__is__image,axiom,
! [X9,X5] :
( is_fun_pname_bool(X5)
=> ( bot_bot_fun_a_bool = image_pname_a(X9,X5)
<=> X5 = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_empty__is__image) ).
fof(gsy_c_hAPP_000tc__Int__Oint_000t__a,axiom,
! [X1,X2] : is_a(hAPP_int_a(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000t__a) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool,axiom,
! [X1,X2] : is_fun1661590463l_bool(hAPP_n850744903l_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool) ).
fof(gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool,axiom,
! [X1,X2] : is_fun1661590463l_bool(hAPP_i1587699435l_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool) ).
fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [X1,X2] : is_fun1661590463l_bool(image_1655916159e_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [X1,X2] : is_fun1661590463l_bool(image_637364955e_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO,axiom,
! [X1,X2] : is_bool(hAPP_f937997336l_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HO,axiom,
! [X1,X2] : is_bool(hAPP_f1593524852l_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HO) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__,axiom,
! [X1,X2] : is_bool(hAPP_f389811538l_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom,
! [X1,X2] : is_bool(hAPP_f292226953l_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom,
! [X1,X2] : is_bool(hAPP_f1637334154l_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom,
! [X1,X2] : is_bool(hAPP_f215623910l_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [X1,X2] : is_bool(hAPP_f54304608l_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [X1,X2] : is_bool(hAPP_f448129468l_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,hypothesis,
! [X1,X2] : is_bool(hAPP_nat_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).
fof(gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool,axiom,
! [X1,X2] : is_bool(hAPP_int_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat,axiom,
! [X1,X2] : is_bool(finite795500164em_nat(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Int__Oint,axiom,
! [X1,X2] : is_bool(finite1432773856em_int(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofolding__one__idem_000tc__Int__Oint) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname,axiom,
! [X1,X2] : is_bool(finite89670078_pname(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname) ).
fof(gsy_c_Finite__Set_Ofolding__one__idem_000t__a,axiom,
! [X1,X2] : is_bool(finite1819937229idem_a(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofolding__one__idem_000t__a) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat,axiom,
! [X1,X2] : is_bool(finite988810631ne_nat(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__Int__Oint,axiom,
! [X1,X2] : is_bool(finite1626084323ne_int(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofolding__one_000tc__Int__Oint) ).
fof(gsy_c_Finite__Set_Ofolding__one_000tc__Com__Opname,axiom,
! [X1,X2] : is_bool(finite1282449217_pname(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofolding__one_000tc__Com__Opname) ).
fof(gsy_c_Finite__Set_Ofolding__one_000t__a,axiom,
! [X1,X2] : is_bool(finite_folding_one_a(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofolding__one_000t__a) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL,axiom,
! [X1,X2] : is_fun949378684l_bool(hAPP_n1414589940l_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL) ).
fof(gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL,axiom,
! [X1,X2] : is_fun949378684l_bool(hAPP_i888906320l_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL) ).
fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1,X2] : is_fun949378684l_bool(image_nat_fun_a_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1,X2] : is_fun949378684l_bool(image_int_fun_a_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [X1,X2] : is_fun_pname_bool(hAPP_n1025906991e_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [X1,X2] : is_fun_pname_bool(hAPP_i7355787e_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom,
! [X1,X2] : is_fun_pname_bool(image_1921560913_pname(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
fof(gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom,
! [X1,X2] : is_fun_pname_bool(image_62782965_pname(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname,axiom,
! [X1,X2] : is_fun_pname_bool(image_nat_pname(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname) ).
fof(gsy_c_Set_Oimage_000tc__Int__Oint_000tc__Com__Opname,axiom,
! [X1,X2] : is_fun_pname_bool(image_int_pname(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Int__Oint_000tc__Com__Opname) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1,X2] : is_fun_a_bool(hAPP_nat_fun_a_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(gsy_c_hAPP_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1,X2] : is_fun_a_bool(hAPP_int_fun_a_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a,axiom,
! [X1,X2] : is_fun_a_bool(image_fun_nat_bool_a(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a) ).
fof(gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000t__a,axiom,
! [X1,X2] : is_fun_a_bool(image_fun_int_bool_a(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000t__a) ).
fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a,axiom,
! [X1,X2] : is_fun_a_bool(image_nat_a(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a) ).
fof(gsy_c_Set_Oimage_000tc__Int__Oint_000t__a,axiom,
! [X1,X2] : is_fun_a_bool(image_int_a(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Int__Oint_000t__a) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
! [X159,X160] :
( is_bool(X159)
=> hAPP_nat_bool(cOMBK_bool_nat(X159),X160) = X159 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Int__Oint_U,axiom,
! [X159,X160] :
( is_bool(X159)
=> hAPP_int_bool(cOMBK_bool_int(X159),X160) = X159 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Int__Oint_U) ).
fof(help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U,axiom,
! [X159,X160] :
( is_a(X159)
=> hAPP_pname_a(cOMBK_a_pname(X159),X160) = X159 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U,axiom,
! [X159,X160] :
( is_bool(X159)
=> hAPP_a_bool(cOMBK_bool_a(X159),X160) = X159 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U) ).
fof(fact_612_image__is__empty,axiom,
! [X9,X5] :
( image_nat_int(X9,X5) = bot_bot_fun_int_bool
<=> X5 = bot_bot_fun_nat_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_image__is__empty) ).
fof(fact_616_empty__is__image,axiom,
! [X9,X5] :
( bot_bot_fun_int_bool = image_nat_int(X9,X5)
<=> X5 = bot_bot_fun_nat_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_empty__is__image) ).
fof(fact_1100_int__eq__0__conv,axiom,
! [X17] :
( hAPP_nat_int(semiri1621563631at_int,X17) = zero_zero_int
<=> X17 = zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1100_int__eq__0__conv) ).
fof(fact_124_Suc__n__not__n,axiom,
! [X14] : hAPP_nat_nat(suc,X14) != X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_Suc__n__not__n) ).
fof(fact_125_n__not__Suc__n,axiom,
! [X14] : X14 != hAPP_nat_nat(suc,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_n__not__Suc__n) ).
fof(fact_975_not0__implies__Suc,axiom,
! [X14] :
( X14 != zero_zero_nat
=> ? [X35] : X14 = hAPP_nat_nat(suc,X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_975_not0__implies__Suc) ).
fof(fact_973_nat_Oexhaust,axiom,
! [X19] :
( X19 != zero_zero_nat
=> ~ ! [X132] : X19 != hAPP_nat_nat(suc,X132) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_973_nat_Oexhaust) ).
fof(help_COMBK_1_1_COMBK_000tc__Int__Oint_000tc__Nat__Onat_U,axiom,
! [X159,X160] : hAPP_nat_int(cOMBK_int_nat(X159),X160) = X159,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Int__Oint_000tc__Nat__Onat_U) ).
fof(fact_943_Suc__not__Zero,axiom,
! [X15] : hAPP_nat_nat(suc,X15) != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_943_Suc__not__Zero) ).
fof(fact_942_nat_Osimps_I3_J,axiom,
! [X128] : hAPP_nat_nat(suc,X128) != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_942_nat_Osimps_I3_J) ).
fof(fact_940_Suc__neq__Zero,axiom,
! [X15] : hAPP_nat_nat(suc,X15) != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_940_Suc__neq__Zero) ).
fof(fact_945_Zero__not__Suc,axiom,
! [X15] : zero_zero_nat != hAPP_nat_nat(suc,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_945_Zero__not__Suc) ).
fof(fact_944_nat_Osimps_I2_J,axiom,
! [X129] : zero_zero_nat != hAPP_nat_nat(suc,X129),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_944_nat_Osimps_I2_J) ).
fof(fact_941_Zero__neq__Suc,axiom,
! [X15] : zero_zero_nat != hAPP_nat_nat(suc,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_941_Zero__neq__Suc) ).
fof(gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [X1] :
( is_fun1661590463l_bool(X1)
=> is_fun1661590463l_bool(collec1974731493e_bool(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(gsy_v_P,axiom,
! [X1] :
( is_fun_a_bool(X1)
=> is_fun949378684l_bool(p(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_P) ).
fof(gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1] :
( is_fun949378684l_bool(X1)
=> is_fun949378684l_bool(collect_fun_a_bool(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(gsy_c_Set_OCollect_000tc__Com__Opname,axiom,
! [X1] :
( is_fun_pname_bool(X1)
=> is_fun_pname_bool(collect_pname(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__Com__Opname) ).
fof(gsy_c_Set_OCollect_000t__a,axiom,
! [X1] :
( is_fun_a_bool(X1)
=> is_fun_a_bool(collect_a(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000t__a) ).
fof(gsy_c_COMBK_000tc__HOL__Obool_000t__a,axiom,
! [X1] :
( is_bool(X1)
=> is_fun_a_bool(cOMBK_bool_a(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000t__a) ).
fof(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U,axiom,
! [X159] : hAPP_nat_nat(cOMBI_nat,X159) = X159,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) ).
fof(fact_614_image__empty,axiom,
! [X9] : image_nat_int(X9,bot_bot_fun_nat_bool) = bot_bot_fun_int_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_image__empty) ).
fof(fact_615_image__empty,axiom,
! [X9] : image_pname_a(X9,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_image__empty) ).
fof(gsy_v_mgt,axiom,
! [X1] : is_a(mgt(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_mgt) ).
fof(gsy_v_wt,axiom,
! [X1] : is_bool(wt(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_wt) ).
fof(help_If_3_1_If_000tc__Nat__Onat_T,axiom,
! [X159] :
( is_bool(X159)
=> ( X159 = fTrue
| X159 = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_000tc__Nat__Onat_T) ).
fof(help_fFalse_1_1_T,axiom,
! [X159] :
( is_bool(X159)
=> ( X159 = fTrue
| X159 = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
fof(help_fFalse_1_1_U,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(fact_539_empty__def,axiom,
bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_empty__def) ).
fof(fact_538_empty__def,axiom,
bot_bot_fun_int_bool = collect_int(cOMBK_bool_int(fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_empty__def) ).
fof(fact_1176_zero__is__num__zero,axiom,
zero_zero_int = number_number_of_int(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1176_zero__is__num__zero) ).
fof(conj_2,hypothesis,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(conj_3,hypothesis,
hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom,
is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool,axiom,
is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).
fof(conj_1,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(conj_4,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(fact_1035_int__0__less__1,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1035_int__0__less__1) ).
fof(fact_1189_rel__simps_I19_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1189_rel__simps_I19_J) ).
fof(fact_1084_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1084_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact_1086_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1086_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(fact_1122_int__Suc0__eq__1,axiom,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,zero_zero_nat)) = one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1122_int__Suc0__eq__1) ).
fof(fact_498_finite_OemptyI,axiom,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_finite_OemptyI) ).
fof(fact_497_finite_OemptyI,axiom,
hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_finite_OemptyI) ).
fof(conj_0,hypothesis,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_499_finite_OemptyI,axiom,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_finite_OemptyI) ).
fof(fact_500_finite_OemptyI,axiom,
hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_finite_OemptyI) ).
fof(fact_1099_int__0,axiom,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1099_int__0) ).
fof(fact_1098_int__1,axiom,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1098_int__1) ).
fof(fact_1116_transfer__int__nat__numerals_I1_J,axiom,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1116_transfer__int__nat__numerals_I1_J) ).
fof(fact_1115_transfer__int__nat__numerals_I2_J,axiom,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1115_transfer__int__nat__numerals_I2_J) ).
fof(fact_957_One__nat__def,axiom,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_957_One__nat__def) ).
fof(fact_1135_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
bot_bot_fun_int_bool = image_nat_int(semiri1621563631at_int,bot_bot_fun_nat_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1135_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J) ).
fof(gsy_c_HOL_Oundefined_000tc__Com__Opname,axiom,
is_pname(undefined_pname(pname)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Com__Opname) ).
fof(gsy_c_HOL_Oundefined_000t__a,axiom,
is_a(undefined_a(x_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000t__a) ).
fof(fact_540_empty__def,axiom,
bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_empty__def) ).
fof(gsy_v_pn,hypothesis,
is_pname(pn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_pn) ).
fof(gsy_c_Finite__Set_Ofinite_000tc__Com__Opname,hypothesis,
is_fun1661590463l_bool(finite_finite_pname),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofinite_000tc__Com__Opname) ).
fof(gsy_c_fTrue,axiom,
is_bool(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_fTrue) ).
fof(gsy_c_fFalse,axiom,
is_bool(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_fFalse) ).
fof(gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool,axiom,
is_bool(bot_bot_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool) ).
fof(gsy_c_Finite__Set_Ofinite_000t__a,axiom,
is_fun949378684l_bool(finite_finite_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofinite_000t__a) ).
fof(gsy_v_U,hypothesis,
is_fun_pname_bool(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_U) ).
fof(gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
is_fun_pname_bool(bot_bo844097828e_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(gsy_v_G,hypothesis,
is_fun_a_bool(g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_G) ).
fof(gsy_c_Orderings_Obot__class_Obot_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
is_fun_a_bool(bot_bot_fun_a_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(fact_1178_nat__number__of__Pls,axiom,
number_number_of_nat(pls) = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1178_nat__number__of__Pls) ).
fof(fact_1179_semiring__norm_I113_J,axiom,
zero_zero_nat = number_number_of_nat(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1179_semiring__norm_I113_J) ).
fof(fact_1072_int__0__neq__1,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1072_int__0__neq__1) ).
fof(fact_1180_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1180_Pls__def) ).
fof(fact_930_bot__nat__def,axiom,
bot_bot_nat = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_930_bot__nat__def) ).
fof(i_0_1387,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X5)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X9)),hAPP_n1699378549t_bool(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_272_pigeonhole__infinite]) ).
fof(i_0_1388,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X5)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X9)),hAPP_n1082236369t_bool(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_271_pigeonhole__infinite]) ).
fof(i_0_1389,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X5)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X9)),hAPP_n1025906991e_bool(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_273_pigeonhole__infinite]) ).
fof(i_0_1390,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X5)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X9)),hAPP_nat_fun_a_bool(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_274_pigeonhole__infinite]) ).
fof(i_0_1391,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
& ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X5)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X9)),hAPP_nat_int(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_281_pigeonhole__infinite]) ).
fof(i_0_1392,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X5))
& ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X5)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X9)),hAPP_i418383825t_bool(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_277_pigeonhole__infinite]) ).
fof(i_0_1393,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X5))
& ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X5)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X9)),hAPP_i1948725293t_bool(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_276_pigeonhole__infinite]) ).
fof(i_0_1394,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X5))
& ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X5)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X9)),hAPP_i7355787e_bool(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_278_pigeonhole__infinite]) ).
fof(i_0_1395,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X5))
& ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X5)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X9)),hAPP_int_fun_a_bool(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_279_pigeonhole__infinite]) ).
fof(i_0_1396,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X5))
& ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X5)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X9)),hAPP_int_a(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_275_pigeonhole__infinite]) ).
fof(i_0_1397,plain,
! [X33,X131] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X131))
=> hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),X131)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X33)))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X131)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,X33))))) ),
inference(fof_simplification,[status(thm)],[fact_965_card__less__Suc2]) ).
fof(i_0_1398,plain,
! [X156,X22,X133] :
( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X133)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X156)),X22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X156)),X22) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> ( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X156)))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X133)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X156)),X22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X133)),X22) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X156)))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X133)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X156)),X22)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X133),X156))),X22) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_1155_nat__number__of__add__left]) ).
fof(i_0_1399,plain,
! [X135] :
( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X135)))
=> number_number_of_nat(bit1(X135)) = zero_zero_nat )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X135)))
=> number_number_of_nat(bit1(X135)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X135)),number_number_of_nat(X135))) ) ),
inference(fof_simplification,[status(thm)],[fact_1164_nat__number__of__Bit1]) ).
fof(i_0_1400,plain,
! [X14,X133] :
( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X133)),X14)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X14) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X133)),X14)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(X133))),X14) ) ),
inference(fof_simplification,[status(thm)],[fact_1161_Suc__nat__number__of__add]) ).
fof(i_0_1401,plain,
! [X133] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X133),pls))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X133)) = one_one_nat )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X133),pls))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X133)) = number_number_of_nat(succ(X133)) ) ),
inference(fof_simplification,[status(thm)],[fact_1165_nat__1__add__number__of]) ).
fof(i_0_1402,plain,
! [X13,X8] :
( ( hBOOL(hAPP_int_bool(X13,X8))
=> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X8)),X13)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool) )
& ( ~ hBOOL(hAPP_int_bool(X13,X8))
=> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X8)),X13)) = bot_bot_fun_int_bool ) ),
inference(fof_simplification,[status(thm)],[fact_631_Collect__conv__if]) ).
fof(i_0_1403,plain,
! [X13,X8] :
( ( hBOOL(hAPP_nat_bool(X13,X8))
=> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X8)),X13)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool) )
& ( ~ hBOOL(hAPP_nat_bool(X13,X8))
=> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X8)),X13)) = bot_bot_fun_nat_bool ) ),
inference(fof_simplification,[status(thm)],[fact_632_Collect__conv__if]) ).
fof(i_0_1404,plain,
! [X154,X155] :
( number_number_of_nat(X154) = number_number_of_nat(X155)
<=> ( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X154)))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X155)),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X154)))
=> ( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X155)))
=> number_number_of_int(X154) = zero_zero_int )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X155)))
=> X154 = X155 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_1154_eq__nat__number__of]) ).
fof(i_0_1405,plain,
! [X13,X8] :
( ( hBOOL(hAPP_int_bool(X13,X8))
=> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X8)),X13)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),bot_bot_fun_int_bool) )
& ( ~ hBOOL(hAPP_int_bool(X13,X8))
=> collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X8)),X13)) = bot_bot_fun_int_bool ) ),
inference(fof_simplification,[status(thm)],[fact_634_Collect__conv__if2]) ).
fof(i_0_1406,plain,
! [X13,X8] :
( ( hBOOL(hAPP_nat_bool(X13,X8))
=> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X8)),X13)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),bot_bot_fun_nat_bool) )
& ( ~ hBOOL(hAPP_nat_bool(X13,X8))
=> collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X8)),X13)) = bot_bot_fun_nat_bool ) ),
inference(fof_simplification,[status(thm)],[fact_635_Collect__conv__if2]) ).
fof(i_0_1407,plain,
! [X133] :
( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> hAPP_nat_nat(suc,number_number_of_nat(X133)) = one_one_nat )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> hAPP_nat_nat(suc,number_number_of_nat(X133)) = number_number_of_nat(succ(X133)) ) ),
inference(fof_simplification,[status(thm)],[fact_1163_Suc__nat__number__of]) ).
fof(i_0_1408,plain,
! [X133] :
( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X133)) = zero_zero_int )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X133)))
=> hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X133)) = number_number_of_int(X133) ) ),
inference(fof_simplification,[status(thm)],[fact_1156_int__nat__number__of]) ).
fof(i_0_1409,plain,
! [X13] :
( bot_bot_fun_nat_bool = collect_nat(X13)
<=> ! [X30] : ~ hBOOL(hAPP_nat_bool(X13,X30)) ),
inference(fof_simplification,[status(thm)],[fact_522_empty__Collect__eq]) ).
fof(i_0_1410,plain,
! [X13] :
( bot_bot_fun_int_bool = collect_int(X13)
<=> ! [X30] : ~ hBOOL(hAPP_int_bool(X13,X30)) ),
inference(fof_simplification,[status(thm)],[fact_521_empty__Collect__eq]) ).
fof(i_0_1411,plain,
! [X13] :
( collect_nat(X13) = bot_bot_fun_nat_bool
<=> ! [X30] : ~ hBOOL(hAPP_nat_bool(X13,X30)) ),
inference(fof_simplification,[status(thm)],[fact_509_Collect__empty__eq]) ).
fof(i_0_1412,plain,
! [X13] :
( collect_int(X13) = bot_bot_fun_int_bool
<=> ! [X30] : ~ hBOOL(hAPP_int_bool(X13,X30)) ),
inference(fof_simplification,[status(thm)],[fact_508_Collect__empty__eq]) ).
fof(i_0_1413,plain,
! [X6608] : hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X6608))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),X6608),
inference(variable_rename,[status(thm)],[fact_1172_Suc3__eq__add__3]) ).
fof(i_0_1414,plain,
! [X6609] : bit1(X6609) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X6609)),X6609),
inference(variable_rename,[status(thm)],[fact_1177_Bit1__def]) ).
fof(i_0_1415,plain,
! [X6382] : number_number_of_int(X6382) = X6382,
inference(variable_rename,[status(thm)],[fact_1071_number__of__is__id]) ).
fof(i_0_1416,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X9,X5)))
=> ? [X30] :
( is_pname(X30)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
& ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X5)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X9)),hAPP_pname_a(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_280_pigeonhole__infinite]) ).
fof(i_0_1417,plain,
! [X6626,X6627] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X6626)),bit1(X6627)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6626),X6627)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6626),X6627))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X6626)),bit1(X6627))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1196_less__int__code_I16_J])]) ).
fof(i_0_1418,plain,
! [X6624,X6625] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X6624)),bit1(X6625)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6624),X6625)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6624),X6625))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X6624)),bit1(X6625))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1195_rel__simps_I17_J])]) ).
fof(i_0_1419,plain,
! [X6621,X6622] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X6621)),bit1(X6622)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6621),X6622)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6621),X6622))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X6621)),bit1(X6622))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1192_less__eq__int__code_I16_J])]) ).
fof(i_0_1420,plain,
! [X6619,X6620] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X6619)),bit1(X6620)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6619),X6620)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6619),X6620))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X6619)),bit1(X6620))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1191_rel__simps_I34_J])]) ).
fof(i_0_1421,plain,
! [X4330,X4331] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk54_2(X4330,X4331)),X4331))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X4330,X4331)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4331)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X4331)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X4330)),hAPP_n1699378549t_bool(X4330,esk54_2(X4330,X4331)))))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X4330,X4331)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4331)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1387])])])]) ).
fof(i_0_1422,plain,
! [X4601] : collect_nat(X4601) = X4601,
inference(variable_rename,[status(thm)],[fact_381_Collect__def]) ).
fof(i_0_1423,plain,
! [X4327,X4328] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk53_2(X4327,X4328)),X4328))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X4327,X4328)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4328)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X4328)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X4327)),hAPP_n1082236369t_bool(X4327,esk53_2(X4327,X4328)))))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X4327,X4328)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4328)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1388])])])]) ).
fof(i_0_1424,plain,
! [X4333,X4334] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk55_2(X4333,X4334)),X4334))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X4333,X4334)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4334)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X4334)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X4333)),hAPP_n1025906991e_bool(X4333,esk55_2(X4333,X4334)))))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X4333,X4334)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4334)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1389])])])]) ).
fof(i_0_1425,plain,
! [X4336,X4337] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk56_2(X4336,X4337)),X4337))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X4336,X4337)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4337)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X4337)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X4336)),hAPP_nat_fun_a_bool(X4336,esk56_2(X4336,X4337)))))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X4336,X4337)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4337)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1390])])])]) ).
fof(i_0_1426,plain,
! [X4357,X4358] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk63_2(X4357,X4358)),X4358))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X4357,X4358)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4358)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X4358)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X4357)),hAPP_nat_int(X4357,esk63_2(X4357,X4358)))))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X4357,X4358)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4358)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1391])])])]) ).
fof(i_0_1427,plain,
! [X4345,X4346] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk59_2(X4345,X4346)),X4346))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X4345,X4346)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4346)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X4346)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X4345)),hAPP_i418383825t_bool(X4345,esk59_2(X4345,X4346)))))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X4345,X4346)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4346)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1392])])])]) ).
fof(i_0_1428,plain,
! [X4600] : collect_int(X4600) = X4600,
inference(variable_rename,[status(thm)],[fact_380_Collect__def]) ).
fof(i_0_1429,plain,
! [X4342,X4343] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk58_2(X4342,X4343)),X4343))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X4342,X4343)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4343)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X4343)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X4342)),hAPP_i1948725293t_bool(X4342,esk58_2(X4342,X4343)))))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X4342,X4343)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4343)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1393])])])]) ).
fof(i_0_1430,plain,
! [X4348,X4349] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk60_2(X4348,X4349)),X4349))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X4348,X4349)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4349)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X4349)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X4348)),hAPP_i7355787e_bool(X4348,esk60_2(X4348,X4349)))))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X4348,X4349)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4349)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1394])])])]) ).
fof(i_0_1431,plain,
! [X4351,X4352] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk61_2(X4351,X4352)),X4352))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X4351,X4352)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4352)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X4352)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X4351)),hAPP_int_fun_a_bool(X4351,esk61_2(X4351,X4352)))))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X4351,X4352)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4352)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1395])])])]) ).
fof(i_0_1432,plain,
! [X4339,X4340] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk57_2(X4339,X4340)),X4340))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X4339,X4340)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4340)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X4340)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X4339)),hAPP_int_a(X4339,esk57_2(X4339,X4340)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X4339,X4340)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4340)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1396])])])]) ).
fof(i_0_1433,plain,
! [X13,X5,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X7),X5))
=> ( hBOOL(hAPP_f54304608l_bool(X13,bot_bot_fun_nat_bool))
=> ( ! [X78,X79] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X79))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X78),X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X78),X79))
=> ( hBOOL(hAPP_f54304608l_bool(X13,X79))
=> hBOOL(hAPP_f54304608l_bool(X13,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X78),X79))) ) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X13,X7)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_680_finite__subset__induct]) ).
fof(i_0_1434,plain,
! [X13,X5,X7] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X7),X5))
=> ( hBOOL(hAPP_f448129468l_bool(X13,bot_bot_fun_int_bool))
=> ( ! [X78,X79] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X79))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X78),X5))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X78),X79))
=> ( hBOOL(hAPP_f448129468l_bool(X13,X79))
=> hBOOL(hAPP_f448129468l_bool(X13,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X78),X79))) ) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X13,X7)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_679_finite__subset__induct]) ).
fof(i_0_1435,plain,
! [X13,X5,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X7),X5))
=> ( hBOOL(hAPP_f1664156314l_bool(X13,bot_bo844097828e_bool))
=> ( ! [X78,X79] :
( ( is_pname(X78)
& is_fun_pname_bool(X79) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X79))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X78),X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X78),X79))
=> ( hBOOL(hAPP_f1664156314l_bool(X13,X79))
=> hBOOL(hAPP_f1664156314l_bool(X13,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X78),X79))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X13,X7)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_681_finite__subset__induct]) ).
fof(i_0_1436,plain,
! [X13,X5,X7] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X7),X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(X13,bot_bot_fun_a_bool))
=> ( ! [X78,X79] :
( ( is_a(X78)
& is_fun_a_bool(X79) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X79))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X78),X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X78),X79))
=> ( hBOOL(hAPP_fun_a_bool_bool(X13,X79))
=> hBOOL(hAPP_fun_a_bool_bool(X13,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X78),X79))) ) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X13,X7)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_678_finite__subset__induct]) ).
fof(i_0_1437,plain,
! [X6623] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X6623)),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6623),pls)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6623),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X6623)),pls)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1194_rel__simps_I12_J])]) ).
fof(i_0_1438,plain,
! [X6628] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X6628)),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6628),pls)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6628),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X6628)),pls)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1197_rel__simps_I29_J])]) ).
fof(i_0_1439,plain,
! [X5,X11,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X10)))
<=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool))),X10)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_567_subset__insert__iff]) ).
fof(i_0_1440,plain,
! [X5,X11,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X10)))
<=> ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool))),X10)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_566_subset__insert__iff]) ).
fof(i_0_1441,plain,
! [X5,X11,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X10)))
<=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool))),X10)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_568_subset__insert__iff]) ).
fof(i_0_1442,plain,
! [X5,X11,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X10)))
<=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool))),X10)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_565_subset__insert__iff]) ).
fof(i_0_1443,plain,
! [X6109,X6110] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X6110))
| hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),X6110)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X6109))))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X6110)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,X6109))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_963_card__less__Suc])]) ).
fof(i_0_1444,plain,
! [X13,X7] :
( is_fun_pname_bool(X7)
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> ( X7 != bot_bo844097828e_bool
=> ( ! [X30] :
( is_pname(X30)
=> hBOOL(hAPP_f1664156314l_bool(X13,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X30),bot_bo844097828e_bool))) )
=> ( ! [X30,X79] :
( ( is_pname(X30)
& is_fun_pname_bool(X79) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X79))
=> ( X79 != bot_bo844097828e_bool
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X79))
=> ( hBOOL(hAPP_f1664156314l_bool(X13,X79))
=> hBOOL(hAPP_f1664156314l_bool(X13,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X30),X79))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X13,X7)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_782_finite__ne__induct]) ).
fof(i_0_1445,plain,
! [X13,X7] :
( is_fun_a_bool(X7)
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> ( X7 != bot_bot_fun_a_bool
=> ( ! [X30] :
( is_a(X30)
=> hBOOL(hAPP_fun_a_bool_bool(X13,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X30),bot_bot_fun_a_bool))) )
=> ( ! [X30,X79] :
( ( is_a(X30)
& is_fun_a_bool(X79) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X79))
=> ( X79 != bot_bot_fun_a_bool
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X79))
=> ( hBOOL(hAPP_fun_a_bool_bool(X13,X79))
=> hBOOL(hAPP_fun_a_bool_bool(X13,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X30),X79))) ) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X13,X7)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_779_finite__ne__induct]) ).
fof(i_0_1446,plain,
! [X13,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> ( X7 != bot_bot_fun_nat_bool
=> ( ! [X30] : hBOOL(hAPP_f54304608l_bool(X13,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),bot_bot_fun_nat_bool)))
=> ( ! [X30,X79] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X79))
=> ( X79 != bot_bot_fun_nat_bool
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X79))
=> ( hBOOL(hAPP_f54304608l_bool(X13,X79))
=> hBOOL(hAPP_f54304608l_bool(X13,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),X79))) ) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X13,X7)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_781_finite__ne__induct]) ).
fof(i_0_1447,plain,
! [X13,X7] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
=> ( X7 != bot_bot_fun_int_bool
=> ( ! [X30] : hBOOL(hAPP_f448129468l_bool(X13,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),bot_bot_fun_int_bool)))
=> ( ! [X30,X79] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X79))
=> ( X79 != bot_bot_fun_int_bool
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X79))
=> ( hBOOL(hAPP_f448129468l_bool(X13,X79))
=> hBOOL(hAPP_f448129468l_bool(X13,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),X79))) ) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X13,X7)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_780_finite__ne__induct]) ).
fof(i_0_1448,plain,
! [X6629] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X6629)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X6629)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X6629))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X6629))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1198_rel__simps_I5_J])]) ).
fof(i_0_1449,plain,
! [X6618] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X6618)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X6618)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X6618))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X6618))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1190_rel__simps_I22_J])]) ).
fof(i_0_1450,plain,
! [X6607] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X6607))))
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6607))) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6607)))
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X6607)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1167_neg__number__of__Bit1])]) ).
fof(i_0_1451,plain,
! [X6113,X6114] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X6114))
| hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),X6114)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X6113)))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X6114)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,X6113))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1397])]) ).
fof(i_0_1452,plain,
! [X13,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> ( hBOOL(hAPP_f54304608l_bool(X13,bot_bot_fun_nat_bool))
=> ( ! [X30,X79] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X79))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X79))
=> ( hBOOL(hAPP_f54304608l_bool(X13,X79))
=> hBOOL(hAPP_f54304608l_bool(X13,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),X79))) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X13,X7)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_689_finite__induct]) ).
fof(i_0_1453,plain,
! [X13,X7] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X7))
=> ( hBOOL(hAPP_f448129468l_bool(X13,bot_bot_fun_int_bool))
=> ( ! [X30,X79] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X79))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X79))
=> ( hBOOL(hAPP_f448129468l_bool(X13,X79))
=> hBOOL(hAPP_f448129468l_bool(X13,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),X79))) ) ) )
=> hBOOL(hAPP_f448129468l_bool(X13,X7)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_688_finite__induct]) ).
fof(i_0_1454,plain,
! [X13,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> ( hBOOL(hAPP_f1664156314l_bool(X13,bot_bo844097828e_bool))
=> ( ! [X30,X79] :
( ( is_pname(X30)
& is_fun_pname_bool(X79) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X79))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X79))
=> ( hBOOL(hAPP_f1664156314l_bool(X13,X79))
=> hBOOL(hAPP_f1664156314l_bool(X13,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X30),X79))) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X13,X7)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_690_finite__induct]) ).
fof(i_0_1455,plain,
! [X13,X7] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(X13,bot_bot_fun_a_bool))
=> ( ! [X30,X79] :
( ( is_a(X30)
& is_fun_a_bool(X79) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X79))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X79))
=> ( hBOOL(hAPP_fun_a_bool_bool(X13,X79))
=> hBOOL(hAPP_fun_a_bool_bool(X13,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X30),X79))) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X13,X7)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_687_finite__induct]) ).
fof(i_0_1456,plain,
! [X10,X8,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X5))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X10))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X8),X10))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10))),one_one_nat) ) ) ),
inference(fof_simplification,[status(thm)],[fact_752_card__Diff__insert]) ).
fof(i_0_1457,plain,
! [X10,X8,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X10))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X8),X10))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10))),one_one_nat) ) ) ),
inference(fof_simplification,[status(thm)],[fact_753_card__Diff__insert]) ).
fof(i_0_1458,plain,
! [X10,X8,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X10))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),X10))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10))),one_one_nat) ) ) ),
inference(fof_simplification,[status(thm)],[fact_751_card__Diff__insert]) ).
fof(i_0_1459,plain,
! [X10,X8,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X10))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X8),X10))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10))),one_one_nat) ) ) ),
inference(fof_simplification,[status(thm)],[fact_754_card__Diff__insert]) ).
fof(i_0_1460,plain,
! [X5394,X5395] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk133_2(X5394,X5395)),hAPP_nat_nat(X5395,esk133_2(X5394,X5395))))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X5395)),X5394)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_695_finite__less__ub])])]) ).
fof(i_0_1461,plain,
! [X31,X9,X5] :
( is_a(X31)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),image_pname_a(X9,X5)))
=> ~ ! [X30] :
( is_pname(X30)
=> ( X31 = hAPP_pname_a(X9,X30)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_476_imageE]) ).
fof(i_0_1462,plain,
! [X31,X9,X5] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X31),image_nat_int(X9,X5)))
=> ~ ! [X30] :
( X31 = hAPP_nat_int(X9,X30)
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_475_imageE]) ).
fof(i_0_1463,plain,
! [X6111,X6112] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X6112))
| hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X6112)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,X6111))))) != zero_zero_nat ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_964_card__less])]) ).
fof(i_0_1464,plain,
! [X15,X22,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X15),X22)),X14))
=> ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X14)) ) ),
inference(fof_simplification,[status(thm)],[fact_832_add__leE]) ).
fof(i_0_1465,plain,
! [X13,X8,X31] :
( hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X8),X31)))
<=> ~ ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X8),X31))
& ~ hBOOL(hAPP_nat_bool(X13,zero_zero_nat)) )
| ? [X130] :
( X8 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X31),X130)
& ~ hBOOL(hAPP_nat_bool(X13,X130)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_962_nat__diff__split__asm]) ).
fof(i_0_1466,plain,
! [X23,X24] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X23),X24)),X23)),
inference(fof_simplification,[status(thm)],[fact_876_not__add__less1]) ).
fof(i_0_1467,plain,
! [X24,X23] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X24),X23)),X23)),
inference(fof_simplification,[status(thm)],[fact_877_not__add__less2]) ).
fof(i_0_1468,plain,
! [X6578,X6579,X6580] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6580)))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X6580)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X6578)),X6579)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X6578)),X6579) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6578)))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X6580)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X6578)),X6579)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X6580)),X6579)
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6580))) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6578)))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X6580)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X6578)),X6579)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6580),X6578))),X6579)
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6580))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1398])])]) ).
fof(i_0_1469,plain,
! [X6610,X6611] :
( ( bit1(X6610) != bit1(X6611)
| X6610 = X6611 )
& ( X6610 != X6611
| bit1(X6610) = bit1(X6611) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1181_rel__simps_I51_J])]) ).
fof(i_0_1470,plain,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X10)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_459_subset__insert]) ).
fof(i_0_1471,plain,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X10)))
<=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_458_subset__insert]) ).
fof(i_0_1472,plain,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X10)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_460_subset__insert]) ).
fof(i_0_1473,plain,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X10)))
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_457_subset__insert]) ).
fof(i_0_1474,plain,
! [X6605] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6605)))
| number_number_of_nat(bit1(X6605)) = zero_zero_nat )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6605)))
| number_number_of_nat(bit1(X6605)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X6605)),number_number_of_nat(X6605))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1399])]) ).
fof(i_0_1475,plain,
! [X11,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,X5)),one_one_nat) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool))) = hAPP_f957591787ol_nat(finite_card_int,X5) ) ) ),
inference(fof_simplification,[status(thm)],[fact_737_card__Diff__singleton__if]) ).
fof(i_0_1476,plain,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,X5)),one_one_nat) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool))) = hAPP_f22106695ol_nat(finite_card_nat,X5) ) ) ),
inference(fof_simplification,[status(thm)],[fact_738_card__Diff__singleton__if]) ).
fof(i_0_1477,plain,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,X5)),one_one_nat) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool))) = hAPP_fun_a_bool_nat(finite_card_a,X5) ) ) ),
inference(fof_simplification,[status(thm)],[fact_736_card__Diff__singleton__if]) ).
fof(i_0_1478,plain,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,X5)),one_one_nat) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool))) = hAPP_f921600141ol_nat(finite_card_pname,X5) ) ) ),
inference(fof_simplification,[status(thm)],[fact_739_card__Diff__singleton__if]) ).
fof(i_0_1479,plain,
! [X32,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)))
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X5))
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_721_Diff__iff]) ).
fof(i_0_1480,plain,
! [X32,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X10)) ),
inference(fof_simplification,[status(thm)],[fact_713_DiffD2]) ).
fof(i_0_1481,plain,
! [X32,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10)))
<=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X5))
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_720_Diff__iff]) ).
fof(i_0_1482,plain,
! [X32,X5,X10] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10)))
=> ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X10)) ),
inference(fof_simplification,[status(thm)],[fact_712_DiffD2]) ).
fof(i_0_1483,plain,
! [X32,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10)))
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X5))
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_723_Diff__iff]) ).
fof(i_0_1484,plain,
! [X32,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10)))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X10)) ),
inference(fof_simplification,[status(thm)],[fact_715_DiffD2]) ).
fof(i_0_1485,plain,
! [X32,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10)))
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X5))
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_722_Diff__iff]) ).
fof(i_0_1486,plain,
! [X32,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10)))
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X10)) ),
inference(fof_simplification,[status(thm)],[fact_714_DiffD2]) ).
fof(i_0_1487,plain,
! [X6601,X6602] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6602)))
| hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X6602)),X6601)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X6601) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6602)))
| hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X6602)),X6601)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(X6602))),X6601) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1400])]) ).
fof(i_0_1488,plain,
! [X6603] : succ(X6603) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6603),one_one_int),
inference(variable_rename,[status(thm)],[fact_1162_succ__def]) ).
fof(i_0_1489,plain,
! [X17,X13] :
( ~ hBOOL(hAPP_nat_bool(X13,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(X13,X17))
=> ? [X119] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X119),X17))
& ! [X126] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X126),X119))
=> ~ hBOOL(hAPP_nat_bool(X13,X126)) )
& hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X119),one_one_nat))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_969_ex__least__nat__less]) ).
fof(i_0_1490,plain,
! [X10,X32,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),X10))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10))) ) ),
inference(fof_simplification,[status(thm)],[fact_709_DiffI]) ).
fof(i_0_1491,plain,
! [X10,X32,X5] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X5))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),X10))
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10))) ) ),
inference(fof_simplification,[status(thm)],[fact_708_DiffI]) ).
fof(i_0_1492,plain,
! [X10,X32,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),X10))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10))) ) ),
inference(fof_simplification,[status(thm)],[fact_711_DiffI]) ).
fof(i_0_1493,plain,
! [X10,X32,X5] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10))) ) ),
inference(fof_simplification,[status(thm)],[fact_710_DiffI]) ).
fof(i_0_1494,plain,
! [X6426,X6427] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk191_2(X6426,X6427)))
| collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X6427)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X6426)) )
& ( ~ hBOOL(hAPP_int_bool(X6427,esk191_2(X6426,X6427)))
| ~ hBOOL(hAPP_int_bool(X6426,esk191_2(X6426,X6427)))
| collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X6427)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X6426)) )
& ( hBOOL(hAPP_int_bool(X6427,esk191_2(X6426,X6427)))
| hBOOL(hAPP_int_bool(X6426,esk191_2(X6426,X6427)))
| collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X6427)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X6426)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1087_transfer__nat__int__set__cong])])])]) ).
fof(i_0_1495,plain,
! [X25,X17] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X17)),X25)) ),
inference(fof_simplification,[status(thm)],[fact_169_not__less__eq__eq]) ).
fof(i_0_1496,plain,
! [X5,X11,X10] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X10))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)),X10) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X10))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)),X10) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_577_insert__Diff__if]) ).
fof(i_0_1497,plain,
! [X5,X11,X10] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)),X10) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)),X10) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_578_insert__Diff__if]) ).
fof(i_0_1498,plain,
! [X5,X11,X10] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)),X10) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)),X10) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_579_insert__Diff__if]) ).
fof(i_0_1499,plain,
! [X5,X11,X10] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10))
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)),X10) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10))
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)),X10) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_576_insert__Diff__if]) ).
fof(i_0_1500,plain,
! [X31,X8,X10] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X10))
=> X8 = X31 )
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X31),X10))) ),
inference(fof_simplification,[status(thm)],[fact_293_insertCI]) ).
fof(i_0_1501,plain,
! [X31,X8,X10] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X10))
=> X8 = X31 )
=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X31),X10))) ),
inference(fof_simplification,[status(thm)],[fact_292_insertCI]) ).
fof(i_0_1502,plain,
! [X31,X8,X10] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X10))
=> X8 = X31 )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X31),X10))) ),
inference(fof_simplification,[status(thm)],[fact_294_insertCI]) ).
fof(i_0_1503,plain,
! [X31,X8,X10] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X10))
=> X8 = X31 )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X31),X10))) ),
inference(fof_simplification,[status(thm)],[fact_291_insertCI]) ).
fof(i_0_1504,plain,
! [X11,X5] :
( is_fun_pname_bool(X5)
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),bot_bo844097828e_bool)) = X5 ) ),
inference(fof_simplification,[status(thm)],[fact_551_Diff__insert__absorb]) ).
fof(i_0_1505,plain,
! [X11,X5] :
( is_fun_a_bool(X5)
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),bot_bot_fun_a_bool)) = X5 ) ),
inference(fof_simplification,[status(thm)],[fact_548_Diff__insert__absorb]) ).
fof(i_0_1506,plain,
! [X11,X5,X9,X7] :
( is_fun_pname_bool(X5)
=> ( hBOOL(finite1282449217_pname(X9,X7))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( X5 != bot_bo844097828e_bool
=> hAPP_f1297739591_pname(X7,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)) = hAPP_pname_pname(hAPP_p1170154830_pname(X9,X11),hAPP_f1297739591_pname(X7,X5)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_758_folding__one_Oinsert]) ).
fof(i_0_1507,plain,
! [X11,X5,X9,X7] :
( is_fun_a_bool(X5)
=> ( hBOOL(finite_folding_one_a(X9,X7))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( X5 != bot_bot_fun_a_bool
=> hAPP_fun_a_bool_a(X7,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)) = hAPP_a_a(hAPP_a_fun_a_a(X9,X11),hAPP_fun_a_bool_a(X7,X5)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_755_folding__one_Oinsert]) ).
fof(i_0_1508,plain,
! [X11,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),bot_bot_fun_int_bool)) = X5 ),
inference(fof_simplification,[status(thm)],[fact_549_Diff__insert__absorb]) ).
fof(i_0_1509,plain,
! [X11,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),bot_bot_fun_nat_bool)) = X5 ),
inference(fof_simplification,[status(thm)],[fact_550_Diff__insert__absorb]) ).
fof(i_0_1510,plain,
! [X17,X13] :
( ~ hBOOL(hAPP_nat_bool(X13,zero_zero_nat))
=> ( hBOOL(hAPP_nat_bool(X13,X17))
=> ? [X119] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X119),X17))
& ! [X126] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X126),X119))
=> ~ hBOOL(hAPP_nat_bool(X13,X126)) )
& hBOOL(hAPP_nat_bool(X13,X119)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_970_ex__least__nat__le]) ).
fof(i_0_1511,plain,
! [X11,X5,X9,X7] :
( hBOOL(finite988810631ne_nat(X9,X7))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( X5 != bot_bot_fun_nat_bool
=> hAPP_f22106695ol_nat(X7,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X9,X11),hAPP_f22106695ol_nat(X7,X5)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_757_folding__one_Oinsert]) ).
fof(i_0_1512,plain,
! [X11,X5,X9,X7] :
( hBOOL(finite1626084323ne_int(X9,X7))
=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> ( X5 != bot_bot_fun_int_bool
=> hAPP_f1594865479ol_int(X7,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)) = hAPP_int_int(hAPP_int_fun_int_int(X9,X11),hAPP_f1594865479ol_int(X7,X5)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_756_folding__one_Oinsert]) ).
fof(i_0_1513,plain,
! [X25,X17] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),hAPP_nat_nat(suc,X25))) ),
inference(fof_simplification,[status(thm)],[fact_865_not__less__eq]) ).
fof(i_0_1514,plain,
! [X5967,X5968] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X5967),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X5968))))),
inference(variable_rename,[status(thm)],[fact_897_finite__M__bounded__by__nat]) ).
fof(i_0_1515,plain,
! [X3913,X3914] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X3913)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X3913),X3914)))) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X3914)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X3913),X3914)))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X3913)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X3914)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X3913),X3914)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_138_finite__Collect__disjI])])]) ).
fof(i_0_1516,plain,
! [X3915,X3916] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X3915)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X3915),X3916)))) )
& ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X3916)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X3915),X3916)))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X3915)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X3916)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X3915),X3916)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_139_finite__Collect__disjI])])]) ).
fof(i_0_1517,plain,
! [X13,X8] :
( ( hBOOL(hAPP_a_bool(X13,X8))
=> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8)),X13)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool) )
& ( ~ hBOOL(hAPP_a_bool(X13,X8))
=> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8)),X13)) = bot_bot_fun_a_bool ) ),
inference(fof_simplification,[status(thm)],[fact_630_Collect__conv__if]) ).
fof(i_0_1518,plain,
! [X10,X11,X5] :
( ( is_fun_pname_bool(X10)
& is_fun_pname_bool(X5) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X10))
=> ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X10)
<=> X5 = X10 ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_392_insert__ident]) ).
fof(i_0_1519,plain,
! [X10,X11,X5] :
( ( is_fun_a_bool(X10)
& is_fun_a_bool(X5) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X10))
=> ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X10)
<=> X5 = X10 ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_389_insert__ident]) ).
fof(i_0_1520,plain,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),hAPP_nat_nat(suc,X14)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> X15 = hAPP_nat_nat(suc,X14) ) ),
inference(fof_simplification,[status(thm)],[fact_165_le__SucE]) ).
fof(i_0_1521,plain,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X10))
=> ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X10)
<=> X5 = X10 ) ) ),
inference(fof_simplification,[status(thm)],[fact_391_insert__ident]) ).
fof(i_0_1522,plain,
! [X10,X11,X5] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X10))
=> ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X10)
<=> X5 = X10 ) ) ),
inference(fof_simplification,[status(thm)],[fact_390_insert__ident]) ).
fof(i_0_1523,plain,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),hAPP_nat_nat(suc,X14)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> X15 = X14 ) ),
inference(fof_simplification,[status(thm)],[fact_873_less__SucE]) ).
fof(i_0_1524,plain,
! [X14,X15] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X15))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),hAPP_nat_nat(suc,X15)))
=> X15 = X14 ) ),
inference(fof_simplification,[status(thm)],[fact_869_less__antisym]) ).
fof(i_0_1525,plain,
! [X17,X25] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),X25))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X17),hAPP_nat_nat(suc,X25)))
<=> X17 = X25 ) ),
inference(fof_simplification,[status(thm)],[fact_868_not__less__less__Suc__eq]) ).
fof(i_0_1526,plain,
! [X6612] : bit1(X6612) != pls,
inference(variable_rename,[status(thm)],[fact_1182_rel__simps_I46_J]) ).
fof(i_0_1527,plain,
! [X6613] : pls != bit1(X6613),
inference(variable_rename,[status(thm)],[fact_1183_rel__simps_I39_J]) ).
fof(i_0_1528,plain,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X14)),X14)),
inference(fof_simplification,[status(thm)],[fact_170_Suc__n__not__le__n]) ).
fof(i_0_1529,plain,
! [X11,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)) = hAPP_f957591787ol_nat(finite_card_int,X5) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_101_card__insert__if]) ).
fof(i_0_1530,plain,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)) = hAPP_f22106695ol_nat(finite_card_nat,X5) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_100_card__insert__if]) ).
fof(i_0_1531,plain,
! [X11,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X11),X5))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X11),X5)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X5) )
& ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X11),X5))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_98_card__insert__if]) ).
fof(i_0_1532,plain,
! [X11,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X11),X5))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X11),X5)) = hAPP_f55526627ol_nat(finite1340463720e_bool,X5) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X11),X5))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_97_card__insert__if]) ).
fof(i_0_1533,plain,
! [X11,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X11),X5))
=> hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X11),X5)) = hAPP_f696928925ol_nat(finite346522414t_bool,X5) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X11),X5))
=> hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_96_card__insert__if]) ).
fof(i_0_1534,plain,
! [X11,X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5))
=> ( ( hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X11),X5))
=> hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X11),X5)) = hAPP_f521865025ol_nat(finite1876863882t_bool,X5) )
& ( ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X11),X5))
=> hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_95_card__insert__if]) ).
fof(i_0_1535,plain,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)) = hAPP_fun_a_bool_nat(finite_card_a,X5) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_102_card__insert__if]) ).
fof(i_0_1536,plain,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)) = hAPP_f921600141ol_nat(finite_card_pname,X5) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_99_card__insert__if]) ).
fof(i_0_1537,plain,
! [X22] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X22)),zero_zero_int)),
inference(fof_simplification,[status(thm)],[fact_1097_int__less__0__conv]) ).
fof(i_0_1538,plain,
! [X13,X8] :
( ( hBOOL(hAPP_a_bool(X13,X8))
=> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X8)),X13)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X8),bot_bot_fun_a_bool) )
& ( ~ hBOOL(hAPP_a_bool(X13,X8))
=> collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X8)),X13)) = bot_bot_fun_a_bool ) ),
inference(fof_simplification,[status(thm)],[fact_633_Collect__conv__if2]) ).
fof(i_0_1539,plain,
! [X4588,X4589] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4588),collect_int(X4589)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X4588))),X4589)),
inference(variable_rename,[status(thm)],[fact_374_insert__Collect]) ).
fof(i_0_1540,plain,
! [X4590,X4591] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4590),collect_nat(X4591)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X4590))),X4591)),
inference(variable_rename,[status(thm)],[fact_375_insert__Collect]) ).
fof(i_0_1541,plain,
! [X11,X5] :
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5))
=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X11),X5))
=> hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X11),X5)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_109_card__insert__disjoint]) ).
fof(i_0_1542,plain,
! [X11,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X11),X5)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_108_card__insert__disjoint]) ).
fof(i_0_1543,plain,
! [X11,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X11),X5))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_106_card__insert__disjoint]) ).
fof(i_0_1544,plain,
! [X11,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X11),X5))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_105_card__insert__disjoint]) ).
fof(i_0_1545,plain,
! [X11,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X11),X5))
=> hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_104_card__insert__disjoint]) ).
fof(i_0_1546,plain,
! [X11,X5] :
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X5))
=> ( ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X11),X5))
=> hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X11),X5)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_103_card__insert__disjoint]) ).
fof(i_0_1547,plain,
! [X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X11),X5)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_110_card__insert__disjoint]) ).
fof(i_0_1548,plain,
! [X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X11),X5)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_107_card__insert__disjoint]) ).
fof(i_0_1549,plain,
! [X5483,X5484] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5483),X5484) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X5483)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X5484)))),
inference(variable_rename,[status(thm)],[fact_724_set__diff__eq]) ).
fof(i_0_1550,plain,
! [X5485,X5486] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5485),X5486) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X5485)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X5486)))),
inference(variable_rename,[status(thm)],[fact_725_set__diff__eq]) ).
fof(i_0_1551,plain,
! [X3874,X3875] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X3875)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X3875),X3874)))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X3874)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X3875),X3874)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_117_finite__Collect__conjI])])]) ).
fof(i_0_1552,plain,
! [X3876,X3877] :
( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X3877)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X3877),X3876)))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X3876)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X3877),X3876)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_118_finite__Collect__conjI])])]) ).
fof(i_0_1553,plain,
! [X19,X18] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X18))
=> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X18),X19) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X18),X19) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X19),X18))
=> hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X18),X19) = zero_zero_int ) ),
inference(fof_simplification,[status(thm)],[fact_1095_tsub__def]) ).
fof(i_0_1554,plain,
! [X5] :
( is_fun_pname_bool(X5)
=> ( X5 != bot_bo844097828e_bool
<=> ? [X30,X83] :
( is_pname(X30)
& is_fun_pname_bool(X83)
& X5 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X30),X83)
& ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X83)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_702_nonempty__iff]) ).
fof(i_0_1555,plain,
! [X5] :
( is_fun_a_bool(X5)
=> ( X5 != bot_bot_fun_a_bool
<=> ? [X30,X83] :
( is_a(X30)
& is_fun_a_bool(X83)
& X5 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X30),X83)
& ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X83)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_699_nonempty__iff]) ).
fof(i_0_1556,plain,
! [X6606] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6606),pls))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X6606)) = one_one_nat )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6606),pls))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X6606)) = number_number_of_nat(succ(X6606)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1401])]) ).
fof(i_0_1557,plain,
! [X15,X14] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X14),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X15),X14)) = X15 ),
inference(fof_simplification,[status(thm)],[fact_910_add__diff__inverse]) ).
fof(i_0_1558,plain,
! [X5218,X5219] :
( ( ~ hBOOL(hAPP_int_bool(X5218,X5219))
| collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X5219)),X5218)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5219),bot_bot_fun_int_bool) )
& ( hBOOL(hAPP_int_bool(X5218,X5219))
| collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X5219)),X5218)) = bot_bot_fun_int_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1402])]) ).
fof(i_0_1559,plain,
! [X5220,X5221] :
( ( ~ hBOOL(hAPP_nat_bool(X5220,X5221))
| collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X5221)),X5220)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5221),bot_bot_fun_nat_bool) )
& ( hBOOL(hAPP_nat_bool(X5220,X5221))
| collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X5221)),X5220)) = bot_bot_fun_nat_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1403])]) ).
fof(i_0_1560,plain,
! [X5] :
( X5 != bot_bot_fun_nat_bool
<=> ? [X30,X83] :
( X5 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X30),X83)
& ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X83)) ) ),
inference(fof_simplification,[status(thm)],[fact_701_nonempty__iff]) ).
fof(i_0_1561,plain,
! [X5] :
( X5 != bot_bot_fun_int_bool
<=> ? [X30,X83] :
( X5 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X30),X83)
& ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X83)) ) ),
inference(fof_simplification,[status(thm)],[fact_700_nonempty__iff]) ).
fof(i_0_1562,plain,
! [X4757,X4758] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4757),X4758) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X4757)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X4758))),
inference(variable_rename,[status(thm)],[fact_438_insert__compr__raw]) ).
fof(i_0_1563,plain,
! [X4580,X4581] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4580),X4581) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X4580)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X4581))),
inference(variable_rename,[status(thm)],[fact_370_insert__compr]) ).
fof(i_0_1564,plain,
! [X4759,X4760] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4759),X4760) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X4759)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X4760))),
inference(variable_rename,[status(thm)],[fact_439_insert__compr__raw]) ).
fof(i_0_1565,plain,
! [X4582,X4583] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4582),X4583) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X4582)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X4583))),
inference(variable_rename,[status(thm)],[fact_371_insert__compr]) ).
fof(i_0_1566,plain,
! [X6576,X6577] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6576)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X6577)),zero_zero_int))
| number_number_of_nat(X6576) != number_number_of_nat(X6577) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6577)))
| number_number_of_int(X6576) = zero_zero_int
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6576)))
| number_number_of_nat(X6576) != number_number_of_nat(X6577) )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6577)))
| X6576 = X6577
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6576)))
| number_number_of_nat(X6576) != number_number_of_nat(X6577) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6576)))
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6576)))
| number_number_of_nat(X6576) = number_number_of_nat(X6577) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6577)))
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6577)))
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6576)))
| number_number_of_nat(X6576) = number_number_of_nat(X6577) )
& ( X6576 != X6577
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6577)))
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6576)))
| number_number_of_nat(X6576) = number_number_of_nat(X6577) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6577)))
| number_number_of_int(X6576) != zero_zero_int
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6576)))
| number_number_of_nat(X6576) = number_number_of_nat(X6577) )
& ( X6576 != X6577
| number_number_of_int(X6576) != zero_zero_int
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6576)))
| number_number_of_nat(X6576) = number_number_of_nat(X6577) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6576)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X6577)),zero_zero_int))
| number_number_of_nat(X6576) = number_number_of_nat(X6577) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6577)))
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6577)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X6577)),zero_zero_int))
| number_number_of_nat(X6576) = number_number_of_nat(X6577) )
& ( X6576 != X6577
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6577)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X6577)),zero_zero_int))
| number_number_of_nat(X6576) = number_number_of_nat(X6577) )
& ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6577)))
| number_number_of_int(X6576) != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X6577)),zero_zero_int))
| number_number_of_nat(X6576) = number_number_of_nat(X6577) )
& ( X6576 != X6577
| number_number_of_int(X6576) != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X6577)),zero_zero_int))
| number_number_of_nat(X6576) = number_number_of_nat(X6577) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1404])])]) ).
fof(i_0_1567,plain,
! [X5224,X5225] :
( ( ~ hBOOL(hAPP_int_bool(X5224,X5225))
| collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X5225)),X5224)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5225),bot_bot_fun_int_bool) )
& ( hBOOL(hAPP_int_bool(X5224,X5225))
| collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X5225)),X5224)) = bot_bot_fun_int_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1405])]) ).
fof(i_0_1568,plain,
! [X5226,X5227] :
( ( ~ hBOOL(hAPP_nat_bool(X5226,X5227))
| collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X5227)),X5226)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5227),bot_bot_fun_nat_bool) )
& ( hBOOL(hAPP_nat_bool(X5226,X5227))
| collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X5227)),X5226)) = bot_bot_fun_nat_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1406])]) ).
fof(i_0_1569,plain,
! [X18,X19] :
( X18 != X19
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X18),X19))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X19),X18)) ) ),
inference(fof_simplification,[status(thm)],[fact_860_linorder__neqE__nat]) ).
fof(i_0_1570,plain,
! [X11] :
( ~ hBOOL(hAPP_int_bool(nat_neg,X11))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X11)) ),
inference(fof_simplification,[status(thm)],[fact_1147_not__neg__eq__ge__0]) ).
fof(i_0_1571,plain,
! [X65,X66] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X65),X66))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X66),X65)) ),
inference(fof_simplification,[status(thm)],[fact_364_linorder__le__cases]) ).
fof(i_0_1572,plain,
! [X65,X66] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X65),X66))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X66),X65)) ),
inference(fof_simplification,[status(thm)],[fact_363_linorder__le__cases]) ).
fof(i_0_1573,plain,
! [X5] :
( is_fun_pname_bool(X5)
=> ( ! [X30] :
( is_pname(X30)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5)) )
<=> X5 = bot_bo844097828e_bool ) ),
inference(fof_simplification,[status(thm)],[fact_534_all__not__in__conv]) ).
fof(i_0_1574,plain,
! [X5] :
( is_fun_a_bool(X5)
=> ( ! [X30] :
( is_a(X30)
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5)) )
<=> X5 = bot_bot_fun_a_bool ) ),
inference(fof_simplification,[status(thm)],[fact_533_all__not__in__conv]) ).
fof(i_0_1575,plain,
! [X18,X19] :
( ( is_pname(X18)
& is_pname(X19) )
=> ( ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X18),X19))
| X18 = X19 ) ),
inference(fof_simplification,[status(thm)],[help_fequal_1_1_fequal_000tc__Com__Opname_T]) ).
fof(i_0_1576,plain,
! [X18,X19] :
( ( is_a(X18)
& is_a(X19) )
=> ( ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X18),X19))
| X18 = X19 ) ),
inference(fof_simplification,[status(thm)],[help_fequal_1_1_fequal_000t__a_T]) ).
fof(i_0_1577,plain,
! [X18,X19] :
( ( is_fun_pname_bool(X18)
& is_fun_pname_bool(X19) )
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X18),X19))
| X18 = X19 ) ),
inference(fof_simplification,[status(thm)],[help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T]) ).
fof(i_0_1578,plain,
! [X18,X19] :
( ( is_fun_a_bool(X18)
& is_fun_a_bool(X19) )
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X18),X19))
| X18 = X19 ) ),
inference(fof_simplification,[status(thm)],[help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T]) ).
fof(i_0_1579,plain,
! [X11,X39,X13] :
( ( hBOOL(X13)
=> hAPP_nat_int(semiri1621563631at_int,X11) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X13),X11),X39)) )
& ( ~ hBOOL(X13)
=> hAPP_nat_int(semiri1621563631at_int,X39) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X13),X11),X39)) ) ),
inference(fof_simplification,[status(thm)],[fact_1138_int__if__cong]) ).
fof(i_0_1580,plain,
! [X159,X160] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X159),X160))
| ~ hBOOL(X159)
| hBOOL(X160) ),
inference(fof_simplification,[status(thm)],[help_fimplies_3_1_U]) ).
fof(i_0_1581,plain,
! [X159,X160] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X159),X160))
| hBOOL(X159)
| hBOOL(X160) ),
inference(fof_simplification,[status(thm)],[help_fdisj_3_1_U]) ).
fof(i_0_1582,plain,
! [X159,X160] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X159),X160))
| hBOOL(X159) ),
inference(fof_simplification,[status(thm)],[help_fconj_2_1_U]) ).
fof(i_0_1583,plain,
! [X159,X160] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X159),X160))
| hBOOL(X160) ),
inference(fof_simplification,[status(thm)],[help_fconj_3_1_U]) ).
fof(i_0_1584,plain,
! [X5] :
( ! [X30] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
<=> X5 = bot_bot_fun_nat_bool ),
inference(fof_simplification,[status(thm)],[fact_532_all__not__in__conv]) ).
fof(i_0_1585,plain,
! [X8,X5] :
( X5 = bot_bot_fun_nat_bool
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5)) ),
inference(fof_simplification,[status(thm)],[fact_505_equals0D]) ).
fof(i_0_1586,plain,
! [X5] :
( ! [X30] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X30),X5))
<=> X5 = bot_bot_fun_int_bool ),
inference(fof_simplification,[status(thm)],[fact_531_all__not__in__conv]) ).
fof(i_0_1587,plain,
! [X8,X5] :
( X5 = bot_bot_fun_int_bool
=> ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),X5)) ),
inference(fof_simplification,[status(thm)],[fact_504_equals0D]) ).
fof(i_0_1588,plain,
! [X8,X5] :
( X5 = bot_bo844097828e_bool
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5)) ),
inference(fof_simplification,[status(thm)],[fact_507_equals0D]) ).
fof(i_0_1589,plain,
! [X8,X5] :
( X5 = bot_bot_fun_a_bool
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5)) ),
inference(fof_simplification,[status(thm)],[fact_506_equals0D]) ).
fof(i_0_1590,plain,
! [X18,X19] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X18),X19))
| X18 = X19 ),
inference(fof_simplification,[status(thm)],[help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T]) ).
fof(i_0_1591,plain,
! [X18,X19] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X18),X19))
| X18 = X19 ),
inference(fof_simplification,[status(thm)],[help_fequal_1_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T]) ).
fof(i_0_1592,plain,
! [X18,X19] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X18),X19))
| X18 = X19 ),
inference(fof_simplification,[status(thm)],[help_fequal_1_1_fequal_000tc__Nat__Onat_T]) ).
fof(i_0_1593,plain,
! [X18,X19] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X18),X19))
| X18 = X19 ),
inference(fof_simplification,[status(thm)],[help_fequal_1_1_fequal_000tc__Int__Oint_T]) ).
fof(i_0_1594,plain,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X14)),
inference(fof_simplification,[status(thm)],[fact_861_less__irrefl__nat]) ).
fof(i_0_1595,plain,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X14)),
inference(fof_simplification,[status(thm)],[fact_858_less__not__refl]) ).
fof(i_0_1596,plain,
! [X6604] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6604)))
| hAPP_nat_nat(suc,number_number_of_nat(X6604)) = one_one_nat )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6604)))
| hAPP_nat_nat(suc,number_number_of_nat(X6604)) = number_number_of_nat(succ(X6604)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1407])]) ).
fof(i_0_1597,plain,
! [X32] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),bot_bot_fun_nat_bool)),
inference(fof_simplification,[status(thm)],[fact_518_empty__iff]) ).
fof(i_0_1598,plain,
! [X8] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),bot_bot_fun_nat_bool)),
inference(fof_simplification,[status(thm)],[fact_491_emptyE]) ).
fof(i_0_1599,plain,
! [X32] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X32),bot_bot_fun_int_bool)),
inference(fof_simplification,[status(thm)],[fact_517_empty__iff]) ).
fof(i_0_1600,plain,
! [X8] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X8),bot_bot_fun_int_bool)),
inference(fof_simplification,[status(thm)],[fact_490_emptyE]) ).
fof(i_0_1601,plain,
! [X32] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),bot_bo844097828e_bool)),
inference(fof_simplification,[status(thm)],[fact_520_empty__iff]) ).
fof(i_0_1602,plain,
! [X8] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),bot_bo844097828e_bool)),
inference(fof_simplification,[status(thm)],[fact_493_emptyE]) ).
fof(i_0_1603,plain,
! [X32] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X32),bot_bot_fun_a_bool)),
inference(fof_simplification,[status(thm)],[fact_519_empty__iff]) ).
fof(i_0_1604,plain,
! [X8] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),bot_bot_fun_a_bool)),
inference(fof_simplification,[status(thm)],[fact_492_emptyE]) ).
fof(i_0_1605,plain,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),zero_zero_nat)),
inference(fof_simplification,[status(thm)],[fact_939_not__less0]) ).
fof(i_0_1606,plain,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),zero_zero_nat)),
inference(fof_simplification,[status(thm)],[fact_937_less__nat__zero__code]) ).
fof(i_0_1607,plain,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),zero_zero_nat)),
inference(fof_simplification,[status(thm)],[fact_921_less__zeroE]) ).
fof(i_0_1608,plain,
! [X14] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,X14))),
inference(fof_simplification,[status(thm)],[fact_1151_not__neg__int]) ).
fof(i_0_1609,plain,
! [X6504] : collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X6504)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(X6504,semiri1621563631at_int))),
inference(variable_rename,[status(thm)],[fact_1117_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J]) ).
fof(i_0_1610,plain,
! [X5872] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X5872)))),
inference(variable_rename,[status(thm)],[fact_857_finite__Collect__less__nat]) ).
fof(i_0_1611,plain,
! [X3880] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X3880)))),
inference(variable_rename,[status(thm)],[fact_120_finite__Collect__le__nat]) ).
fof(i_0_1612,plain,
! [X160,X159] :
( ~ hBOOL(X159)
| ~ hBOOL(X160)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X159),X160)) ),
inference(fof_simplification,[status(thm)],[help_fconj_1_1_U]) ).
fof(i_0_1613,plain,
! [X159,X160] :
( ~ hBOOL(X160)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X159),X160)) ),
inference(fof_simplification,[status(thm)],[help_fimplies_2_1_U]) ).
fof(i_0_1614,plain,
! [X160,X159] :
( ~ hBOOL(X159)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X159),X160)) ),
inference(fof_simplification,[status(thm)],[help_fdisj_1_1_U]) ).
fof(i_0_1615,plain,
! [X159,X160] :
( ~ hBOOL(X160)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X159),X160)) ),
inference(fof_simplification,[status(thm)],[help_fdisj_2_1_U]) ).
fof(i_0_1616,plain,
! [X5,X10] :
( X5 = X10
=> ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_429_equalityE]) ).
fof(i_0_1617,plain,
! [X5,X10] :
( X5 = X10
=> ~ ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5),X10))
=> ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X10),X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_428_equalityE]) ).
fof(i_0_1618,plain,
! [X5,X10] :
( X5 = X10
=> ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_430_equalityE]) ).
fof(i_0_1619,plain,
! [X13] :
( collect_a(X13) = bot_bot_fun_a_bool
<=> ! [X30] :
( is_a(X30)
=> ~ hBOOL(hAPP_a_bool(X13,X30)) ) ),
inference(fof_simplification,[status(thm)],[fact_510_Collect__empty__eq]) ).
fof(i_0_1620,plain,
! [X13] :
( bot_bot_fun_a_bool = collect_a(X13)
<=> ! [X30] :
( is_a(X30)
=> ~ hBOOL(hAPP_a_bool(X13,X30)) ) ),
inference(fof_simplification,[status(thm)],[fact_523_empty__Collect__eq]) ).
fof(i_0_1621,plain,
! [X6581] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6581)))
| hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X6581)) = zero_zero_int )
& ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6581)))
| hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X6581)) = number_number_of_int(X6581) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1408])]) ).
fof(i_0_1622,plain,
! [X3881] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X3881))) = hAPP_nat_nat(suc,X3881),
inference(variable_rename,[status(thm)],[fact_121_card__Collect__le__nat]) ).
fof(i_0_1623,plain,
! [X5229] : collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X5229)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5229),bot_bot_fun_int_bool),
inference(variable_rename,[status(thm)],[fact_637_singleton__conv]) ).
fof(i_0_1624,plain,
! [X5230] : collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X5230)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5230),bot_bot_fun_nat_bool),
inference(variable_rename,[status(thm)],[fact_638_singleton__conv]) ).
fof(i_0_1625,plain,
! [X159] :
( ~ hBOOL(hAPP_bool_bool(fNot,X159))
| ~ hBOOL(X159) ),
inference(fof_simplification,[status(thm)],[help_fNot_1_1_U]) ).
fof(i_0_1626,plain,
! [X4979,X4980,X4981] :
( ( bot_bot_fun_nat_bool != collect_nat(X4979)
| ~ hBOOL(hAPP_nat_bool(X4979,X4980)) )
& ( hBOOL(hAPP_nat_bool(X4981,esk91_1(X4981)))
| bot_bot_fun_nat_bool = collect_nat(X4981) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1409])])])])]) ).
fof(i_0_1627,plain,
! [X4975,X4976,X4977] :
( ( bot_bot_fun_int_bool != collect_int(X4975)
| ~ hBOOL(hAPP_int_bool(X4975,X4976)) )
& ( hBOOL(hAPP_int_bool(X4977,esk90_1(X4977)))
| bot_bot_fun_int_bool = collect_int(X4977) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1410])])])])]) ).
fof(i_0_1628,plain,
! [X4957,X4958,X4959] :
( ( collect_nat(X4957) != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_nat_bool(X4957,X4958)) )
& ( hBOOL(hAPP_nat_bool(X4959,esk88_1(X4959)))
| collect_nat(X4959) = bot_bot_fun_nat_bool ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1411])])])])]) ).
fof(i_0_1629,plain,
! [X4953,X4954,X4955] :
( ( collect_int(X4953) != bot_bot_fun_int_bool
| ~ hBOOL(hAPP_int_bool(X4953,X4954)) )
& ( hBOOL(hAPP_int_bool(X4955,esk87_1(X4955)))
| collect_int(X4955) = bot_bot_fun_int_bool ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1412])])])])]) ).
fof(i_0_1630,plain,
! [X5232] : collect_int(hAPP_i1948725293t_bool(fequal_int,X5232)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5232),bot_bot_fun_int_bool),
inference(variable_rename,[status(thm)],[fact_640_singleton__conv2]) ).
fof(i_0_1631,plain,
! [X5233] : collect_nat(hAPP_n1699378549t_bool(fequal_nat,X5233)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5233),bot_bot_fun_nat_bool),
inference(variable_rename,[status(thm)],[fact_641_singleton__conv2]) ).
fof(i_0_1632,plain,
! [X6575] :
( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X6575)))
| number_number_of_nat(X6575) = zero_zero_nat ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1153_neg__imp__number__of__eq__0])]) ).
fof(i_0_1633,plain,
! [X5966] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X5966))) = X5966,
inference(variable_rename,[status(thm)],[fact_896_card__Collect__less__nat]) ).
fof(i_0_1634,plain,
~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(pls))),
inference(fof_simplification,[status(thm)],[fact_1168_not__neg__number__of__Pls]) ).
fof(i_0_1635,plain,
! [X6595,X6596,X6597,X6598] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6598),esk221_4(X6595,X6596,X6597,X6598)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6595),hAPP_nat_int(X6596,X6597)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6596,X6598)),X6595))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6598),X6597))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6598),esk220_4(X6595,X6596,X6597,X6598))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk221_4(X6595,X6596,X6597,X6598)),X6597))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6595),hAPP_nat_int(X6596,X6597)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6596,X6598)),X6595))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6598),X6597))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6598),esk220_4(X6595,X6596,X6597,X6598))) )
& ( hAPP_nat_int(X6596,esk221_4(X6595,X6596,X6597,X6598)) = X6595
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6595),hAPP_nat_int(X6596,X6597)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6596,X6598)),X6595))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6598),X6597))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6598),esk220_4(X6595,X6596,X6597,X6598))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6598),esk221_4(X6595,X6596,X6597,X6598)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6595),hAPP_nat_int(X6596,X6597)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6596,X6598)),X6595))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6598),X6597))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk220_4(X6595,X6596,X6597,X6598)),X6597)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk221_4(X6595,X6596,X6597,X6598)),X6597))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6595),hAPP_nat_int(X6596,X6597)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6596,X6598)),X6595))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6598),X6597))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk220_4(X6595,X6596,X6597,X6598)),X6597)) )
& ( hAPP_nat_int(X6596,esk221_4(X6595,X6596,X6597,X6598)) = X6595
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6595),hAPP_nat_int(X6596,X6597)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6596,X6598)),X6595))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6598),X6597))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk220_4(X6595,X6596,X6597,X6598)),X6597)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6598),esk221_4(X6595,X6596,X6597,X6598)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6595),hAPP_nat_int(X6596,X6597)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6596,X6598)),X6595))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6598),X6597))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X6596,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk220_4(X6595,X6596,X6597,X6598)),one_one_nat))),hAPP_nat_int(X6596,esk220_4(X6595,X6596,X6597,X6598))))),one_one_int)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk221_4(X6595,X6596,X6597,X6598)),X6597))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6595),hAPP_nat_int(X6596,X6597)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6596,X6598)),X6595))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6598),X6597))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X6596,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk220_4(X6595,X6596,X6597,X6598)),one_one_nat))),hAPP_nat_int(X6596,esk220_4(X6595,X6596,X6597,X6598))))),one_one_int)) )
& ( hAPP_nat_int(X6596,esk221_4(X6595,X6596,X6597,X6598)) = X6595
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6595),hAPP_nat_int(X6596,X6597)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6596,X6598)),X6595))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6598),X6597))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X6596,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk220_4(X6595,X6596,X6597,X6598)),one_one_nat))),hAPP_nat_int(X6596,esk220_4(X6595,X6596,X6597,X6598))))),one_one_int)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1160_nat__intermed__int__val])])])]) ).
fof(i_0_1636,plain,
! [X6590,X6591,X6592] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk219_3(X6590,X6591,X6592)),X6592))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6590),hAPP_nat_int(X6591,X6592)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6591,zero_zero_nat)),X6590))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk218_3(X6590,X6591,X6592)),X6592)) )
& ( hAPP_nat_int(X6591,esk219_3(X6590,X6591,X6592)) = X6590
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6590),hAPP_nat_int(X6591,X6592)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6591,zero_zero_nat)),X6590))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk218_3(X6590,X6591,X6592)),X6592)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk219_3(X6590,X6591,X6592)),X6592))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6590),hAPP_nat_int(X6591,X6592)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6591,zero_zero_nat)),X6590))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X6591,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk218_3(X6590,X6591,X6592)),one_one_nat))),hAPP_nat_int(X6591,esk218_3(X6590,X6591,X6592))))),one_one_int)) )
& ( hAPP_nat_int(X6591,esk219_3(X6590,X6591,X6592)) = X6590
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6590),hAPP_nat_int(X6591,X6592)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6591,zero_zero_nat)),X6590))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X6591,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk218_3(X6590,X6591,X6592)),one_one_nat))),hAPP_nat_int(X6591,esk218_3(X6590,X6591,X6592))))),one_one_int)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1159_nat0__intermed__int__val])])])]) ).
fof(i_0_1637,plain,
! [X6585,X6586,X6587] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk217_3(X6585,X6586,X6587)),X6587))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6585),hAPP_nat_int(X6586,X6587)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6586,zero_zero_nat)),X6585))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk216_3(X6585,X6586,X6587)),X6587)) )
& ( hAPP_nat_int(X6586,esk217_3(X6585,X6586,X6587)) = X6585
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6585),hAPP_nat_int(X6586,X6587)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6586,zero_zero_nat)),X6585))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk216_3(X6585,X6586,X6587)),X6587)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk217_3(X6585,X6586,X6587)),X6587))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6585),hAPP_nat_int(X6586,X6587)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6586,zero_zero_nat)),X6585))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X6586,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk216_3(X6585,X6586,X6587)),one_one_nat))),hAPP_nat_int(X6586,esk216_3(X6585,X6586,X6587))))),one_one_int)) )
& ( hAPP_nat_int(X6586,esk217_3(X6585,X6586,X6587)) = X6585
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6585),hAPP_nat_int(X6586,X6587)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X6586,zero_zero_nat)),X6585))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X6586,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk216_3(X6585,X6586,X6587)),one_one_nat))),hAPP_nat_int(X6586,esk216_3(X6585,X6586,X6587))))),one_one_int)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1158_int__val__lemma])])])]) ).
fof(i_0_1638,plain,
! [X6565,X6566,X6567] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6567))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6565),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6565),X6566))),one_one_int)),X6567))),X6566)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1144_decr__lemma])]) ).
cnf(i_0_1639,plain,
hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X1))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),X1),
inference(split_conjunct,[status(thm)],[i_0_1413]) ).
cnf(i_0_1640,plain,
bit1(X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1),
inference(split_conjunct,[status(thm)],[i_0_1414]) ).
fof(i_0_1641,plain,
! [X6366,X6367,X6368,X6369,X6370] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6370),X6366)),X6367)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6369),X6366)),X6368)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6370),X6369)),X6366)),X6367)),X6368))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6369),X6370)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6370),X6369)),X6366)),X6367)),X6368))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6370),X6366)),X6367)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6369),X6366)),X6368)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6369),X6370)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1068_nat__less__add__iff1])])]) ).
fof(i_0_1642,plain,
! [X6336,X6337,X6338,X6339,X6340] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6340),X6336)),X6337)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6339),X6336)),X6338)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6340),X6339)),X6336)),X6337)),X6338))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6339),X6340)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6340),X6339)),X6336)),X6337)),X6338))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6340),X6336)),X6337)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6339),X6336)),X6338)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6339),X6340)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1062_nat__le__add__iff1])])]) ).
fof(i_0_1643,plain,
! [X6582,X6583,X6584] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6584))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6582),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6583),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6583),X6582))),one_one_int)),X6584)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1157_incr__lemma])]) ).
fof(i_0_1644,plain,
! [X5596,X5597,X5598] :
( ( is_pname(esk148_3(X5596,X5597,X5598))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(X5598,X5596)),X5596))
| X5596 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5596))
| ~ hBOOL(finite1282449217_pname(X5597,X5598))
| ~ is_fun_pname_bool(X5596) )
& ( is_pname(esk149_3(X5596,X5597,X5598))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(X5598,X5596)),X5596))
| X5596 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5596))
| ~ hBOOL(finite1282449217_pname(X5597,X5598))
| ~ is_fun_pname_bool(X5596) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(X5597,esk148_3(X5596,X5597,X5598)),esk149_3(X5596,X5597,X5598))),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk148_3(X5596,X5597,X5598)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk149_3(X5596,X5597,X5598)),bot_bo844097828e_bool))))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(X5598,X5596)),X5596))
| X5596 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5596))
| ~ hBOOL(finite1282449217_pname(X5597,X5598))
| ~ is_fun_pname_bool(X5596) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_762_folding__one_Oclosed])])])])])]) ).
fof(i_0_1645,plain,
! [X5581,X5582,X5583] :
( ( is_a(esk142_3(X5581,X5582,X5583))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(X5583,X5581)),X5581))
| X5581 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5581))
| ~ hBOOL(finite_folding_one_a(X5582,X5583))
| ~ is_fun_a_bool(X5581) )
& ( is_a(esk143_3(X5581,X5582,X5583))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(X5583,X5581)),X5581))
| X5581 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5581))
| ~ hBOOL(finite_folding_one_a(X5582,X5583))
| ~ is_fun_a_bool(X5581) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_a_a(hAPP_a_fun_a_a(X5582,esk142_3(X5581,X5582,X5583)),esk143_3(X5581,X5582,X5583))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk142_3(X5581,X5582,X5583)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk143_3(X5581,X5582,X5583)),bot_bot_fun_a_bool))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(X5583,X5581)),X5581))
| X5581 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5581))
| ~ hBOOL(finite_folding_one_a(X5582,X5583))
| ~ is_fun_a_bool(X5581) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_759_folding__one_Oclosed])])])])])]) ).
fof(i_0_1646,plain,
! [X5591,X5592,X5593] :
( ~ hBOOL(finite988810631ne_nat(X5592,X5593))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5591))
| X5591 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(X5592,esk146_3(X5591,X5592,X5593)),esk147_3(X5591,X5592,X5593))),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk146_3(X5591,X5592,X5593)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk147_3(X5591,X5592,X5593)),bot_bot_fun_nat_bool))))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(X5593,X5591)),X5591)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_761_folding__one_Oclosed])])]) ).
fof(i_0_1647,plain,
! [X5586,X5587,X5588] :
( ~ hBOOL(finite1626084323ne_int(X5587,X5588))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5586))
| X5586 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(X5587,esk144_3(X5586,X5587,X5588)),esk145_3(X5586,X5587,X5588))),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk144_3(X5586,X5587,X5588)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk145_3(X5586,X5587,X5588)),bot_bot_fun_int_bool))))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(X5588,X5586)),X5586)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_760_folding__one_Oclosed])])]) ).
cnf(i_0_1648,plain,
number_number_of_int(bit1(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit1(bit1(pls)))),
inference(split_conjunct,[status(thm)],[fact_1169_transfer__int__nat__numerals_I4_J]) ).
cnf(i_0_1649,plain,
number_number_of_int(X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_1415]) ).
fof(i_0_1650,plain,
! [X6459,X6460,X6461,X6464,X6466] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6464),esk202_4(X6459,X6460,X6461,X6464)))
| ~ hBOOL(hAPP_int_bool(X6460,X6466))
| hBOOL(hAPP_int_bool(X6459,esk203_3(X6459,X6460,X6461)))
| ~ hBOOL(hAPP_int_bool(X6460,esk200_3(X6459,X6460,X6461)))
| ~ hBOOL(hAPP_int_bool(X6460,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk200_3(X6459,X6460,X6461)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk201_3(X6459,X6460,X6461)),X6461))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6461)) )
& ( ~ hBOOL(hAPP_int_bool(X6459,esk202_4(X6459,X6460,X6461,X6464)))
| ~ hBOOL(hAPP_int_bool(X6460,esk202_4(X6459,X6460,X6461,X6464)))
| ~ hBOOL(hAPP_int_bool(X6460,X6466))
| hBOOL(hAPP_int_bool(X6459,esk203_3(X6459,X6460,X6461)))
| ~ hBOOL(hAPP_int_bool(X6460,esk200_3(X6459,X6460,X6461)))
| ~ hBOOL(hAPP_int_bool(X6460,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk200_3(X6459,X6460,X6461)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk201_3(X6459,X6460,X6461)),X6461))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6461)) )
& ( hBOOL(hAPP_int_bool(X6459,esk202_4(X6459,X6460,X6461,X6464)))
| hBOOL(hAPP_int_bool(X6460,esk202_4(X6459,X6460,X6461,X6464)))
| ~ hBOOL(hAPP_int_bool(X6460,X6466))
| hBOOL(hAPP_int_bool(X6459,esk203_3(X6459,X6460,X6461)))
| ~ hBOOL(hAPP_int_bool(X6460,esk200_3(X6459,X6460,X6461)))
| ~ hBOOL(hAPP_int_bool(X6460,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk200_3(X6459,X6460,X6461)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk201_3(X6459,X6460,X6461)),X6461))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6461)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6464),esk202_4(X6459,X6460,X6461,X6464)))
| ~ hBOOL(hAPP_int_bool(X6460,X6466))
| hBOOL(hAPP_int_bool(X6459,esk203_3(X6459,X6460,X6461)))
| hBOOL(hAPP_int_bool(X6460,esk200_3(X6459,X6460,X6461)))
| hBOOL(hAPP_int_bool(X6460,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk200_3(X6459,X6460,X6461)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk201_3(X6459,X6460,X6461)),X6461))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6461)) )
& ( ~ hBOOL(hAPP_int_bool(X6459,esk202_4(X6459,X6460,X6461,X6464)))
| ~ hBOOL(hAPP_int_bool(X6460,esk202_4(X6459,X6460,X6461,X6464)))
| ~ hBOOL(hAPP_int_bool(X6460,X6466))
| hBOOL(hAPP_int_bool(X6459,esk203_3(X6459,X6460,X6461)))
| hBOOL(hAPP_int_bool(X6460,esk200_3(X6459,X6460,X6461)))
| hBOOL(hAPP_int_bool(X6460,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk200_3(X6459,X6460,X6461)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk201_3(X6459,X6460,X6461)),X6461))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6461)) )
& ( hBOOL(hAPP_int_bool(X6459,esk202_4(X6459,X6460,X6461,X6464)))
| hBOOL(hAPP_int_bool(X6460,esk202_4(X6459,X6460,X6461,X6464)))
| ~ hBOOL(hAPP_int_bool(X6460,X6466))
| hBOOL(hAPP_int_bool(X6459,esk203_3(X6459,X6460,X6461)))
| hBOOL(hAPP_int_bool(X6460,esk200_3(X6459,X6460,X6461)))
| hBOOL(hAPP_int_bool(X6460,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk200_3(X6459,X6460,X6461)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk201_3(X6459,X6460,X6461)),X6461))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6461)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1094_plusinfinity])])])])]) ).
fof(i_0_1651,plain,
! [X6450,X6451,X6452,X6455,X6457] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,esk198_4(X6450,X6451,X6452,X6455)),X6455))
| ~ hBOOL(hAPP_int_bool(X6451,X6457))
| hBOOL(hAPP_int_bool(X6450,esk199_3(X6450,X6451,X6452)))
| ~ hBOOL(hAPP_int_bool(X6451,esk196_3(X6450,X6451,X6452)))
| ~ hBOOL(hAPP_int_bool(X6451,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk196_3(X6450,X6451,X6452)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk197_3(X6450,X6451,X6452)),X6452))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6452)) )
& ( ~ hBOOL(hAPP_int_bool(X6450,esk198_4(X6450,X6451,X6452,X6455)))
| ~ hBOOL(hAPP_int_bool(X6451,esk198_4(X6450,X6451,X6452,X6455)))
| ~ hBOOL(hAPP_int_bool(X6451,X6457))
| hBOOL(hAPP_int_bool(X6450,esk199_3(X6450,X6451,X6452)))
| ~ hBOOL(hAPP_int_bool(X6451,esk196_3(X6450,X6451,X6452)))
| ~ hBOOL(hAPP_int_bool(X6451,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk196_3(X6450,X6451,X6452)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk197_3(X6450,X6451,X6452)),X6452))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6452)) )
& ( hBOOL(hAPP_int_bool(X6450,esk198_4(X6450,X6451,X6452,X6455)))
| hBOOL(hAPP_int_bool(X6451,esk198_4(X6450,X6451,X6452,X6455)))
| ~ hBOOL(hAPP_int_bool(X6451,X6457))
| hBOOL(hAPP_int_bool(X6450,esk199_3(X6450,X6451,X6452)))
| ~ hBOOL(hAPP_int_bool(X6451,esk196_3(X6450,X6451,X6452)))
| ~ hBOOL(hAPP_int_bool(X6451,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk196_3(X6450,X6451,X6452)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk197_3(X6450,X6451,X6452)),X6452))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6452)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,esk198_4(X6450,X6451,X6452,X6455)),X6455))
| ~ hBOOL(hAPP_int_bool(X6451,X6457))
| hBOOL(hAPP_int_bool(X6450,esk199_3(X6450,X6451,X6452)))
| hBOOL(hAPP_int_bool(X6451,esk196_3(X6450,X6451,X6452)))
| hBOOL(hAPP_int_bool(X6451,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk196_3(X6450,X6451,X6452)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk197_3(X6450,X6451,X6452)),X6452))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6452)) )
& ( ~ hBOOL(hAPP_int_bool(X6450,esk198_4(X6450,X6451,X6452,X6455)))
| ~ hBOOL(hAPP_int_bool(X6451,esk198_4(X6450,X6451,X6452,X6455)))
| ~ hBOOL(hAPP_int_bool(X6451,X6457))
| hBOOL(hAPP_int_bool(X6450,esk199_3(X6450,X6451,X6452)))
| hBOOL(hAPP_int_bool(X6451,esk196_3(X6450,X6451,X6452)))
| hBOOL(hAPP_int_bool(X6451,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk196_3(X6450,X6451,X6452)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk197_3(X6450,X6451,X6452)),X6452))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6452)) )
& ( hBOOL(hAPP_int_bool(X6450,esk198_4(X6450,X6451,X6452,X6455)))
| hBOOL(hAPP_int_bool(X6451,esk198_4(X6450,X6451,X6452,X6455)))
| ~ hBOOL(hAPP_int_bool(X6451,X6457))
| hBOOL(hAPP_int_bool(X6450,esk199_3(X6450,X6451,X6452)))
| hBOOL(hAPP_int_bool(X6451,esk196_3(X6450,X6451,X6452)))
| hBOOL(hAPP_int_bool(X6451,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk196_3(X6450,X6451,X6452)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk197_3(X6450,X6451,X6452)),X6452))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6452)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1093_minusinfinity])])])])]) ).
fof(i_0_1652,plain,
! [X6230,X6231,X6232,X6233,X6234] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6233),X6230)),X6231)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6234),X6230)),X6232)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6231),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6234),X6233)),X6230)),X6232)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6233),X6234)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6231),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6234),X6233)),X6230)),X6232)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6233),X6230)),X6231)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6234),X6230)),X6232)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6233),X6234)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1015_nat__less__add__iff2])])]) ).
fof(i_0_1653,plain,
! [X6351,X6352,X6353,X6354,X6355] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6354),X6351)),X6352)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6355),X6351)),X6353)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6352),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6355),X6354)),X6351)),X6353)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6354),X6355)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6352),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6355),X6354)),X6351)),X6353)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6354),X6351)),X6352)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6355),X6351)),X6353)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6354),X6355)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1065_nat__le__add__iff2])])]) ).
cnf(i_0_1654,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
inference(split_conjunct,[status(thm)],[fact_1188_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J]) ).
fof(i_0_1655,plain,
! [X4354,X4355] :
( ( is_pname(esk62_2(X4354,X4355))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X4354,X4355)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4355)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk62_2(X4354,X4355)),X4355))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X4354,X4355)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4355)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X4355)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X4354)),hAPP_pname_a(X4354,esk62_2(X4354,X4355)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X4354,X4355)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4355)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1416])])])]) ).
fof(i_0_1656,plain,
! [X6341,X6342,X6343,X6344,X6345] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6344),X6345))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6345),X6341)),X6342)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6344),X6341)),X6343)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6345),X6344)),X6341)),X6342)),X6343) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1063_nat__diff__add__eq1])]) ).
fof(i_0_1657,plain,
! [X6377,X6378,X6379,X6380,X6381] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6377),X6378)),X6379)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6377),X6380)),X6381)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6381),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6377),X6381))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6377),X6379))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6380),X6378)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1070_unique__quotient__lemma__neg])]) ).
fof(i_0_1658,plain,
! [X6395,X6396,X6397,X6398,X6399] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6395),X6396)),X6397)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6395),X6398)),X6399)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6397))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6397),X6395))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6399),X6395))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6396),X6398)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1077_unique__quotient__lemma])]) ).
cnf(i_0_1659,plain,
number_number_of_nat(bit1(bit1(pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),
inference(split_conjunct,[status(thm)],[fact_1171_numeral__3__eq__3]) ).
fof(i_0_1660,plain,
! [X4319,X4320,X4321] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X4321,esk51_3(X4319,X4320,X4321))),hAPP_n1699378549t_bool(X4321,hAPP_nat_nat(suc,esk51_3(X4319,X4320,X4321)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4319),X4320))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X4321,X4319)),hAPP_n1699378549t_bool(X4321,X4320))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_269_lift__Suc__mono__le])])]) ).
fof(i_0_1661,plain,
! [X4323,X4324,X4325] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(X4325,esk52_3(X4323,X4324,X4325))),hAPP_n1082236369t_bool(X4325,hAPP_nat_nat(suc,esk52_3(X4323,X4324,X4325)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4323),X4324))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(X4325,X4323)),hAPP_n1082236369t_bool(X4325,X4324))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_270_lift__Suc__mono__le])])]) ).
fof(i_0_1662,plain,
! [X4299,X4300,X4301] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X4301,esk46_3(X4299,X4300,X4301))),hAPP_n1025906991e_bool(X4301,hAPP_nat_nat(suc,esk46_3(X4299,X4300,X4301)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4299),X4300))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X4301,X4299)),hAPP_n1025906991e_bool(X4301,X4300))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_264_lift__Suc__mono__le])])]) ).
fof(i_0_1663,plain,
! [X4307,X4308,X4309] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X4309,esk48_3(X4307,X4308,X4309))),hAPP_nat_fun_a_bool(X4309,hAPP_nat_nat(suc,esk48_3(X4307,X4308,X4309)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4307),X4308))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X4309,X4307)),hAPP_nat_fun_a_bool(X4309,X4308))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_266_lift__Suc__mono__le])])]) ).
fof(i_0_1664,plain,
! [X4311,X4312,X4313] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X4313,esk49_3(X4311,X4312,X4313))),hAPP_nat_nat(X4313,hAPP_nat_nat(suc,esk49_3(X4311,X4312,X4313)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4311),X4312))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X4313,X4311)),hAPP_nat_nat(X4313,X4312))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_267_lift__Suc__mono__le])])]) ).
fof(i_0_1665,plain,
! [X4315,X4316,X4317] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X4317,esk50_3(X4315,X4316,X4317))),hAPP_nat_int(X4317,hAPP_nat_nat(suc,esk50_3(X4315,X4316,X4317)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4315),X4316))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X4317,X4315)),hAPP_nat_int(X4317,X4316))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_268_lift__Suc__mono__le])])]) ).
fof(i_0_1666,plain,
! [X4303,X4304,X4305] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X4305,esk47_3(X4303,X4304,X4305))),hAPP_nat_bool(X4305,hAPP_nat_nat(suc,esk47_3(X4303,X4304,X4305)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4303),X4304))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X4305,X4303)),hAPP_nat_bool(X4305,X4304))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_265_lift__Suc__mono__le])])]) ).
fof(i_0_1667,plain,
! [X6007,X6008,X6009] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk166_3(X6007,X6008,X6009)),esk167_3(X6007,X6008,X6009)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(X6009,X6007)),X6008)),hAPP_nat_nat(X6009,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6007),X6008)))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X6009,esk166_3(X6007,X6008,X6009))),hAPP_nat_nat(X6009,esk167_3(X6007,X6008,X6009))))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(X6009,X6007)),X6008)),hAPP_nat_nat(X6009,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6007),X6008)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_914_mono__nat__linear__lb])])])]) ).
fof(i_0_1668,plain,
! [X6371,X6372,X6373,X6374,X6375,X6376] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6371),X6372)),X6373) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6374),X6375)),X6376)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6374),X6375)),X6376)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6373),X6371))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6376))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6374))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6374),X6371))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6375),X6372)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1069_zdiv__mono2__neg__lemma])]) ).
cnf(i_0_1669,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1417]) ).
cnf(i_0_1670,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1418]) ).
cnf(i_0_1671,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1419]) ).
cnf(i_0_1672,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1420]) ).
fof(i_0_1673,plain,
! [X6445,X6446,X6447] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,esk195_3(X6445,X6446,X6447)),X6447))
| hBOOL(hAPP_int_bool(X6446,X6445))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6447),esk194_3(X6445,X6446,X6447)))
| ~ hBOOL(hAPP_int_bool(X6446,X6447)) )
& ( hBOOL(hAPP_int_bool(X6446,esk195_3(X6445,X6446,X6447)))
| hBOOL(hAPP_int_bool(X6446,X6445))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6447),esk194_3(X6445,X6446,X6447)))
| ~ hBOOL(hAPP_int_bool(X6446,X6447)) )
& ( ~ hBOOL(hAPP_int_bool(X6446,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk195_3(X6445,X6446,X6447)),one_one_int)))
| hBOOL(hAPP_int_bool(X6446,X6445))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6447),esk194_3(X6445,X6446,X6447)))
| ~ hBOOL(hAPP_int_bool(X6446,X6447)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,esk195_3(X6445,X6446,X6447)),X6447))
| hBOOL(hAPP_int_bool(X6446,X6445))
| hBOOL(hAPP_int_bool(X6446,esk194_3(X6445,X6446,X6447)))
| ~ hBOOL(hAPP_int_bool(X6446,X6447)) )
& ( hBOOL(hAPP_int_bool(X6446,esk195_3(X6445,X6446,X6447)))
| hBOOL(hAPP_int_bool(X6446,X6445))
| hBOOL(hAPP_int_bool(X6446,esk194_3(X6445,X6446,X6447)))
| ~ hBOOL(hAPP_int_bool(X6446,X6447)) )
& ( ~ hBOOL(hAPP_int_bool(X6446,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk195_3(X6445,X6446,X6447)),one_one_int)))
| hBOOL(hAPP_int_bool(X6446,X6445))
| hBOOL(hAPP_int_bool(X6446,esk194_3(X6445,X6446,X6447)))
| ~ hBOOL(hAPP_int_bool(X6446,X6447)) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,esk195_3(X6445,X6446,X6447)),X6447))
| hBOOL(hAPP_int_bool(X6446,X6445))
| ~ hBOOL(hAPP_int_bool(X6446,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,esk194_3(X6445,X6446,X6447)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X6446,X6447)) )
& ( hBOOL(hAPP_int_bool(X6446,esk195_3(X6445,X6446,X6447)))
| hBOOL(hAPP_int_bool(X6446,X6445))
| ~ hBOOL(hAPP_int_bool(X6446,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,esk194_3(X6445,X6446,X6447)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X6446,X6447)) )
& ( ~ hBOOL(hAPP_int_bool(X6446,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk195_3(X6445,X6446,X6447)),one_one_int)))
| hBOOL(hAPP_int_bool(X6446,X6445))
| ~ hBOOL(hAPP_int_bool(X6446,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,esk194_3(X6445,X6446,X6447)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X6446,X6447)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1092_int__induct])])])]) ).
fof(i_0_1674,plain,
! [X6356,X6357,X6358,X6359,X6360] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6359),X6360))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6359),X6356)),X6357)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6360),X6356)),X6358)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6357),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6360),X6359)),X6356)),X6358)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1066_nat__diff__add__eq2])]) ).
fof(i_0_1675,plain,
! [X6022,X6023,X6024] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk171_3(X6022,X6023,X6024)),esk172_3(X6022,X6023,X6024)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6022),X6023))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X6024,X6022)),hAPP_nat_nat(X6024,X6023))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X6024,esk171_3(X6022,X6023,X6024))),hAPP_nat_nat(X6024,esk172_3(X6022,X6023,X6024))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6022),X6023))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X6024,X6022)),hAPP_nat_nat(X6024,X6023))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_918_less__mono__imp__le__mono])])])]) ).
fof(i_0_1676,plain,
! [X6392,X6393,X6394] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6392),X6393)),X6394)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6394))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6392))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6393),zero_zero_int)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1076_q__neg__lemma])]) ).
cnf(i_0_1677,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X2)),hAPP_n1699378549t_bool(X2,esk54_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1421]) ).
cnf(i_0_1678,plain,
collect_nat(X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_1422]) ).
cnf(i_0_1679,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X2)),hAPP_n1082236369t_bool(X2,esk53_2(X2,X1)))))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1423]) ).
cnf(i_0_1680,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X2)),hAPP_n1025906991e_bool(X2,esk55_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1424]) ).
cnf(i_0_1681,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X2)),hAPP_nat_fun_a_bool(X2,esk56_2(X2,X1)))))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1425]) ).
cnf(i_0_1682,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X2)),hAPP_nat_int(X2,esk63_2(X2,X1)))))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1426]) ).
cnf(i_0_1683,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X2)),hAPP_i418383825t_bool(X2,esk59_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1427]) ).
cnf(i_0_1684,plain,
collect_int(X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_1428]) ).
cnf(i_0_1685,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X2)),hAPP_i1948725293t_bool(X2,esk58_2(X2,X1)))))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1429]) ).
cnf(i_0_1686,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X2)),hAPP_i7355787e_bool(X2,esk60_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1430]) ).
cnf(i_0_1687,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X2)),hAPP_int_fun_a_bool(X2,esk61_2(X2,X1)))))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1431]) ).
cnf(i_0_1688,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X2)),hAPP_int_a(X2,esk57_2(X2,X1)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1432]) ).
fof(i_0_1689,plain,
! [X5328,X5329,X5330] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk106_3(X5328,X5329,X5330)))
| hBOOL(hAPP_f54304608l_bool(X5328,X5330))
| ~ hBOOL(hAPP_f54304608l_bool(X5328,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5330),X5329))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5330)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk105_3(X5328,X5329,X5330)),X5329))
| hBOOL(hAPP_f54304608l_bool(X5328,X5330))
| ~ hBOOL(hAPP_f54304608l_bool(X5328,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5330),X5329))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5330)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk105_3(X5328,X5329,X5330)),esk106_3(X5328,X5329,X5330)))
| hBOOL(hAPP_f54304608l_bool(X5328,X5330))
| ~ hBOOL(hAPP_f54304608l_bool(X5328,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5330),X5329))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5330)) )
& ( hBOOL(hAPP_f54304608l_bool(X5328,esk106_3(X5328,X5329,X5330)))
| hBOOL(hAPP_f54304608l_bool(X5328,X5330))
| ~ hBOOL(hAPP_f54304608l_bool(X5328,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5330),X5329))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5330)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(X5328,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk105_3(X5328,X5329,X5330)),esk106_3(X5328,X5329,X5330))))
| hBOOL(hAPP_f54304608l_bool(X5328,X5330))
| ~ hBOOL(hAPP_f54304608l_bool(X5328,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5330),X5329))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5330)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1433])])])]) ).
fof(i_0_1690,plain,
! [X5323,X5324,X5325] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk104_3(X5323,X5324,X5325)))
| hBOOL(hAPP_f448129468l_bool(X5323,X5325))
| ~ hBOOL(hAPP_f448129468l_bool(X5323,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5325),X5324))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5325)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk103_3(X5323,X5324,X5325)),X5324))
| hBOOL(hAPP_f448129468l_bool(X5323,X5325))
| ~ hBOOL(hAPP_f448129468l_bool(X5323,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5325),X5324))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5325)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk103_3(X5323,X5324,X5325)),esk104_3(X5323,X5324,X5325)))
| hBOOL(hAPP_f448129468l_bool(X5323,X5325))
| ~ hBOOL(hAPP_f448129468l_bool(X5323,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5325),X5324))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5325)) )
& ( hBOOL(hAPP_f448129468l_bool(X5323,esk104_3(X5323,X5324,X5325)))
| hBOOL(hAPP_f448129468l_bool(X5323,X5325))
| ~ hBOOL(hAPP_f448129468l_bool(X5323,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5325),X5324))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5325)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(X5323,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk103_3(X5323,X5324,X5325)),esk104_3(X5323,X5324,X5325))))
| hBOOL(hAPP_f448129468l_bool(X5323,X5325))
| ~ hBOOL(hAPP_f448129468l_bool(X5323,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5325),X5324))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5325)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1434])])])]) ).
fof(i_0_1691,plain,
! [X5333,X5334,X5335] :
( ( is_pname(esk107_3(X5333,X5334,X5335))
| hBOOL(hAPP_f1664156314l_bool(X5333,X5335))
| ~ hBOOL(hAPP_f1664156314l_bool(X5333,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5335),X5334))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5335)) )
& ( is_fun_pname_bool(esk108_3(X5333,X5334,X5335))
| hBOOL(hAPP_f1664156314l_bool(X5333,X5335))
| ~ hBOOL(hAPP_f1664156314l_bool(X5333,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5335),X5334))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5335)) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk108_3(X5333,X5334,X5335)))
| hBOOL(hAPP_f1664156314l_bool(X5333,X5335))
| ~ hBOOL(hAPP_f1664156314l_bool(X5333,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5335),X5334))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5335)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk107_3(X5333,X5334,X5335)),X5334))
| hBOOL(hAPP_f1664156314l_bool(X5333,X5335))
| ~ hBOOL(hAPP_f1664156314l_bool(X5333,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5335),X5334))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5335)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk107_3(X5333,X5334,X5335)),esk108_3(X5333,X5334,X5335)))
| hBOOL(hAPP_f1664156314l_bool(X5333,X5335))
| ~ hBOOL(hAPP_f1664156314l_bool(X5333,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5335),X5334))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5335)) )
& ( hBOOL(hAPP_f1664156314l_bool(X5333,esk108_3(X5333,X5334,X5335)))
| hBOOL(hAPP_f1664156314l_bool(X5333,X5335))
| ~ hBOOL(hAPP_f1664156314l_bool(X5333,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5335),X5334))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5335)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(X5333,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk107_3(X5333,X5334,X5335)),esk108_3(X5333,X5334,X5335))))
| hBOOL(hAPP_f1664156314l_bool(X5333,X5335))
| ~ hBOOL(hAPP_f1664156314l_bool(X5333,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5335),X5334))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5335)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1435])])])]) ).
fof(i_0_1692,plain,
! [X5318,X5319,X5320] :
( ( is_a(esk101_3(X5318,X5319,X5320))
| hBOOL(hAPP_fun_a_bool_bool(X5318,X5320))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5318,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5320),X5319))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5320)) )
& ( is_fun_a_bool(esk102_3(X5318,X5319,X5320))
| hBOOL(hAPP_fun_a_bool_bool(X5318,X5320))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5318,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5320),X5319))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5320)) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk102_3(X5318,X5319,X5320)))
| hBOOL(hAPP_fun_a_bool_bool(X5318,X5320))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5318,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5320),X5319))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5320)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk101_3(X5318,X5319,X5320)),X5319))
| hBOOL(hAPP_fun_a_bool_bool(X5318,X5320))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5318,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5320),X5319))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5320)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk101_3(X5318,X5319,X5320)),esk102_3(X5318,X5319,X5320)))
| hBOOL(hAPP_fun_a_bool_bool(X5318,X5320))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5318,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5320),X5319))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5320)) )
& ( hBOOL(hAPP_fun_a_bool_bool(X5318,esk102_3(X5318,X5319,X5320)))
| hBOOL(hAPP_fun_a_bool_bool(X5318,X5320))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5318,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5320),X5319))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5320)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(X5318,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk101_3(X5318,X5319,X5320)),esk102_3(X5318,X5319,X5320))))
| hBOOL(hAPP_fun_a_bool_bool(X5318,X5320))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5318,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5320),X5319))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5320)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1436])])])]) ).
fof(i_0_1693,plain,
! [X6440,X6441,X6442,X6444] :
( ( hBOOL(hAPP_int_bool(X6441,esk193_3(X6440,X6441,X6442)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6440))
| ~ hBOOL(hAPP_int_bool(X6441,X6444))
| hBOOL(hAPP_int_bool(X6441,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6444),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6440),X6442))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6442)) )
& ( ~ hBOOL(hAPP_int_bool(X6441,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,esk193_3(X6440,X6441,X6442)),X6442)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6440))
| ~ hBOOL(hAPP_int_bool(X6441,X6444))
| hBOOL(hAPP_int_bool(X6441,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6444),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6440),X6442))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6442)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1091_incr__mult__lemma])])])])]) ).
fof(i_0_1694,plain,
! [X6429,X6430,X6431,X6433] :
( ( hBOOL(hAPP_int_bool(X6430,esk192_3(X6429,X6430,X6431)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6429))
| ~ hBOOL(hAPP_int_bool(X6430,X6433))
| hBOOL(hAPP_int_bool(X6430,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6433),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6429),X6431))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6431)) )
& ( ~ hBOOL(hAPP_int_bool(X6430,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk192_3(X6429,X6430,X6431)),X6431)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6429))
| ~ hBOOL(hAPP_int_bool(X6430,X6433))
| hBOOL(hAPP_int_bool(X6430,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6433),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6429),X6431))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6431)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1088_decr__mult__lemma])])])])]) ).
fof(i_0_1695,plain,
! [X6400,X6401,X6402,X6403,X6404,X6405] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6400),X6401)),X6402) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6403),X6404)),X6405)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6403),X6404)),X6405)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6405),X6403))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6402))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6403))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6403),X6400))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6401),X6404)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1078_zdiv__mono2__lemma])]) ).
cnf(i_0_1696,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),pls)) ),
inference(split_conjunct,[status(thm)],[i_0_1437]) ).
cnf(i_0_1697,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),pls)) ),
inference(split_conjunct,[status(thm)],[i_0_1438]) ).
fof(i_0_1698,plain,
! [X6279] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X6279)),X6279)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6279),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6279),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X6279)),X6279)),zero_zero_int)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1039_odd__less__0])]) ).
fof(i_0_1699,plain,
! [X5338,X5339] :
( ~ hBOOL(hAPP_fun_a_bool_bool(p(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X5338)),X5339)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(the_com(body(X5338)))),bot_bot_fun_a_bool)))
| hBOOL(hAPP_fun_a_bool_bool(p(X5339),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X5338)),bot_bot_fun_a_bool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_682_assms_I2_J])]) ).
cnf(i_0_1700,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1417]) ).
cnf(i_0_1701,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1418]) ).
cnf(i_0_1702,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1419]) ).
cnf(i_0_1703,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),bit1(X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1420]) ).
fof(i_0_1704,plain,
! [X6406,X6407,X6408] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,esk187_3(X6406,X6407,X6408)),X6408))
| hBOOL(hAPP_int_bool(X6406,X6407))
| ~ hBOOL(hAPP_int_bool(X6406,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6408),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6407),X6408)) )
& ( hBOOL(hAPP_int_bool(X6406,esk187_3(X6406,X6407,X6408)))
| hBOOL(hAPP_int_bool(X6406,X6407))
| ~ hBOOL(hAPP_int_bool(X6406,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6408),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6407),X6408)) )
& ( ~ hBOOL(hAPP_int_bool(X6406,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk187_3(X6406,X6407,X6408)),one_one_int)))
| hBOOL(hAPP_int_bool(X6406,X6407))
| ~ hBOOL(hAPP_int_bool(X6406,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6408),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6407),X6408)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1079_int__less__induct])])])]) ).
fof(i_0_1705,plain,
! [X6414,X6415,X6416] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6415),esk189_3(X6414,X6415,X6416)))
| hBOOL(hAPP_int_bool(X6414,X6416))
| ~ hBOOL(hAPP_int_bool(X6414,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6415),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6415),X6416)) )
& ( hBOOL(hAPP_int_bool(X6414,esk189_3(X6414,X6415,X6416)))
| hBOOL(hAPP_int_bool(X6414,X6416))
| ~ hBOOL(hAPP_int_bool(X6414,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6415),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6415),X6416)) )
& ( ~ hBOOL(hAPP_int_bool(X6414,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,esk189_3(X6414,X6415,X6416)),one_one_int)))
| hBOOL(hAPP_int_bool(X6414,X6416))
| ~ hBOOL(hAPP_int_bool(X6414,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6415),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6415),X6416)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1081_int__gr__induct])])])]) ).
fof(i_0_1706,plain,
! [X5252,X5253] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5253))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5253),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5252),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,X5253))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_651_card__Diff1__le])]) ).
fof(i_0_1707,plain,
! [X5254,X5255] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5255))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5255),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5254),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,X5255))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_652_card__Diff1__le])]) ).
fof(i_0_1708,plain,
! [X5250,X5251] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5251))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5251),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5250),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,X5251))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_650_card__Diff1__le])]) ).
fof(i_0_1709,plain,
! [X5256,X5257] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5257))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5257),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5256),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,X5257))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_653_card__Diff1__le])]) ).
fof(i_0_1710,plain,
! [X4900,X4901,X4902] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk79_3(X4900,X4901,X4902)),X4902))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X4900,X4902)),X4901)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X4900,esk79_3(X4900,X4901,X4902))),X4901))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X4900,X4902)),X4901)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_481_image__subsetI])])])]) ).
fof(i_0_1711,plain,
! [X4904,X4905,X4906] :
( ( is_pname(esk80_3(X4904,X4905,X4906))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X4904,X4906)),X4905)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk80_3(X4904,X4905,X4906)),X4906))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X4904,X4906)),X4905)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X4904,esk80_3(X4904,X4905,X4906))),X4905))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X4904,X4906)),X4905)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_482_image__subsetI])])])]) ).
fof(i_0_1712,plain,
! [X6410,X6411,X6412] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,esk188_3(X6410,X6411,X6412)),X6412))
| hBOOL(hAPP_int_bool(X6410,X6411))
| ~ hBOOL(hAPP_int_bool(X6410,X6412))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6411),X6412)) )
& ( hBOOL(hAPP_int_bool(X6410,esk188_3(X6410,X6411,X6412)))
| hBOOL(hAPP_int_bool(X6410,X6411))
| ~ hBOOL(hAPP_int_bool(X6410,X6412))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6411),X6412)) )
& ( ~ hBOOL(hAPP_int_bool(X6410,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk188_3(X6410,X6411,X6412)),one_one_int)))
| hBOOL(hAPP_int_bool(X6410,X6411))
| ~ hBOOL(hAPP_int_bool(X6410,X6412))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6411),X6412)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1080_int__le__induct])])])]) ).
fof(i_0_1713,plain,
! [X6418,X6419,X6420] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6419),esk190_3(X6418,X6419,X6420)))
| hBOOL(hAPP_int_bool(X6418,X6420))
| ~ hBOOL(hAPP_int_bool(X6418,X6419))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6419),X6420)) )
& ( hBOOL(hAPP_int_bool(X6418,esk190_3(X6418,X6419,X6420)))
| hBOOL(hAPP_int_bool(X6418,X6420))
| ~ hBOOL(hAPP_int_bool(X6418,X6419))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6419),X6420)) )
& ( ~ hBOOL(hAPP_int_bool(X6418,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,esk190_3(X6418,X6419,X6420)),one_one_int)))
| hBOOL(hAPP_int_bool(X6418,X6420))
| ~ hBOOL(hAPP_int_bool(X6418,X6419))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6419),X6420)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1082_int__ge__induct])])])]) ).
fof(i_0_1714,plain,
! [X5348,X5349] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk114_2(X5348,X5349)))
| hBOOL(hAPP_f54304608l_bool(X5348,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(X5348,X5349))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5349)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk113_2(X5348,X5349)),esk114_2(X5348,X5349)))
| hBOOL(hAPP_f54304608l_bool(X5348,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(X5348,X5349))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5349)) )
& ( hBOOL(hAPP_f54304608l_bool(X5348,esk114_2(X5348,X5349)))
| hBOOL(hAPP_f54304608l_bool(X5348,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(X5348,X5349))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5349)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(X5348,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,esk114_2(X5348,X5349)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk113_2(X5348,X5349)),bot_bot_fun_nat_bool))))
| hBOOL(hAPP_f54304608l_bool(X5348,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(X5348,X5349))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5349)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_685_finite__empty__induct])])])]) ).
fof(i_0_1715,plain,
! [X5344,X5345] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk112_2(X5344,X5345)))
| hBOOL(hAPP_f448129468l_bool(X5344,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(X5344,X5345))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5345)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk111_2(X5344,X5345)),esk112_2(X5344,X5345)))
| hBOOL(hAPP_f448129468l_bool(X5344,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(X5344,X5345))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5345)) )
& ( hBOOL(hAPP_f448129468l_bool(X5344,esk112_2(X5344,X5345)))
| hBOOL(hAPP_f448129468l_bool(X5344,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(X5344,X5345))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5345)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(X5344,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,esk112_2(X5344,X5345)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk111_2(X5344,X5345)),bot_bot_fun_int_bool))))
| hBOOL(hAPP_f448129468l_bool(X5344,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(X5344,X5345))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5345)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_684_finite__empty__induct])])])]) ).
fof(i_0_1716,plain,
! [X5352,X5353] :
( ( is_pname(esk115_2(X5352,X5353))
| hBOOL(hAPP_f1664156314l_bool(X5352,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(X5352,X5353))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5353)) )
& ( is_fun_pname_bool(esk116_2(X5352,X5353))
| hBOOL(hAPP_f1664156314l_bool(X5352,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(X5352,X5353))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5353)) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk116_2(X5352,X5353)))
| hBOOL(hAPP_f1664156314l_bool(X5352,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(X5352,X5353))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5353)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk115_2(X5352,X5353)),esk116_2(X5352,X5353)))
| hBOOL(hAPP_f1664156314l_bool(X5352,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(X5352,X5353))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5353)) )
& ( hBOOL(hAPP_f1664156314l_bool(X5352,esk116_2(X5352,X5353)))
| hBOOL(hAPP_f1664156314l_bool(X5352,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(X5352,X5353))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5353)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(X5352,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,esk116_2(X5352,X5353)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk115_2(X5352,X5353)),bot_bo844097828e_bool))))
| hBOOL(hAPP_f1664156314l_bool(X5352,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(X5352,X5353))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5353)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_686_finite__empty__induct])])])]) ).
fof(i_0_1717,plain,
! [X5340,X5341] :
( ( is_a(esk109_2(X5340,X5341))
| hBOOL(hAPP_fun_a_bool_bool(X5340,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5340,X5341))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5341)) )
& ( is_fun_a_bool(esk110_2(X5340,X5341))
| hBOOL(hAPP_fun_a_bool_bool(X5340,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5340,X5341))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5341)) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk110_2(X5340,X5341)))
| hBOOL(hAPP_fun_a_bool_bool(X5340,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5340,X5341))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5341)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk109_2(X5340,X5341)),esk110_2(X5340,X5341)))
| hBOOL(hAPP_fun_a_bool_bool(X5340,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5340,X5341))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5341)) )
& ( hBOOL(hAPP_fun_a_bool_bool(X5340,esk110_2(X5340,X5341)))
| hBOOL(hAPP_fun_a_bool_bool(X5340,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5340,X5341))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5341)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(X5340,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,esk110_2(X5340,X5341)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk109_2(X5340,X5341)),bot_bot_fun_a_bool))))
| hBOOL(hAPP_fun_a_bool_bool(X5340,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5340,X5341))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5341)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_683_finite__empty__induct])])])]) ).
fof(i_0_1718,plain,
! [X5070,X5071,X5072] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5070),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5071),bot_bot_fun_nat_bool))),X5072))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5071),X5070))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5070),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5071),X5072))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_563_diff__single__insert])]) ).
fof(i_0_1719,plain,
! [X5082,X5083,X5084] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5083),X5082))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5082),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5083),bot_bot_fun_nat_bool))),X5084))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5082),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5083),X5084))) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5083),X5082))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5082),X5084))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5082),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5083),X5084))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5083),X5082))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5083),X5082))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5082),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5083),X5084))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5082),X5084))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5083),X5082))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5082),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5083),X5084))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5083),X5082))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5082),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5083),bot_bot_fun_nat_bool))),X5084))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5082),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5083),X5084))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5082),X5084))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5082),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5083),bot_bot_fun_nat_bool))),X5084))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5082),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5083),X5084))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1439])])]) ).
fof(i_0_1720,plain,
! [X5067,X5068,X5069] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5067),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5068),bot_bot_fun_int_bool))),X5069))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5068),X5067))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5067),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5068),X5069))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_562_diff__single__insert])]) ).
fof(i_0_1721,plain,
! [X5079,X5080,X5081] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5080),X5079))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5079),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5080),bot_bot_fun_int_bool))),X5081))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5079),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5080),X5081))) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5080),X5079))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5079),X5081))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5079),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5080),X5081))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5080),X5079))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5080),X5079))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5079),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5080),X5081))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5079),X5081))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5080),X5079))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5079),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5080),X5081))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5080),X5079))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5079),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5080),bot_bot_fun_int_bool))),X5081))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5079),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5080),X5081))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5079),X5081))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5079),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5080),bot_bot_fun_int_bool))),X5081))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5079),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5080),X5081))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1440])])]) ).
fof(i_0_1722,plain,
! [X5073,X5074,X5075] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5073),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5074),bot_bo844097828e_bool))),X5075))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5074),X5073))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5073),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5074),X5075))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_564_diff__single__insert])]) ).
fof(i_0_1723,plain,
! [X5085,X5086,X5087] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5086),X5085))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5085),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5086),bot_bo844097828e_bool))),X5087))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5085),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5086),X5087))) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5086),X5085))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5085),X5087))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5085),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5086),X5087))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5086),X5085))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5086),X5085))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5085),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5086),X5087))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5085),X5087))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5086),X5085))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5085),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5086),X5087))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5086),X5085))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5085),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5086),bot_bo844097828e_bool))),X5087))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5085),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5086),X5087))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5085),X5087))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5085),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5086),bot_bo844097828e_bool))),X5087))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5085),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5086),X5087))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1441])])]) ).
fof(i_0_1724,plain,
! [X5064,X5065,X5066] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5064),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5065),bot_bot_fun_a_bool))),X5066))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5065),X5064))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5064),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5065),X5066))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_561_diff__single__insert])]) ).
fof(i_0_1725,plain,
! [X5076,X5077,X5078] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5077),X5076))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5076),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5077),bot_bot_fun_a_bool))),X5078))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5076),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5077),X5078))) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5077),X5076))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5076),X5078))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5076),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5077),X5078))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5077),X5076))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5077),X5076))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5076),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5077),X5078))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5076),X5078))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5077),X5076))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5076),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5077),X5078))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5077),X5076))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5076),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5077),bot_bot_fun_a_bool))),X5078))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5076),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5077),X5078))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5076),X5078))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5076),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5077),bot_bot_fun_a_bool))),X5078))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5076),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5077),X5078))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1442])])]) ).
fof(i_0_1726,plain,
! [X6202,X6203,X6204] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X6202)),X6203)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X6202)),X6204)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6203),X6204)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6203),X6204))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X6202)),X6203)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X6202)),X6204))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1003_Suc__mult__less__cancel1])]) ).
fof(i_0_1727,plain,
! [X6209,X6210,X6211] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X6209)),X6210)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X6209)),X6211)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6210),X6211)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6210),X6211))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X6209)),X6210)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X6209)),X6211))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1006_Suc__mult__le__cancel1])]) ).
cnf(i_0_1728,plain,
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),X1)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X2))))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,X2)))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1443]) ).
fof(i_0_1729,plain,
! [X6346,X6347,X6348,X6349,X6350] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6350),X6346)),X6347) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6349),X6346)),X6348)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6350),X6349)),X6346)),X6347) = X6348
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6349),X6350)) )
& ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6350),X6349)),X6346)),X6347) != X6348
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6350),X6346)),X6347) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6349),X6346)),X6348)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6349),X6350)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1064_nat__eq__add__iff1])])]) ).
fof(i_0_1730,plain,
! [X6361,X6362,X6363,X6364,X6365] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6364),X6361)),X6362) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6365),X6361)),X6363)
| X6362 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6365),X6364)),X6361)),X6363)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6364),X6365)) )
& ( X6362 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6365),X6364)),X6361)),X6363)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6364),X6361)),X6362) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6365),X6361)),X6363)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6364),X6365)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1067_nat__eq__add__iff2])])]) ).
fof(i_0_1731,plain,
! [X6389,X6390,X6391] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6389),X6390)),X6391)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6391),X6389))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6389))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6390)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1075_q__pos__lemma])]) ).
cnf(i_0_1732,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[i_0_1437]) ).
cnf(i_0_1733,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[i_0_1438]) ).
fof(i_0_1734,plain,
! [X4923,X4924] :
( ( is_pname(esk86_2(X4923,X4924))
| hBOOL(hAPP_fun_a_bool_bool(p(X4923),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X4924)),bot_bot_fun_a_bool)))
| ~ hBOOL(wt(X4924)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk86_2(X4923,X4924)),u))
| hBOOL(hAPP_fun_a_bool_bool(p(X4923),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X4924)),bot_bot_fun_a_bool)))
| ~ hBOOL(wt(X4924)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(p(X4923),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,esk86_2(X4923,X4924))),bot_bot_fun_a_bool)))
| hBOOL(hAPP_fun_a_bool_bool(p(X4923),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X4924)),bot_bot_fun_a_bool)))
| ~ hBOOL(wt(X4924)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_487_assms_I3_J])])])]) ).
fof(i_0_1735,plain,
! [X5664,X5665] :
( ( is_pname(esk160_2(X5664,X5665))
| hBOOL(hAPP_f1664156314l_bool(X5664,X5665))
| is_pname(esk159_2(X5664,X5665))
| X5665 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5665))
| ~ is_fun_pname_bool(X5665) )
& ( is_fun_pname_bool(esk161_2(X5664,X5665))
| hBOOL(hAPP_f1664156314l_bool(X5664,X5665))
| is_pname(esk159_2(X5664,X5665))
| X5665 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5665))
| ~ is_fun_pname_bool(X5665) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk161_2(X5664,X5665)))
| hBOOL(hAPP_f1664156314l_bool(X5664,X5665))
| is_pname(esk159_2(X5664,X5665))
| X5665 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5665))
| ~ is_fun_pname_bool(X5665) )
& ( esk161_2(X5664,X5665) != bot_bo844097828e_bool
| hBOOL(hAPP_f1664156314l_bool(X5664,X5665))
| is_pname(esk159_2(X5664,X5665))
| X5665 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5665))
| ~ is_fun_pname_bool(X5665) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk160_2(X5664,X5665)),esk161_2(X5664,X5665)))
| hBOOL(hAPP_f1664156314l_bool(X5664,X5665))
| is_pname(esk159_2(X5664,X5665))
| X5665 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5665))
| ~ is_fun_pname_bool(X5665) )
& ( hBOOL(hAPP_f1664156314l_bool(X5664,esk161_2(X5664,X5665)))
| hBOOL(hAPP_f1664156314l_bool(X5664,X5665))
| is_pname(esk159_2(X5664,X5665))
| X5665 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5665))
| ~ is_fun_pname_bool(X5665) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(X5664,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk160_2(X5664,X5665)),esk161_2(X5664,X5665))))
| hBOOL(hAPP_f1664156314l_bool(X5664,X5665))
| is_pname(esk159_2(X5664,X5665))
| X5665 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5665))
| ~ is_fun_pname_bool(X5665) )
& ( is_pname(esk160_2(X5664,X5665))
| hBOOL(hAPP_f1664156314l_bool(X5664,X5665))
| ~ hBOOL(hAPP_f1664156314l_bool(X5664,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk159_2(X5664,X5665)),bot_bo844097828e_bool)))
| X5665 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5665))
| ~ is_fun_pname_bool(X5665) )
& ( is_fun_pname_bool(esk161_2(X5664,X5665))
| hBOOL(hAPP_f1664156314l_bool(X5664,X5665))
| ~ hBOOL(hAPP_f1664156314l_bool(X5664,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk159_2(X5664,X5665)),bot_bo844097828e_bool)))
| X5665 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5665))
| ~ is_fun_pname_bool(X5665) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk161_2(X5664,X5665)))
| hBOOL(hAPP_f1664156314l_bool(X5664,X5665))
| ~ hBOOL(hAPP_f1664156314l_bool(X5664,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk159_2(X5664,X5665)),bot_bo844097828e_bool)))
| X5665 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5665))
| ~ is_fun_pname_bool(X5665) )
& ( esk161_2(X5664,X5665) != bot_bo844097828e_bool
| hBOOL(hAPP_f1664156314l_bool(X5664,X5665))
| ~ hBOOL(hAPP_f1664156314l_bool(X5664,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk159_2(X5664,X5665)),bot_bo844097828e_bool)))
| X5665 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5665))
| ~ is_fun_pname_bool(X5665) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk160_2(X5664,X5665)),esk161_2(X5664,X5665)))
| hBOOL(hAPP_f1664156314l_bool(X5664,X5665))
| ~ hBOOL(hAPP_f1664156314l_bool(X5664,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk159_2(X5664,X5665)),bot_bo844097828e_bool)))
| X5665 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5665))
| ~ is_fun_pname_bool(X5665) )
& ( hBOOL(hAPP_f1664156314l_bool(X5664,esk161_2(X5664,X5665)))
| hBOOL(hAPP_f1664156314l_bool(X5664,X5665))
| ~ hBOOL(hAPP_f1664156314l_bool(X5664,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk159_2(X5664,X5665)),bot_bo844097828e_bool)))
| X5665 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5665))
| ~ is_fun_pname_bool(X5665) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(X5664,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk160_2(X5664,X5665)),esk161_2(X5664,X5665))))
| hBOOL(hAPP_f1664156314l_bool(X5664,X5665))
| ~ hBOOL(hAPP_f1664156314l_bool(X5664,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk159_2(X5664,X5665)),bot_bo844097828e_bool)))
| X5665 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5665))
| ~ is_fun_pname_bool(X5665) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1444])])])]) ).
fof(i_0_1736,plain,
! [X5649,X5650] :
( ( is_a(esk151_2(X5649,X5650))
| hBOOL(hAPP_fun_a_bool_bool(X5649,X5650))
| is_a(esk150_2(X5649,X5650))
| X5650 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5650))
| ~ is_fun_a_bool(X5650) )
& ( is_fun_a_bool(esk152_2(X5649,X5650))
| hBOOL(hAPP_fun_a_bool_bool(X5649,X5650))
| is_a(esk150_2(X5649,X5650))
| X5650 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5650))
| ~ is_fun_a_bool(X5650) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk152_2(X5649,X5650)))
| hBOOL(hAPP_fun_a_bool_bool(X5649,X5650))
| is_a(esk150_2(X5649,X5650))
| X5650 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5650))
| ~ is_fun_a_bool(X5650) )
& ( esk152_2(X5649,X5650) != bot_bot_fun_a_bool
| hBOOL(hAPP_fun_a_bool_bool(X5649,X5650))
| is_a(esk150_2(X5649,X5650))
| X5650 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5650))
| ~ is_fun_a_bool(X5650) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk151_2(X5649,X5650)),esk152_2(X5649,X5650)))
| hBOOL(hAPP_fun_a_bool_bool(X5649,X5650))
| is_a(esk150_2(X5649,X5650))
| X5650 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5650))
| ~ is_fun_a_bool(X5650) )
& ( hBOOL(hAPP_fun_a_bool_bool(X5649,esk152_2(X5649,X5650)))
| hBOOL(hAPP_fun_a_bool_bool(X5649,X5650))
| is_a(esk150_2(X5649,X5650))
| X5650 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5650))
| ~ is_fun_a_bool(X5650) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(X5649,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk151_2(X5649,X5650)),esk152_2(X5649,X5650))))
| hBOOL(hAPP_fun_a_bool_bool(X5649,X5650))
| is_a(esk150_2(X5649,X5650))
| X5650 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5650))
| ~ is_fun_a_bool(X5650) )
& ( is_a(esk151_2(X5649,X5650))
| hBOOL(hAPP_fun_a_bool_bool(X5649,X5650))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5649,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk150_2(X5649,X5650)),bot_bot_fun_a_bool)))
| X5650 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5650))
| ~ is_fun_a_bool(X5650) )
& ( is_fun_a_bool(esk152_2(X5649,X5650))
| hBOOL(hAPP_fun_a_bool_bool(X5649,X5650))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5649,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk150_2(X5649,X5650)),bot_bot_fun_a_bool)))
| X5650 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5650))
| ~ is_fun_a_bool(X5650) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk152_2(X5649,X5650)))
| hBOOL(hAPP_fun_a_bool_bool(X5649,X5650))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5649,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk150_2(X5649,X5650)),bot_bot_fun_a_bool)))
| X5650 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5650))
| ~ is_fun_a_bool(X5650) )
& ( esk152_2(X5649,X5650) != bot_bot_fun_a_bool
| hBOOL(hAPP_fun_a_bool_bool(X5649,X5650))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5649,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk150_2(X5649,X5650)),bot_bot_fun_a_bool)))
| X5650 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5650))
| ~ is_fun_a_bool(X5650) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk151_2(X5649,X5650)),esk152_2(X5649,X5650)))
| hBOOL(hAPP_fun_a_bool_bool(X5649,X5650))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5649,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk150_2(X5649,X5650)),bot_bot_fun_a_bool)))
| X5650 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5650))
| ~ is_fun_a_bool(X5650) )
& ( hBOOL(hAPP_fun_a_bool_bool(X5649,esk152_2(X5649,X5650)))
| hBOOL(hAPP_fun_a_bool_bool(X5649,X5650))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5649,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk150_2(X5649,X5650)),bot_bot_fun_a_bool)))
| X5650 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5650))
| ~ is_fun_a_bool(X5650) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(X5649,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk151_2(X5649,X5650)),esk152_2(X5649,X5650))))
| hBOOL(hAPP_fun_a_bool_bool(X5649,X5650))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5649,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk150_2(X5649,X5650)),bot_bot_fun_a_bool)))
| X5650 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5650))
| ~ is_fun_a_bool(X5650) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1445])])])]) ).
fof(i_0_1737,plain,
! [X5659,X5660] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk158_2(X5659,X5660)))
| hBOOL(hAPP_f54304608l_bool(X5659,X5660))
| ~ hBOOL(hAPP_f54304608l_bool(X5659,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk156_2(X5659,X5660)),bot_bot_fun_nat_bool)))
| X5660 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5660)) )
& ( esk158_2(X5659,X5660) != bot_bot_fun_nat_bool
| hBOOL(hAPP_f54304608l_bool(X5659,X5660))
| ~ hBOOL(hAPP_f54304608l_bool(X5659,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk156_2(X5659,X5660)),bot_bot_fun_nat_bool)))
| X5660 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5660)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk157_2(X5659,X5660)),esk158_2(X5659,X5660)))
| hBOOL(hAPP_f54304608l_bool(X5659,X5660))
| ~ hBOOL(hAPP_f54304608l_bool(X5659,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk156_2(X5659,X5660)),bot_bot_fun_nat_bool)))
| X5660 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5660)) )
& ( hBOOL(hAPP_f54304608l_bool(X5659,esk158_2(X5659,X5660)))
| hBOOL(hAPP_f54304608l_bool(X5659,X5660))
| ~ hBOOL(hAPP_f54304608l_bool(X5659,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk156_2(X5659,X5660)),bot_bot_fun_nat_bool)))
| X5660 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5660)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(X5659,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk157_2(X5659,X5660)),esk158_2(X5659,X5660))))
| hBOOL(hAPP_f54304608l_bool(X5659,X5660))
| ~ hBOOL(hAPP_f54304608l_bool(X5659,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk156_2(X5659,X5660)),bot_bot_fun_nat_bool)))
| X5660 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5660)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1446])])])]) ).
fof(i_0_1738,plain,
! [X5654,X5655] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk155_2(X5654,X5655)))
| hBOOL(hAPP_f448129468l_bool(X5654,X5655))
| ~ hBOOL(hAPP_f448129468l_bool(X5654,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk153_2(X5654,X5655)),bot_bot_fun_int_bool)))
| X5655 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5655)) )
& ( esk155_2(X5654,X5655) != bot_bot_fun_int_bool
| hBOOL(hAPP_f448129468l_bool(X5654,X5655))
| ~ hBOOL(hAPP_f448129468l_bool(X5654,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk153_2(X5654,X5655)),bot_bot_fun_int_bool)))
| X5655 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5655)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk154_2(X5654,X5655)),esk155_2(X5654,X5655)))
| hBOOL(hAPP_f448129468l_bool(X5654,X5655))
| ~ hBOOL(hAPP_f448129468l_bool(X5654,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk153_2(X5654,X5655)),bot_bot_fun_int_bool)))
| X5655 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5655)) )
& ( hBOOL(hAPP_f448129468l_bool(X5654,esk155_2(X5654,X5655)))
| hBOOL(hAPP_f448129468l_bool(X5654,X5655))
| ~ hBOOL(hAPP_f448129468l_bool(X5654,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk153_2(X5654,X5655)),bot_bot_fun_int_bool)))
| X5655 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5655)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(X5654,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk154_2(X5654,X5655)),esk155_2(X5654,X5655))))
| hBOOL(hAPP_f448129468l_bool(X5654,X5655))
| ~ hBOOL(hAPP_f448129468l_bool(X5654,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk153_2(X5654,X5655)),bot_bot_fun_int_bool)))
| X5655 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5655)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1447])])])]) ).
fof(i_0_1739,plain,
! [X5270,X5271,X5272] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(X5270,X5271)),image_nat_int(X5270,X5272))),image_nat_int(X5270,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5271),X5272)))),
inference(variable_rename,[status(thm)],[fact_658_image__diff__subset]) ).
fof(i_0_1740,plain,
! [X5273,X5274,X5275] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(X5273,X5274)),image_pname_a(X5273,X5275))),image_pname_a(X5273,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5274),X5275)))),
inference(variable_rename,[status(thm)],[fact_659_image__diff__subset]) ).
fof(i_0_1741,plain,
! [X6323,X6324,X6325,X6326] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6323),X6324)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6325),X6324)),X6326)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6323),X6325)),X6324)),X6326),
inference(variable_rename,[status(thm)],[fact_1058_left__add__mult__distrib]) ).
fof(i_0_1742,plain,
! [X5310,X5311] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5311))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,X5310)),hAPP_f957591787ol_nat(finite_card_int,X5311))),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5310),X5311)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_674_diff__card__le__card__Diff])]) ).
fof(i_0_1743,plain,
! [X5312,X5313] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5313))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,X5312)),hAPP_f22106695ol_nat(finite_card_nat,X5313))),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5312),X5313)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_675_diff__card__le__card__Diff])]) ).
fof(i_0_1744,plain,
! [X5314,X5315] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5315))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,X5314)),hAPP_fun_a_bool_nat(finite_card_a,X5315))),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5314),X5315)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_676_diff__card__le__card__Diff])]) ).
fof(i_0_1745,plain,
! [X5316,X5317] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5317))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,X5316)),hAPP_f921600141ol_nat(finite_card_pname,X5317))),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5316),X5317)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_677_diff__card__le__card__Diff])]) ).
fof(i_0_1746,plain,
! [X6529,X6530,X6531] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6530),X6531))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6529))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X6529)),X6530)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X6529)),X6531))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1127_zmult__zless__mono2__lemma])]) ).
cnf(i_0_1747,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1448]) ).
cnf(i_0_1748,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1449]) ).
fof(i_0_1749,plain,
! [X6534,X6535,X6536] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6536),X6535))
| hBOOL(hAPP_int_bool(X6534,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X6535)),hAPP_nat_int(semiri1621563631at_int,X6536))))
| ~ hBOOL(hAPP_int_bool(X6534,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6535),X6536)))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6535),X6536))
| hBOOL(hAPP_int_bool(X6534,zero_zero_int))
| ~ hBOOL(hAPP_int_bool(X6534,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6535),X6536)))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6535),X6536))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6536),X6535))
| hBOOL(hAPP_int_bool(X6534,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6535),X6536)))) )
& ( ~ hBOOL(hAPP_int_bool(X6534,zero_zero_int))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6536),X6535))
| hBOOL(hAPP_int_bool(X6534,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6535),X6536)))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6535),X6536))
| ~ hBOOL(hAPP_int_bool(X6534,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X6535)),hAPP_nat_int(semiri1621563631at_int,X6536))))
| hBOOL(hAPP_int_bool(X6534,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6535),X6536)))) )
& ( ~ hBOOL(hAPP_int_bool(X6534,zero_zero_int))
| ~ hBOOL(hAPP_int_bool(X6534,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X6535)),hAPP_nat_int(semiri1621563631at_int,X6536))))
| hBOOL(hAPP_int_bool(X6534,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6535),X6536)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1129_zdiff__int__split])])]) ).
cnf(i_0_1750,plain,
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1450]) ).
fof(i_0_1751,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_6])]) ).
fof(i_0_1752,plain,
! [X6003,X6004,X6005] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6005),X6004)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6003),X6004)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6005),X6003))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6004),X6003))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6004),X6005)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6005),X6003))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6005),X6004)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6003),X6004)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6004),X6003))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6004),X6005)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_912_less__diff__iff])])]) ).
fof(i_0_1753,plain,
! [X3983,X3984,X3985] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3985),X3984)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3983),X3984)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3985),X3983))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3984),X3983))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3984),X3985)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3985),X3983))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3985),X3984)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3983),X3984)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3984),X3983))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3984),X3985)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_173_le__diff__iff])])]) ).
cnf(i_0_1754,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X1))
| hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),X1)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X2)))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,X2))))) ),
inference(split_conjunct,[status(thm)],[i_0_1451]) ).
fof(i_0_1755,plain,
! [X6330,X6331,X6332] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6332),X6330)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6332),X6331)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6330),X6331))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6332)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6330),X6331))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6332),X6330)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6332),X6331)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6332)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1060_nat__mult__less__cancel1])])]) ).
fof(i_0_1756,plain,
! [X6225,X6226,X6227] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6225),X6226)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6227),X6226)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6226))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6225),X6227)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6226))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6225),X6226)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6227),X6226))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6225),X6227))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6225),X6226)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6227),X6226))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1013_mult__le__cancel2])])]) ).
fof(i_0_1757,plain,
! [X6333,X6334,X6335] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6335),X6333)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6335),X6334)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6333),X6334))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6335)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6333),X6334))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6335),X6333)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6335),X6334)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6335)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1061_nat__mult__le__cancel1])])]) ).
fof(i_0_1758,plain,
! [X6222,X6223,X6224] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6222),X6223)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6222),X6224)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6222))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6223),X6224)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6222))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6222),X6223)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6222),X6224))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6223),X6224))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6222),X6223)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6222),X6224))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1012_mult__le__cancel1])])]) ).
fof(i_0_1759,plain,
! [X4911,X4912] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X4911,esk82_2(X4911,X4912))),hAPP_nat_bool(X4912,esk82_2(X4911,X4912))))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4911),X4912)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_484_le__funI])])]) ).
fof(i_0_1760,plain,
! [X4769,X4770,X4771,X4772,X4773] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4769),X4770))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X4769,X4771)),hAPP_nat_bool(X4770,X4771))) )
& ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X4772,esk69_2(X4772,X4773))),hAPP_nat_bool(X4773,esk69_2(X4772,X4773))))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4772),X4773)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_442_le__fun__def])])])])]) ).
fof(i_0_1761,plain,
! [X4908,X4909] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X4908,esk81_2(X4908,X4909))),hAPP_int_bool(X4909,esk81_2(X4908,X4909))))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4908),X4909)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_483_le__funI])])]) ).
fof(i_0_1762,plain,
! [X4763,X4764,X4765,X4766,X4767] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4763),X4764))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X4763,X4765)),hAPP_int_bool(X4764,X4765))) )
& ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X4766,esk68_2(X4766,X4767))),hAPP_int_bool(X4767,esk68_2(X4766,X4767))))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4766),X4767)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_441_le__fun__def])])])])]) ).
fof(i_0_1763,plain,
! [X4914,X4915] :
( ( is_a(esk83_2(X4914,X4915))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4914),X4915)) )
& ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X4914,esk83_2(X4914,X4915))),hAPP_a_bool(X4915,esk83_2(X4914,X4915))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4914),X4915)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_485_le__funI])])])]) ).
fof(i_0_1764,plain,
! [X4775,X4776,X4777,X4778,X4779] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4775),X4776))
| ~ is_a(X4777)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X4775,X4777)),hAPP_a_bool(X4776,X4777))) )
& ( is_a(esk70_2(X4778,X4779))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4778),X4779)) )
& ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X4778,esk70_2(X4778,X4779))),hAPP_a_bool(X4779,esk70_2(X4778,X4779))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4778),X4779)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_443_le__fun__def])])])])])]) ).
fof(i_0_1765,plain,
! [X5830,X5831,X5832] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5831),X5832))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5830),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5832),X5830)),X5831))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_840_le__add__diff])]) ).
fof(i_0_1766,plain,
! [X5838,X5839,X5840] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5838),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5840),X5839)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5838),X5839)),X5840))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5839),X5840)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5838),X5839)),X5840))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5838),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5840),X5839)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5839),X5840)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_843_le__diff__conv2])])]) ).
fof(i_0_1767,plain,
! [X5264,X5265,X5266] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5264),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5265),X5266))))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5264),X5266))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5264),X5266)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5264),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5265),X5266)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_656_finite__Diff__insert])]) ).
fof(i_0_1768,plain,
! [X5261,X5262,X5263] :
( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5261),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5262),X5263))))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5261),X5263))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5261),X5263)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5261),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5262),X5263)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_655_finite__Diff__insert])]) ).
fof(i_0_1769,plain,
! [X5267,X5268,X5269] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5267),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5268),X5269))))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5267),X5269))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5267),X5269)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5267),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5268),X5269)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_657_finite__Diff__insert])]) ).
fof(i_0_1770,plain,
! [X5258,X5259,X5260] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5258),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5259),X5260))))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5258),X5260))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5258),X5260)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5258),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5259),X5260)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_654_finite__Diff__insert])]) ).
fof(i_0_1771,plain,
! [X5364,X5365] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk122_2(X5364,X5365)))
| hBOOL(hAPP_f54304608l_bool(X5364,X5365))
| ~ hBOOL(hAPP_f54304608l_bool(X5364,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5365)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk121_2(X5364,X5365)),esk122_2(X5364,X5365)))
| hBOOL(hAPP_f54304608l_bool(X5364,X5365))
| ~ hBOOL(hAPP_f54304608l_bool(X5364,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5365)) )
& ( hBOOL(hAPP_f54304608l_bool(X5364,esk122_2(X5364,X5365)))
| hBOOL(hAPP_f54304608l_bool(X5364,X5365))
| ~ hBOOL(hAPP_f54304608l_bool(X5364,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5365)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(X5364,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk121_2(X5364,X5365)),esk122_2(X5364,X5365))))
| hBOOL(hAPP_f54304608l_bool(X5364,X5365))
| ~ hBOOL(hAPP_f54304608l_bool(X5364,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5365)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1452])])])]) ).
fof(i_0_1772,plain,
! [X5360,X5361] :
( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk120_2(X5360,X5361)))
| hBOOL(hAPP_f448129468l_bool(X5360,X5361))
| ~ hBOOL(hAPP_f448129468l_bool(X5360,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5361)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk119_2(X5360,X5361)),esk120_2(X5360,X5361)))
| hBOOL(hAPP_f448129468l_bool(X5360,X5361))
| ~ hBOOL(hAPP_f448129468l_bool(X5360,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5361)) )
& ( hBOOL(hAPP_f448129468l_bool(X5360,esk120_2(X5360,X5361)))
| hBOOL(hAPP_f448129468l_bool(X5360,X5361))
| ~ hBOOL(hAPP_f448129468l_bool(X5360,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5361)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(X5360,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk119_2(X5360,X5361)),esk120_2(X5360,X5361))))
| hBOOL(hAPP_f448129468l_bool(X5360,X5361))
| ~ hBOOL(hAPP_f448129468l_bool(X5360,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5361)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1453])])])]) ).
fof(i_0_1773,plain,
! [X5368,X5369] :
( ( is_pname(esk123_2(X5368,X5369))
| hBOOL(hAPP_f1664156314l_bool(X5368,X5369))
| ~ hBOOL(hAPP_f1664156314l_bool(X5368,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5369)) )
& ( is_fun_pname_bool(esk124_2(X5368,X5369))
| hBOOL(hAPP_f1664156314l_bool(X5368,X5369))
| ~ hBOOL(hAPP_f1664156314l_bool(X5368,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5369)) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk124_2(X5368,X5369)))
| hBOOL(hAPP_f1664156314l_bool(X5368,X5369))
| ~ hBOOL(hAPP_f1664156314l_bool(X5368,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5369)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk123_2(X5368,X5369)),esk124_2(X5368,X5369)))
| hBOOL(hAPP_f1664156314l_bool(X5368,X5369))
| ~ hBOOL(hAPP_f1664156314l_bool(X5368,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5369)) )
& ( hBOOL(hAPP_f1664156314l_bool(X5368,esk124_2(X5368,X5369)))
| hBOOL(hAPP_f1664156314l_bool(X5368,X5369))
| ~ hBOOL(hAPP_f1664156314l_bool(X5368,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5369)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(X5368,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk123_2(X5368,X5369)),esk124_2(X5368,X5369))))
| hBOOL(hAPP_f1664156314l_bool(X5368,X5369))
| ~ hBOOL(hAPP_f1664156314l_bool(X5368,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5369)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1454])])])]) ).
fof(i_0_1774,plain,
! [X5356,X5357] :
( ( is_a(esk117_2(X5356,X5357))
| hBOOL(hAPP_fun_a_bool_bool(X5356,X5357))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5356,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5357)) )
& ( is_fun_a_bool(esk118_2(X5356,X5357))
| hBOOL(hAPP_fun_a_bool_bool(X5356,X5357))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5356,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5357)) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk118_2(X5356,X5357)))
| hBOOL(hAPP_fun_a_bool_bool(X5356,X5357))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5356,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5357)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk117_2(X5356,X5357)),esk118_2(X5356,X5357)))
| hBOOL(hAPP_fun_a_bool_bool(X5356,X5357))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5356,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5357)) )
& ( hBOOL(hAPP_fun_a_bool_bool(X5356,esk118_2(X5356,X5357)))
| hBOOL(hAPP_fun_a_bool_bool(X5356,X5357))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5356,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5357)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(X5356,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk117_2(X5356,X5357)),esk118_2(X5356,X5357))))
| hBOOL(hAPP_fun_a_bool_bool(X5356,X5357))
| ~ hBOOL(hAPP_fun_a_bool_bool(X5356,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5357)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1455])])])]) ).
fof(i_0_1775,plain,
! [X6194,X6195,X6196] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6195))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6194),X6195)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6196),X6195))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6194),X6196))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6194),X6195)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6196),X6195))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6195))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6194),X6196))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6194),X6195)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6196),X6195))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1000_mult__less__cancel2])])]) ).
fof(i_0_1776,plain,
! [X6197,X6198,X6199] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6197))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6197),X6198)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6197),X6199))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6198),X6199))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6197),X6198)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6197),X6199))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6197))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6198),X6199))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6197),X6198)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6197),X6199))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1001_mult__less__cancel1])])]) ).
fof(i_0_1777,plain,
! [X5913,X5914,X5915] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5913),X5914)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5913),X5915)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5914),X5915)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5914),X5915))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5913),X5914)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5913),X5915))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_878_nat__add__left__cancel__less])]) ).
fof(i_0_1778,plain,
! [X5757,X5758,X5759] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5757),X5758)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5759),X5758)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5757),X5759)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_814_add__le__imp__le__right])]) ).
fof(i_0_1779,plain,
! [X5725,X5726,X5727] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5725),X5726)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5727),X5726)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5725),X5727)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5725),X5727))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5725),X5726)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5727),X5726))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_804_add__le__cancel__right])]) ).
fof(i_0_1780,plain,
! [X5786,X5787,X5788] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5786),X5787)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5786),X5788)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5787),X5788)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5787),X5788))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5786),X5787)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5786),X5788))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_825_nat__add__left__cancel__le])]) ).
fof(i_0_1781,plain,
! [X5763,X5764,X5765] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5763),X5764)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5763),X5765)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5764),X5765)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_816_add__le__imp__le__left])]) ).
fof(i_0_1782,plain,
! [X5731,X5732,X5733] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5731),X5732)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5731),X5733)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5732),X5733)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5732),X5733))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5731),X5732)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5731),X5733))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_806_add__le__cancel__left])]) ).
fof(i_0_1783,plain,
! [X5754,X5755,X5756] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5754),X5755)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5756),X5755)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5754),X5756)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_813_add__le__imp__le__right])]) ).
fof(i_0_1784,plain,
! [X5722,X5723,X5724] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5722),X5723)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5724),X5723)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5722),X5724)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5722),X5724))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5722),X5723)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5724),X5723))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_803_add__le__cancel__right])]) ).
fof(i_0_1785,plain,
! [X5760,X5761,X5762] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5760),X5761)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5760),X5762)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5761),X5762)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_815_add__le__imp__le__left])]) ).
fof(i_0_1786,plain,
! [X5728,X5729,X5730] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5728),X5729)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5728),X5730)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5729),X5730)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5729),X5730))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5728),X5729)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5728),X5730))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_805_add__le__cancel__left])]) ).
cnf(i_0_1787,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1448]) ).
cnf(i_0_1788,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1449]) ).
fof(i_0_1789,plain,
! [X5556,X5557,X5558] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5558))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5557),X5558))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5557),X5556))
| hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5558),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5557),X5556))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5558),X5556))),one_one_nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1456])]) ).
fof(i_0_1790,plain,
! [X5559,X5560,X5561] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5561))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5560),X5561))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5560),X5559))
| hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5561),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5560),X5559))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5561),X5559))),one_one_nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1457])]) ).
fof(i_0_1791,plain,
! [X5553,X5554,X5555] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5555))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5554),X5555))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5554),X5553))
| hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5555),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5554),X5553))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5555),X5553))),one_one_nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1458])]) ).
fof(i_0_1792,plain,
! [X5562,X5563,X5564] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5564))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5563),X5564))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5563),X5562))
| hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5564),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5563),X5562))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5564),X5562))),one_one_nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1459])]) ).
fof(i_0_1793,plain,
! [X5519,X5520,X5521,X5522] :
( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5520),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5519),bot_bo844097828e_bool)) != bot_bo844097828e_bool
| hAPP_f1297739591_pname(X5522,X5520) = X5519
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5519),X5520))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5520))
| ~ hBOOL(finite1282449217_pname(X5521,X5522))
| ~ is_pname(X5519) )
& ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5520),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5519),bot_bo844097828e_bool)) = bot_bo844097828e_bool
| hAPP_f1297739591_pname(X5522,X5520) = hAPP_pname_pname(hAPP_p1170154830_pname(X5521,X5519),hAPP_f1297739591_pname(X5522,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5520),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5519),bot_bo844097828e_bool))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5519),X5520))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5520))
| ~ hBOOL(finite1282449217_pname(X5521,X5522))
| ~ is_pname(X5519) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_735_folding__one_Oremove])])]) ).
fof(i_0_1794,plain,
! [X5507,X5508,X5509,X5510] :
( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5508),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5507),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool
| hAPP_fun_a_bool_a(X5510,X5508) = X5507
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5507),X5508))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5508))
| ~ hBOOL(finite_folding_one_a(X5509,X5510))
| ~ is_a(X5507) )
& ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5508),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5507),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool
| hAPP_fun_a_bool_a(X5510,X5508) = hAPP_a_a(hAPP_a_fun_a_a(X5509,X5507),hAPP_fun_a_bool_a(X5510,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5508),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5507),bot_bot_fun_a_bool))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5507),X5508))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5508))
| ~ hBOOL(finite_folding_one_a(X5509,X5510))
| ~ is_a(X5507) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_732_folding__one_Oremove])])]) ).
fof(i_0_1795,plain,
! [X5511,X5512,X5513,X5514] :
( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5512),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5511),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool
| hAPP_f1594865479ol_int(X5514,X5512) = X5511
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5511),X5512))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5512))
| ~ hBOOL(finite1626084323ne_int(X5513,X5514)) )
& ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5512),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5511),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool
| hAPP_f1594865479ol_int(X5514,X5512) = hAPP_int_int(hAPP_int_fun_int_int(X5513,X5511),hAPP_f1594865479ol_int(X5514,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5512),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5511),bot_bot_fun_int_bool))))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5511),X5512))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5512))
| ~ hBOOL(finite1626084323ne_int(X5513,X5514)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_733_folding__one_Oremove])])]) ).
fof(i_0_1796,plain,
! [X5515,X5516,X5517,X5518] :
( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5516),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5515),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
| hAPP_f22106695ol_nat(X5518,X5516) = X5515
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5515),X5516))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5516))
| ~ hBOOL(finite988810631ne_nat(X5517,X5518)) )
& ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5516),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5515),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
| hAPP_f22106695ol_nat(X5518,X5516) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X5517,X5515),hAPP_f22106695ol_nat(X5518,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5516),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5515),bot_bot_fun_nat_bool))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5515),X5516))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5516))
| ~ hBOOL(finite988810631ne_nat(X5517,X5518)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_734_folding__one_Oremove])])]) ).
cnf(i_0_1797,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X2)),X1))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk133_2(X1,X2)),hAPP_nat_nat(X2,esk133_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1460]) ).
fof(i_0_1798,plain,
! [X5995,X5996,X5997] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5995),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5996),X5997)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5995),X5997)),X5996)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5995),X5997)),X5996))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5995),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5996),X5997))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_909_less__diff__conv])]) ).
fof(i_0_1799,plain,
! [X5827,X5828,X5829] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5827),X5828)),X5829))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5827),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5829),X5828))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5827),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5829),X5828)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5827),X5828)),X5829)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_839_le__diff__conv])]) ).
fof(i_0_1800,plain,
! [X6218,X6219] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X6219))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X6218))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6218),X6219))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1010_one__less__mult])]) ).
fof(i_0_1801,plain,
! [X6220,X6221] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X6220))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6220),X6221))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X6221))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6220),X6221))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X6220))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X6221))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6220),X6221))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1011_one__le__mult__iff])])]) ).
fof(i_0_1802,plain,
! [X5503,X5504,X5505,X5506] :
( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5504),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5503),bot_bo844097828e_bool)) != bot_bo844097828e_bool
| hAPP_f1297739591_pname(X5506,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5503),X5504)) = X5503
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5504))
| ~ hBOOL(finite1282449217_pname(X5505,X5506))
| ~ is_pname(X5503) )
& ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5504),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5503),bot_bo844097828e_bool)) = bot_bo844097828e_bool
| hAPP_f1297739591_pname(X5506,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5503),X5504)) = hAPP_pname_pname(hAPP_p1170154830_pname(X5505,X5503),hAPP_f1297739591_pname(X5506,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5504),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5503),bot_bo844097828e_bool))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5504))
| ~ hBOOL(finite1282449217_pname(X5505,X5506))
| ~ is_pname(X5503) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_731_folding__one_Oinsert__remove])])]) ).
fof(i_0_1803,plain,
! [X5491,X5492,X5493,X5494] :
( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5492),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5491),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool
| hAPP_fun_a_bool_a(X5494,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5491),X5492)) = X5491
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5492))
| ~ hBOOL(finite_folding_one_a(X5493,X5494))
| ~ is_a(X5491) )
& ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5492),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5491),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool
| hAPP_fun_a_bool_a(X5494,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5491),X5492)) = hAPP_a_a(hAPP_a_fun_a_a(X5493,X5491),hAPP_fun_a_bool_a(X5494,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5492),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5491),bot_bot_fun_a_bool))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5492))
| ~ hBOOL(finite_folding_one_a(X5493,X5494))
| ~ is_a(X5491) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_728_folding__one_Oinsert__remove])])]) ).
fof(i_0_1804,plain,
! [X5495,X5496,X5497,X5498] :
( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5496),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5495),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool
| hAPP_f1594865479ol_int(X5498,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5495),X5496)) = X5495
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5496))
| ~ hBOOL(finite1626084323ne_int(X5497,X5498)) )
& ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5496),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5495),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool
| hAPP_f1594865479ol_int(X5498,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5495),X5496)) = hAPP_int_int(hAPP_int_fun_int_int(X5497,X5495),hAPP_f1594865479ol_int(X5498,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5496),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5495),bot_bot_fun_int_bool))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5496))
| ~ hBOOL(finite1626084323ne_int(X5497,X5498)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_729_folding__one_Oinsert__remove])])]) ).
fof(i_0_1805,plain,
! [X5499,X5500,X5501,X5502] :
( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5500),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5499),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
| hAPP_f22106695ol_nat(X5502,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5499),X5500)) = X5499
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5500))
| ~ hBOOL(finite988810631ne_nat(X5501,X5502)) )
& ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5500),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5499),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
| hAPP_f22106695ol_nat(X5502,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5499),X5500)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X5501,X5499),hAPP_f22106695ol_nat(X5502,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5500),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5499),bot_bot_fun_nat_bool))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5500))
| ~ hBOOL(finite988810631ne_nat(X5501,X5502)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_730_folding__one_Oinsert__remove])])]) ).
fof(i_0_1806,plain,
! [X4163,X4164,X4165] :
( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,esk12_3(X4163,X4164,X4165)),X4164))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4165),image_1921560913_pname(X4163,X4164)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4165))
| ~ is_fun_pname_bool(X4165) )
& ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk12_3(X4163,X4164,X4165)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4165),image_1921560913_pname(X4163,X4164)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4165))
| ~ is_fun_pname_bool(X4165) )
& ( X4165 = image_1921560913_pname(X4163,esk12_3(X4163,X4164,X4165))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4165),image_1921560913_pname(X4163,X4164)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4165))
| ~ is_fun_pname_bool(X4165) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_230_finite__subset__image])])])]) ).
fof(i_0_1807,plain,
! [X4123,X4124,X4125] :
( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,esk2_3(X4123,X4124,X4125)),X4124))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4125),image_fun_nat_bool_a(X4123,X4124)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4125))
| ~ is_fun_a_bool(X4125) )
& ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk2_3(X4123,X4124,X4125)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4125),image_fun_nat_bool_a(X4123,X4124)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4125))
| ~ is_fun_a_bool(X4125) )
& ( X4125 = image_fun_nat_bool_a(X4123,esk2_3(X4123,X4124,X4125))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4125),image_fun_nat_bool_a(X4123,X4124)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4125))
| ~ is_fun_a_bool(X4125) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_220_finite__subset__image])])])]) ).
fof(i_0_1808,plain,
! [X4159,X4160,X4161] :
( ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,esk11_3(X4159,X4160,X4161)),X4160))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4161),image_62782965_pname(X4159,X4160)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4161))
| ~ is_fun_pname_bool(X4161) )
& ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,esk11_3(X4159,X4160,X4161)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4161),image_62782965_pname(X4159,X4160)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4161))
| ~ is_fun_pname_bool(X4161) )
& ( X4161 = image_62782965_pname(X4159,esk11_3(X4159,X4160,X4161))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4161),image_62782965_pname(X4159,X4160)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4161))
| ~ is_fun_pname_bool(X4161) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_229_finite__subset__image])])])]) ).
fof(i_0_1809,plain,
! [X4119,X4120,X4121] :
( ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,esk1_3(X4119,X4120,X4121)),X4120))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4121),image_fun_int_bool_a(X4119,X4120)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4121))
| ~ is_fun_a_bool(X4121) )
& ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,esk1_3(X4119,X4120,X4121)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4121),image_fun_int_bool_a(X4119,X4120)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4121))
| ~ is_fun_a_bool(X4121) )
& ( X4121 = image_fun_int_bool_a(X4119,esk1_3(X4119,X4120,X4121))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4121),image_fun_int_bool_a(X4119,X4120)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4121))
| ~ is_fun_a_bool(X4121) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_219_finite__subset__image])])])]) ).
fof(i_0_1810,plain,
! [X4167,X4168,X4169] :
( ( is_fun1661590463l_bool(esk13_3(X4167,X4168,X4169))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4169),image_1283814551_pname(X4167,X4168)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4169))
| ~ is_fun_pname_bool(X4169) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,esk13_3(X4167,X4168,X4169)),X4168))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4169),image_1283814551_pname(X4167,X4168)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4169))
| ~ is_fun_pname_bool(X4169) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk13_3(X4167,X4168,X4169)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4169),image_1283814551_pname(X4167,X4168)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4169))
| ~ is_fun_pname_bool(X4169) )
& ( X4169 = image_1283814551_pname(X4167,esk13_3(X4167,X4168,X4169))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4169),image_1283814551_pname(X4167,X4168)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4169))
| ~ is_fun_pname_bool(X4169) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_231_finite__subset__image])])])]) ).
fof(i_0_1811,plain,
! [X4127,X4128,X4129] :
( ( is_fun1661590463l_bool(esk3_3(X4127,X4128,X4129))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4129),image_876012084bool_a(X4127,X4128)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4129))
| ~ is_fun_a_bool(X4129) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,esk3_3(X4127,X4128,X4129)),X4128))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4129),image_876012084bool_a(X4127,X4128)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4129))
| ~ is_fun_a_bool(X4129) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk3_3(X4127,X4128,X4129)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4129),image_876012084bool_a(X4127,X4128)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4129))
| ~ is_fun_a_bool(X4129) )
& ( X4129 = image_876012084bool_a(X4127,esk3_3(X4127,X4128,X4129))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4129),image_876012084bool_a(X4127,X4128)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4129))
| ~ is_fun_a_bool(X4129) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_221_finite__subset__image])])])]) ).
fof(i_0_1812,plain,
! [X4171,X4172,X4173] :
( ( is_fun949378684l_bool(esk14_3(X4171,X4172,X4173))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4173),image_1854862208_pname(X4171,X4172)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4173))
| ~ is_fun_pname_bool(X4173) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,esk14_3(X4171,X4172,X4173)),X4172))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4173),image_1854862208_pname(X4171,X4172)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4173))
| ~ is_fun_pname_bool(X4173) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk14_3(X4171,X4172,X4173)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4173),image_1854862208_pname(X4171,X4172)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4173))
| ~ is_fun_pname_bool(X4173) )
& ( X4173 = image_1854862208_pname(X4171,esk14_3(X4171,X4172,X4173))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4173),image_1854862208_pname(X4171,X4172)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4173))
| ~ is_fun_pname_bool(X4173) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_232_finite__subset__image])])])]) ).
fof(i_0_1813,plain,
! [X4131,X4132,X4133] :
( ( is_fun949378684l_bool(esk4_3(X4131,X4132,X4133))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4133),image_fun_a_bool_a(X4131,X4132)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4133))
| ~ is_fun_a_bool(X4133) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,esk4_3(X4131,X4132,X4133)),X4132))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4133),image_fun_a_bool_a(X4131,X4132)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4133))
| ~ is_fun_a_bool(X4133) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk4_3(X4131,X4132,X4133)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4133),image_fun_a_bool_a(X4131,X4132)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4133))
| ~ is_fun_a_bool(X4133) )
& ( X4133 = image_fun_a_bool_a(X4131,esk4_3(X4131,X4132,X4133))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4133),image_fun_a_bool_a(X4131,X4132)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4133))
| ~ is_fun_a_bool(X4133) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_222_finite__subset__image])])])]) ).
fof(i_0_1814,plain,
! [X4263,X4264,X4265] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk37_3(X4263,X4264,X4265)),X4264))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4265),image_nat_pname(X4263,X4264)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4265))
| ~ is_fun_pname_bool(X4265) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk37_3(X4263,X4264,X4265)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4265),image_nat_pname(X4263,X4264)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4265))
| ~ is_fun_pname_bool(X4265) )
& ( X4265 = image_nat_pname(X4263,esk37_3(X4263,X4264,X4265))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4265),image_nat_pname(X4263,X4264)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4265))
| ~ is_fun_pname_bool(X4265) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_255_finite__subset__image])])])]) ).
fof(i_0_1815,plain,
! [X4259,X4260,X4261] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk36_3(X4259,X4260,X4261)),X4260))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4261),image_nat_fun_a_bool(X4259,X4260)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4261))
| ~ is_fun949378684l_bool(X4261) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk36_3(X4259,X4260,X4261)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4261),image_nat_fun_a_bool(X4259,X4260)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4261))
| ~ is_fun949378684l_bool(X4261) )
& ( X4261 = image_nat_fun_a_bool(X4259,esk36_3(X4259,X4260,X4261))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4261),image_nat_fun_a_bool(X4259,X4260)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4261))
| ~ is_fun949378684l_bool(X4261) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_254_finite__subset__image])])])]) ).
fof(i_0_1816,plain,
! [X4255,X4256,X4257] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk35_3(X4255,X4256,X4257)),X4256))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4257),image_1655916159e_bool(X4255,X4256)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4257))
| ~ is_fun1661590463l_bool(X4257) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk35_3(X4255,X4256,X4257)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4257),image_1655916159e_bool(X4255,X4256)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4257))
| ~ is_fun1661590463l_bool(X4257) )
& ( X4257 = image_1655916159e_bool(X4255,esk35_3(X4255,X4256,X4257))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4257),image_1655916159e_bool(X4255,X4256)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4257))
| ~ is_fun1661590463l_bool(X4257) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_253_finite__subset__image])])])]) ).
fof(i_0_1817,plain,
! [X4243,X4244,X4245] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk32_3(X4243,X4244,X4245)),X4244))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4245),image_nat_a(X4243,X4244)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4245))
| ~ is_fun_a_bool(X4245) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk32_3(X4243,X4244,X4245)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4245),image_nat_a(X4243,X4244)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4245))
| ~ is_fun_a_bool(X4245) )
& ( X4245 = image_nat_a(X4243,esk32_3(X4243,X4244,X4245))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4245),image_nat_a(X4243,X4244)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4245))
| ~ is_fun_a_bool(X4245) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_250_finite__subset__image])])])]) ).
fof(i_0_1818,plain,
! [X4287,X4288,X4289] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,esk43_3(X4287,X4288,X4289)),X4288))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4289),image_int_pname(X4287,X4288)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4289))
| ~ is_fun_pname_bool(X4289) )
& ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk43_3(X4287,X4288,X4289)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4289),image_int_pname(X4287,X4288)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4289))
| ~ is_fun_pname_bool(X4289) )
& ( X4289 = image_int_pname(X4287,esk43_3(X4287,X4288,X4289))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4289),image_int_pname(X4287,X4288)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4289))
| ~ is_fun_pname_bool(X4289) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_261_finite__subset__image])])])]) ).
fof(i_0_1819,plain,
! [X4283,X4284,X4285] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,esk42_3(X4283,X4284,X4285)),X4284))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4285),image_int_fun_a_bool(X4283,X4284)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4285))
| ~ is_fun949378684l_bool(X4285) )
& ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk42_3(X4283,X4284,X4285)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4285),image_int_fun_a_bool(X4283,X4284)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4285))
| ~ is_fun949378684l_bool(X4285) )
& ( X4285 = image_int_fun_a_bool(X4283,esk42_3(X4283,X4284,X4285))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4285),image_int_fun_a_bool(X4283,X4284)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4285))
| ~ is_fun949378684l_bool(X4285) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_260_finite__subset__image])])])]) ).
fof(i_0_1820,plain,
! [X4279,X4280,X4281] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,esk41_3(X4279,X4280,X4281)),X4280))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4281),image_637364955e_bool(X4279,X4280)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4281))
| ~ is_fun1661590463l_bool(X4281) )
& ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk41_3(X4279,X4280,X4281)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4281),image_637364955e_bool(X4279,X4280)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4281))
| ~ is_fun1661590463l_bool(X4281) )
& ( X4281 = image_637364955e_bool(X4279,esk41_3(X4279,X4280,X4281))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4281),image_637364955e_bool(X4279,X4280)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4281))
| ~ is_fun1661590463l_bool(X4281) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_259_finite__subset__image])])])]) ).
fof(i_0_1821,plain,
! [X4267,X4268,X4269] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,esk38_3(X4267,X4268,X4269)),X4268))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4269),image_int_a(X4267,X4268)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4269))
| ~ is_fun_a_bool(X4269) )
& ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk38_3(X4267,X4268,X4269)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4269),image_int_a(X4267,X4268)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4269))
| ~ is_fun_a_bool(X4269) )
& ( X4269 = image_int_a(X4267,esk38_3(X4267,X4268,X4269))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4269),image_int_a(X4267,X4268)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4269))
| ~ is_fun_a_bool(X4269) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_256_finite__subset__image])])])]) ).
fof(i_0_1822,plain,
! [X4291,X4292,X4293] :
( ( is_fun_pname_bool(esk44_3(X4291,X4292,X4293))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4293),image_pname_a(X4291,X4292)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4293))
| ~ is_fun_a_bool(X4293) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk44_3(X4291,X4292,X4293)),X4292))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4293),image_pname_a(X4291,X4292)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4293))
| ~ is_fun_a_bool(X4293) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk44_3(X4291,X4292,X4293)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4293),image_pname_a(X4291,X4292)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4293))
| ~ is_fun_a_bool(X4293) )
& ( X4293 = image_pname_a(X4291,esk44_3(X4291,X4292,X4293))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4293),image_pname_a(X4291,X4292)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4293))
| ~ is_fun_a_bool(X4293) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_262_finite__subset__image])])])]) ).
fof(i_0_1823,plain,
! [X4239,X4240,X4241] :
( ( is_fun_pname_bool(esk31_3(X4239,X4240,X4241))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4241),image_pname_pname(X4239,X4240)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4241))
| ~ is_fun_pname_bool(X4241) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk31_3(X4239,X4240,X4241)),X4240))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4241),image_pname_pname(X4239,X4240)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4241))
| ~ is_fun_pname_bool(X4241) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk31_3(X4239,X4240,X4241)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4241),image_pname_pname(X4239,X4240)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4241))
| ~ is_fun_pname_bool(X4241) )
& ( X4241 = image_pname_pname(X4239,esk31_3(X4239,X4240,X4241))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4241),image_pname_pname(X4239,X4240)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4241))
| ~ is_fun_pname_bool(X4241) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_249_finite__subset__image])])])]) ).
fof(i_0_1824,plain,
! [X4235,X4236,X4237] :
( ( is_fun_pname_bool(esk30_3(X4235,X4236,X4237))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4237),image_112932426a_bool(X4235,X4236)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4237))
| ~ is_fun949378684l_bool(X4237) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk30_3(X4235,X4236,X4237)),X4236))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4237),image_112932426a_bool(X4235,X4236)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4237))
| ~ is_fun949378684l_bool(X4237) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk30_3(X4235,X4236,X4237)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4237),image_112932426a_bool(X4235,X4236)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4237))
| ~ is_fun949378684l_bool(X4237) )
& ( X4237 = image_112932426a_bool(X4235,esk30_3(X4235,X4236,X4237))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4237),image_112932426a_bool(X4235,X4236)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4237))
| ~ is_fun949378684l_bool(X4237) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_248_finite__subset__image])])])]) ).
fof(i_0_1825,plain,
! [X4231,X4232,X4233] :
( ( is_fun_pname_bool(esk29_3(X4231,X4232,X4233))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4233),image_47868345e_bool(X4231,X4232)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4233))
| ~ is_fun1661590463l_bool(X4233) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk29_3(X4231,X4232,X4233)),X4232))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4233),image_47868345e_bool(X4231,X4232)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4233))
| ~ is_fun1661590463l_bool(X4233) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk29_3(X4231,X4232,X4233)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4233),image_47868345e_bool(X4231,X4232)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4233))
| ~ is_fun1661590463l_bool(X4233) )
& ( X4233 = image_47868345e_bool(X4231,esk29_3(X4231,X4232,X4233))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4233),image_47868345e_bool(X4231,X4232)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4233))
| ~ is_fun1661590463l_bool(X4233) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_247_finite__subset__image])])])]) ).
fof(i_0_1826,plain,
! [X4155,X4156,X4157] :
( ( is_fun_a_bool(esk10_3(X4155,X4156,X4157))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4157),image_a_pname(X4155,X4156)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4157))
| ~ is_fun_pname_bool(X4157) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk10_3(X4155,X4156,X4157)),X4156))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4157),image_a_pname(X4155,X4156)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4157))
| ~ is_fun_pname_bool(X4157) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk10_3(X4155,X4156,X4157)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4157),image_a_pname(X4155,X4156)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4157))
| ~ is_fun_pname_bool(X4157) )
& ( X4157 = image_a_pname(X4155,esk10_3(X4155,X4156,X4157))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4157),image_a_pname(X4155,X4156)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4157))
| ~ is_fun_pname_bool(X4157) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_228_finite__subset__image])])])]) ).
fof(i_0_1827,plain,
! [X4151,X4152,X4153] :
( ( is_fun_a_bool(esk9_3(X4151,X4152,X4153))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4153),image_a_fun_a_bool(X4151,X4152)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4153))
| ~ is_fun949378684l_bool(X4153) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk9_3(X4151,X4152,X4153)),X4152))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4153),image_a_fun_a_bool(X4151,X4152)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4153))
| ~ is_fun949378684l_bool(X4153) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk9_3(X4151,X4152,X4153)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4153),image_a_fun_a_bool(X4151,X4152)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4153))
| ~ is_fun949378684l_bool(X4153) )
& ( X4153 = image_a_fun_a_bool(X4151,esk9_3(X4151,X4152,X4153))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4153),image_a_fun_a_bool(X4151,X4152)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4153))
| ~ is_fun949378684l_bool(X4153) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_227_finite__subset__image])])])]) ).
fof(i_0_1828,plain,
! [X4147,X4148,X4149] :
( ( is_fun_a_bool(esk8_3(X4147,X4148,X4149))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4149),image_819518260e_bool(X4147,X4148)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4149))
| ~ is_fun1661590463l_bool(X4149) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk8_3(X4147,X4148,X4149)),X4148))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4149),image_819518260e_bool(X4147,X4148)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4149))
| ~ is_fun1661590463l_bool(X4149) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk8_3(X4147,X4148,X4149)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4149),image_819518260e_bool(X4147,X4148)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4149))
| ~ is_fun1661590463l_bool(X4149) )
& ( X4149 = image_819518260e_bool(X4147,esk8_3(X4147,X4148,X4149))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4149),image_819518260e_bool(X4147,X4148)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4149))
| ~ is_fun1661590463l_bool(X4149) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_226_finite__subset__image])])])]) ).
fof(i_0_1829,plain,
! [X4135,X4136,X4137] :
( ( is_fun_a_bool(esk5_3(X4135,X4136,X4137))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4137),image_a_a(X4135,X4136)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4137))
| ~ is_fun_a_bool(X4137) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk5_3(X4135,X4136,X4137)),X4136))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4137),image_a_a(X4135,X4136)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4137))
| ~ is_fun_a_bool(X4137) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk5_3(X4135,X4136,X4137)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4137),image_a_a(X4135,X4136)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4137))
| ~ is_fun_a_bool(X4137) )
& ( X4137 = image_a_a(X4135,esk5_3(X4135,X4136,X4137))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4137),image_a_a(X4135,X4136)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4137))
| ~ is_fun_a_bool(X4137) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_223_finite__subset__image])])])]) ).
fof(i_0_1830,plain,
! [X4207,X4208,X4209] :
( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,esk23_3(X4207,X4208,X4209)),X4208))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4209),image_1133522419ol_int(X4207,X4208)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4209)) )
& ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk23_3(X4207,X4208,X4209)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4209),image_1133522419ol_int(X4207,X4208)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4209)) )
& ( X4209 = image_1133522419ol_int(X4207,esk23_3(X4207,X4208,X4209))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4209),image_1133522419ol_int(X4207,X4208)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4209)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_241_finite__subset__image])])])]) ).
fof(i_0_1831,plain,
! [X4183,X4184,X4185] :
( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,esk17_3(X4183,X4184,X4185)),X4184))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4185),image_496248727ol_nat(X4183,X4184)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4185)) )
& ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk17_3(X4183,X4184,X4185)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4185),image_496248727ol_nat(X4183,X4184)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4185)) )
& ( X4185 = image_496248727ol_nat(X4183,esk17_3(X4183,X4184,X4185))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4185),image_496248727ol_nat(X4183,X4184)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4185)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_235_finite__subset__image])])])]) ).
fof(i_0_1832,plain,
! [X4203,X4204,X4205] :
( ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,esk22_3(X4203,X4204,X4205)),X4204))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4205),image_2069007511ol_int(X4203,X4204)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4205)) )
& ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,esk22_3(X4203,X4204,X4205)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4205),image_2069007511ol_int(X4203,X4204)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4205)) )
& ( X4205 = image_2069007511ol_int(X4203,esk22_3(X4203,X4204,X4205))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4205),image_2069007511ol_int(X4203,X4204)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4205)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_240_finite__subset__image])])])]) ).
fof(i_0_1833,plain,
! [X4179,X4180,X4181] :
( ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,esk16_3(X4179,X4180,X4181)),X4180))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4181),image_1431733819ol_nat(X4179,X4180)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4181)) )
& ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,esk16_3(X4179,X4180,X4181)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4181),image_1431733819ol_nat(X4179,X4180)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4181)) )
& ( X4181 = image_1431733819ol_nat(X4179,esk16_3(X4179,X4180,X4181))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4181),image_1431733819ol_nat(X4179,X4180)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4181)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_234_finite__subset__image])])])]) ).
fof(i_0_1834,plain,
! [X4211,X4212,X4213] :
( ( is_fun1661590463l_bool(esk24_3(X4211,X4212,X4213))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4213),image_41399353ol_int(X4211,X4212)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4213)) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,esk24_3(X4211,X4212,X4213)),X4212))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4213),image_41399353ol_int(X4211,X4212)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4213)) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk24_3(X4211,X4212,X4213)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4213),image_41399353ol_int(X4211,X4212)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4213)) )
& ( X4213 = image_41399353ol_int(X4211,esk24_3(X4211,X4212,X4213))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4213),image_41399353ol_int(X4211,X4212)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4213)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_242_finite__subset__image])])])]) ).
fof(i_0_1835,plain,
! [X4187,X4188,X4189] :
( ( is_fun1661590463l_bool(esk18_3(X4187,X4188,X4189))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4189),image_1551609309ol_nat(X4187,X4188)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4189)) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,esk18_3(X4187,X4188,X4189)),X4188))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4189),image_1551609309ol_nat(X4187,X4188)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4189)) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk18_3(X4187,X4188,X4189)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4189),image_1551609309ol_nat(X4187,X4188)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4189)) )
& ( X4189 = image_1551609309ol_nat(X4187,esk18_3(X4187,X4188,X4189))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4189),image_1551609309ol_nat(X4187,X4188)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4189)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_236_finite__subset__image])])])]) ).
fof(i_0_1836,plain,
! [X4215,X4216,X4217] :
( ( is_fun949378684l_bool(esk25_3(X4215,X4216,X4217))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4217),image_fun_a_bool_int(X4215,X4216)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4217)) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,esk25_3(X4215,X4216,X4217)),X4216))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4217),image_fun_a_bool_int(X4215,X4216)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4217)) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk25_3(X4215,X4216,X4217)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4217),image_fun_a_bool_int(X4215,X4216)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4217)) )
& ( X4217 = image_fun_a_bool_int(X4215,esk25_3(X4215,X4216,X4217))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4217),image_fun_a_bool_int(X4215,X4216)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4217)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_243_finite__subset__image])])])]) ).
fof(i_0_1837,plain,
! [X4191,X4192,X4193] :
( ( is_fun949378684l_bool(esk19_3(X4191,X4192,X4193))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4193),image_fun_a_bool_nat(X4191,X4192)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4193)) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,esk19_3(X4191,X4192,X4193)),X4192))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4193),image_fun_a_bool_nat(X4191,X4192)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4193)) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk19_3(X4191,X4192,X4193)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4193),image_fun_a_bool_nat(X4191,X4192)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4193)) )
& ( X4193 = image_fun_a_bool_nat(X4191,esk19_3(X4191,X4192,X4193))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4193),image_fun_a_bool_nat(X4191,X4192)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4193)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_237_finite__subset__image])])])]) ).
fof(i_0_1838,plain,
! [X4295,X4296,X4297] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk45_3(X4295,X4296,X4297)),X4296))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4297),image_nat_int(X4295,X4296)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4297)) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk45_3(X4295,X4296,X4297)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4297),image_nat_int(X4295,X4296)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4297)) )
& ( X4297 = image_nat_int(X4295,esk45_3(X4295,X4296,X4297))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4297),image_nat_int(X4295,X4296)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4297)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_263_finite__subset__image])])])]) ).
fof(i_0_1839,plain,
! [X4251,X4252,X4253] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk34_3(X4251,X4252,X4253)),X4252))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4253),image_26036933t_bool(X4251,X4252)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4253)) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk34_3(X4251,X4252,X4253)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4253),image_26036933t_bool(X4251,X4252)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4253)) )
& ( X4253 = image_26036933t_bool(X4251,esk34_3(X4251,X4252,X4253))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4253),image_26036933t_bool(X4251,X4252)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4253)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_252_finite__subset__image])])])]) ).
fof(i_0_1840,plain,
! [X4247,X4248,X4249] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk33_3(X4247,X4248,X4249)),X4248))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4249),image_1556378401t_bool(X4247,X4248)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4249)) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk33_3(X4247,X4248,X4249)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4249),image_1556378401t_bool(X4247,X4248)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4249)) )
& ( X4249 = image_1556378401t_bool(X4247,esk33_3(X4247,X4248,X4249))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4249),image_1556378401t_bool(X4247,X4248)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4249)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_251_finite__subset__image])])])]) ).
fof(i_0_1841,plain,
! [X4275,X4276,X4277] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,esk40_3(X4275,X4276,X4277)),X4276))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4277),image_892525857t_bool(X4275,X4276)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4277)) )
& ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk40_3(X4275,X4276,X4277)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4277),image_892525857t_bool(X4275,X4276)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4277)) )
& ( X4277 = image_892525857t_bool(X4275,esk40_3(X4275,X4276,X4277))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4277),image_892525857t_bool(X4275,X4276)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4277)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_258_finite__subset__image])])])]) ).
fof(i_0_1842,plain,
! [X4271,X4272,X4273] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,esk39_3(X4271,X4272,X4273)),X4272))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4273),image_275383677t_bool(X4271,X4272)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4273)) )
& ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk39_3(X4271,X4272,X4273)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4273),image_275383677t_bool(X4271,X4272)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4273)) )
& ( X4273 = image_275383677t_bool(X4271,esk39_3(X4271,X4272,X4273))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4273),image_275383677t_bool(X4271,X4272)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4273)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_257_finite__subset__image])])])]) ).
fof(i_0_1843,plain,
! [X4227,X4228,X4229] :
( ( is_fun_pname_bool(esk28_3(X4227,X4228,X4229))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4229),image_2129980159t_bool(X4227,X4228)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4229)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk28_3(X4227,X4228,X4229)),X4228))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4229),image_2129980159t_bool(X4227,X4228)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4229)) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk28_3(X4227,X4228,X4229)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4229),image_2129980159t_bool(X4227,X4228)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4229)) )
& ( X4229 = image_2129980159t_bool(X4227,esk28_3(X4227,X4228,X4229))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4229),image_2129980159t_bool(X4227,X4228)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4229)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_246_finite__subset__image])])])]) ).
fof(i_0_1844,plain,
! [X4223,X4224,X4225] :
( ( is_fun_pname_bool(esk27_3(X4223,X4224,X4225))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4225),image_1512837979t_bool(X4223,X4224)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4225)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk27_3(X4223,X4224,X4225)),X4224))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4225),image_1512837979t_bool(X4223,X4224)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4225)) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk27_3(X4223,X4224,X4225)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4225),image_1512837979t_bool(X4223,X4224)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4225)) )
& ( X4225 = image_1512837979t_bool(X4223,esk27_3(X4223,X4224,X4225))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4225),image_1512837979t_bool(X4223,X4224)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4225)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_245_finite__subset__image])])])]) ).
fof(i_0_1845,plain,
! [X4219,X4220,X4221] :
( ( is_fun_pname_bool(esk26_3(X4219,X4220,X4221))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4221),image_pname_int(X4219,X4220)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4221)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk26_3(X4219,X4220,X4221)),X4220))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4221),image_pname_int(X4219,X4220)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4221)) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk26_3(X4219,X4220,X4221)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4221),image_pname_int(X4219,X4220)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4221)) )
& ( X4221 = image_pname_int(X4219,esk26_3(X4219,X4220,X4221))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4221),image_pname_int(X4219,X4220)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4221)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_244_finite__subset__image])])])]) ).
fof(i_0_1846,plain,
! [X4195,X4196,X4197] :
( ( is_fun_pname_bool(esk20_3(X4195,X4196,X4197))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4197),image_pname_nat(X4195,X4196)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4197)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk20_3(X4195,X4196,X4197)),X4196))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4197),image_pname_nat(X4195,X4196)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4197)) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk20_3(X4195,X4196,X4197)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4197),image_pname_nat(X4195,X4196)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4197)) )
& ( X4197 = image_pname_nat(X4195,esk20_3(X4195,X4196,X4197))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4197),image_pname_nat(X4195,X4196)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4197)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_238_finite__subset__image])])])]) ).
fof(i_0_1847,plain,
! [X4199,X4200,X4201] :
( ( is_fun_a_bool(esk21_3(X4199,X4200,X4201))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4201),image_a_int(X4199,X4200)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4201)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk21_3(X4199,X4200,X4201)),X4200))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4201),image_a_int(X4199,X4200)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4201)) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk21_3(X4199,X4200,X4201)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4201),image_a_int(X4199,X4200)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4201)) )
& ( X4201 = image_a_int(X4199,esk21_3(X4199,X4200,X4201))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4201),image_a_int(X4199,X4200)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4201)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_239_finite__subset__image])])])]) ).
fof(i_0_1848,plain,
! [X4175,X4176,X4177] :
( ( is_fun_a_bool(esk15_3(X4175,X4176,X4177))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4177),image_a_nat(X4175,X4176)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4177)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk15_3(X4175,X4176,X4177)),X4176))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4177),image_a_nat(X4175,X4176)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4177)) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk15_3(X4175,X4176,X4177)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4177),image_a_nat(X4175,X4176)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4177)) )
& ( X4177 = image_a_nat(X4175,esk15_3(X4175,X4176,X4177))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4177),image_a_nat(X4175,X4176)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4177)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_233_finite__subset__image])])])]) ).
fof(i_0_1849,plain,
! [X4143,X4144,X4145] :
( ( is_fun_a_bool(esk7_3(X4143,X4144,X4145))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4145),image_a_fun_nat_bool(X4143,X4144)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4145)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk7_3(X4143,X4144,X4145)),X4144))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4145),image_a_fun_nat_bool(X4143,X4144)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4145)) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk7_3(X4143,X4144,X4145)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4145),image_a_fun_nat_bool(X4143,X4144)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4145)) )
& ( X4145 = image_a_fun_nat_bool(X4143,esk7_3(X4143,X4144,X4145))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4145),image_a_fun_nat_bool(X4143,X4144)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4145)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_225_finite__subset__image])])])]) ).
fof(i_0_1850,plain,
! [X4139,X4140,X4141] :
( ( is_fun_a_bool(esk6_3(X4139,X4140,X4141))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4141),image_a_fun_int_bool(X4139,X4140)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4141)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk6_3(X4139,X4140,X4141)),X4140))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4141),image_a_fun_int_bool(X4139,X4140)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4141)) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk6_3(X4139,X4140,X4141)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4141),image_a_fun_int_bool(X4139,X4140)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4141)) )
& ( X4141 = image_a_fun_int_bool(X4139,esk6_3(X4139,X4140,X4141))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4141),image_a_fun_int_bool(X4139,X4140)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4141)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_224_finite__subset__image])])])]) ).
fof(i_0_1851,plain,
! [X5131,X5132,X5133,X5134] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5133),X5134))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5131),X5132))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5133),X5132)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5134),X5131))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_584_Diff__mono])]) ).
fof(i_0_1852,plain,
! [X5127,X5128,X5129,X5130] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5129),X5130))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5127),X5128))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5129),X5128)),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5130),X5127))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_583_Diff__mono])]) ).
fof(i_0_1853,plain,
! [X5135,X5136,X5137,X5138] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5137),X5138))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5135),X5136))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5137),X5136)),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5138),X5135))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_585_Diff__mono])]) ).
fof(i_0_1854,plain,
! [X5925,X5926,X5927,X5928] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5927),X5928))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5925),X5926))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5927),X5925)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5928),X5926))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_882_add__less__mono])]) ).
fof(i_0_1855,plain,
! [X6000,X6001,X6002] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6001),X6002))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6000),X6001))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6001),X6000)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6002),X6000))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_911_diff__less__mono])]) ).
fof(i_0_1856,plain,
! [X5957,X5958,X5959] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5958),X5959))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5958),X5957))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5957),X5959)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5957),X5958))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_894_diff__less__mono2])]) ).
fof(i_0_1857,plain,
! [X6162,X6163,X6164,X6165] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6164),X6165))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6162),X6163))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6164),X6162)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6165),X6163))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_986_mult__le__mono])]) ).
fof(i_0_1858,plain,
! [X5798,X5799,X5800,X5801] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5800),X5801))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5798),X5799))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5800),X5798)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5801),X5799))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_829_add__le__mono])]) ).
fof(i_0_1859,plain,
! [X5750,X5751,X5752,X5753] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5752),X5753))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5750),X5751))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5752),X5750)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5753),X5751))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_812_add__mono])]) ).
fof(i_0_1860,plain,
! [X6308,X6309,X6310,X6311] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6310),X6311))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6308),X6309))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6310),X6308)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6311),X6309))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1052_zadd__zless__mono])]) ).
fof(i_0_1861,plain,
! [X5746,X5747,X5748,X5749] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5748),X5749))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5746),X5747))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5748),X5746)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5749),X5747))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_811_add__mono])]) ).
cnf(i_0_1862,plain,
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(X1))))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1450]) ).
fof(i_0_1863,plain,
! [X6191,X6192,X6193] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6192),X6193))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6191))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6192),X6191)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6193),X6191))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_999_mult__less__mono1])]) ).
fof(i_0_1864,plain,
! [X6188,X6189,X6190] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6189),X6190))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6188))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6188),X6189)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6188),X6190))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_998_mult__less__mono2])]) ).
fof(i_0_1865,plain,
! [X6267,X6268,X6269] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6268),X6269))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6267))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6267),X6268)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6267),X6269))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1030_zmult__zless__mono2])]) ).
fof(i_0_1866,plain,
! [X4410,X4411,X4412] :
( ( hBOOL(hAPP_nat_bool(X4411,hAPP_nat_nat(suc,esk64_3(X4410,X4411,X4412))))
| hBOOL(hAPP_nat_bool(X4411,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X4412),X4410)))
| ~ hBOOL(hAPP_nat_bool(X4411,X4412)) )
& ( ~ hBOOL(hAPP_nat_bool(X4411,esk64_3(X4410,X4411,X4412)))
| hBOOL(hAPP_nat_bool(X4411,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X4412),X4410)))
| ~ hBOOL(hAPP_nat_bool(X4411,X4412)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_299_zero__induct__lemma])])])]) ).
fof(i_0_1867,plain,
! [X4867,X4868,X4869,X4871,X4872,X4873] :
( ( is_fun_pname_bool(esk72_3(X4867,X4868,X4869))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4867),image_pname_a(X4868,X4869)))
| ~ is_fun_a_bool(X4867) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk72_3(X4867,X4868,X4869)),X4869))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4867),image_pname_a(X4868,X4869)))
| ~ is_fun_a_bool(X4867) )
& ( X4867 = image_pname_a(X4868,esk72_3(X4867,X4868,X4869))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4867),image_pname_a(X4868,X4869)))
| ~ is_fun_a_bool(X4867) )
& ( ~ is_fun_pname_bool(X4873)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4873),X4872))
| X4867 != image_pname_a(X4871,X4873)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4867),image_pname_a(X4871,X4872)))
| ~ is_fun_a_bool(X4867) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_472_subset__image__iff])])])])])]) ).
fof(i_0_1868,plain,
! [X4884,X4885,X4886] :
( ( is_pname(esk74_3(X4884,X4885,X4886))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4884),image_pname_a(X4885,X4886)))
| ~ is_a(X4884) )
& ( X4884 = hAPP_pname_a(X4885,esk74_3(X4884,X4885,X4886))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4884),image_pname_a(X4885,X4886)))
| ~ is_a(X4884) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk74_3(X4884,X4885,X4886)),X4886))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4884),image_pname_a(X4885,X4886)))
| ~ is_a(X4884) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1461])])])])])]) ).
fof(i_0_1869,plain,
! [X4734,X4735,X4736,X4738,X4739,X4740] :
( ( is_pname(esk67_3(X4734,X4735,X4736))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4734),image_pname_a(X4735,X4736)))
| ~ is_a(X4734) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk67_3(X4734,X4735,X4736)),X4736))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4734),image_pname_a(X4735,X4736)))
| ~ is_a(X4734) )
& ( X4734 = hAPP_pname_a(X4735,esk67_3(X4734,X4735,X4736))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4734),image_pname_a(X4735,X4736)))
| ~ is_a(X4734) )
& ( ~ is_pname(X4740)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4740),X4739))
| X4734 != hAPP_pname_a(X4738,X4740)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4734),image_pname_a(X4738,X4739)))
| ~ is_a(X4734) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_432_image__iff])])])])])]) ).
fof(i_0_1870,plain,
! [X6216,X6217] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X6217))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X6216))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6217),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6217),X6216))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1009_n__less__n__mult__m])]) ).
fof(i_0_1871,plain,
! [X6214,X6215] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X6215))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X6214))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6215),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6214),X6215))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1008_n__less__m__mult__n])]) ).
fof(i_0_1872,plain,
! [X4880,X4881,X4882] :
( ( X4880 = hAPP_nat_int(X4881,esk73_3(X4880,X4881,X4882))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4880),image_nat_int(X4881,X4882))) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk73_3(X4880,X4881,X4882)),X4882))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4880),image_nat_int(X4881,X4882))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1462])])])]) ).
fof(i_0_1873,plain,
! [X4726,X4727,X4728,X4730,X4731,X4732,X4733] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk66_3(X4726,X4727,X4728)),X4728))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4726),image_nat_int(X4727,X4728))) )
& ( X4726 = hAPP_nat_int(X4727,esk66_3(X4726,X4727,X4728))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4726),image_nat_int(X4727,X4728))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4733),X4732))
| X4730 != hAPP_nat_int(X4731,X4733)
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4730),image_nat_int(X4731,X4732))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_431_image__iff])])])])])]) ).
fof(i_0_1874,plain,
! [X4859,X4860,X4861,X4863,X4864,X4865,X4866] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk71_3(X4859,X4860,X4861)),X4861))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4859),image_nat_int(X4860,X4861))) )
& ( X4859 = image_nat_int(X4860,esk71_3(X4859,X4860,X4861))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4859),image_nat_int(X4860,X4861))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4866),X4865))
| X4863 != image_nat_int(X4864,X4866)
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4863),image_nat_int(X4864,X4865))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_471_subset__image__iff])])])])])]) ).
fof(i_0_1875,plain,
! [X6012,X6013,X6014] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk168_3(X6012,X6013,X6014)),X6014))
| hBOOL(hAPP_nat_bool(X6012,X6013))
| ~ hBOOL(hAPP_nat_bool(X6012,X6014))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6013),X6014)) )
& ( hBOOL(hAPP_nat_bool(X6012,hAPP_nat_nat(suc,esk168_3(X6012,X6013,X6014))))
| hBOOL(hAPP_nat_bool(X6012,X6013))
| ~ hBOOL(hAPP_nat_bool(X6012,X6014))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6013),X6014)) )
& ( ~ hBOOL(hAPP_nat_bool(X6012,esk168_3(X6012,X6013,X6014)))
| hBOOL(hAPP_nat_bool(X6012,X6013))
| ~ hBOOL(hAPP_nat_bool(X6012,X6014))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6013),X6014)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_915_inc__induct])])])]) ).
cnf(i_0_1876,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X1))
| hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,X2))))) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_1463]) ).
fof(i_0_1877,plain,
! [X6091,X6092] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6092))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6092),hAPP_nat_nat(suc,X6091))),X6092)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_960_diff__Suc__less])]) ).
fof(i_0_1878,plain,
! [X5603,X5604] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5604))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5603),X5604))
| hAPP_f957591787ol_nat(finite_card_int,X5604) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5604),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5603),bot_bot_fun_int_bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_764_card_Oremove])]) ).
fof(i_0_1879,plain,
! [X5605,X5606] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5606))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5605),X5606))
| hAPP_f22106695ol_nat(finite_card_nat,X5606) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5606),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5605),bot_bot_fun_nat_bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_765_card_Oremove])]) ).
fof(i_0_1880,plain,
! [X5601,X5602] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5602))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5601),X5602))
| hAPP_fun_a_bool_nat(finite_card_a,X5602) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5602),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5601),bot_bot_fun_a_bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_763_card_Oremove])]) ).
fof(i_0_1881,plain,
! [X5607,X5608] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5608))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5607),X5608))
| hAPP_f921600141ol_nat(finite_card_pname,X5608) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5608),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5607),bot_bo844097828e_bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_766_card_Oremove])]) ).
fof(i_0_1882,plain,
! [X4811,X4812,X4813] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4811),X4813))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4811),X4812)),X4813)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4812),X4813))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4811),X4812)),X4813)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4811),X4813))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4812),X4813))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4811),X4812)),X4813)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_455_insert__subset])])]) ).
fof(i_0_1883,plain,
! [X4808,X4809,X4810] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4808),X4810))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4808),X4809)),X4810)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4809),X4810))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4808),X4809)),X4810)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4808),X4810))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4809),X4810))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4808),X4809)),X4810)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_454_insert__subset])])]) ).
fof(i_0_1884,plain,
! [X4814,X4815,X4816] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4814),X4816))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4814),X4815)),X4816)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4815),X4816))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4814),X4815)),X4816)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4814),X4816))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4815),X4816))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4814),X4815)),X4816)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_456_insert__subset])])]) ).
fof(i_0_1885,plain,
! [X4805,X4806,X4807] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4805),X4807))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4805),X4806)),X4807)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4806),X4807))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4805),X4806)),X4807)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4805),X4807))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4806),X4807))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4805),X4806)),X4807)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_453_insert__subset])])]) ).
fof(i_0_1886,plain,
! [X5933,X5934,X5935] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5933),X5934)),X5935))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5933),X5935)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_884_add__lessD1])]) ).
fof(i_0_1887,plain,
! [X5808,X5809,X5810] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5808),X5810))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5808),X5809)),X5810)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5809),X5810))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5808),X5809)),X5810)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1464])])]) ).
fof(i_0_1888,plain,
! [X5805,X5806,X5807] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5805),X5806)),X5807))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5805),X5807)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_831_add__leD1])]) ).
fof(i_0_1889,plain,
! [X5802,X5803,X5804] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5802),X5803)),X5804))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5803),X5804)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_830_add__leD2])]) ).
fof(i_0_1890,plain,
! [X5860,X5861,X5862] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5861),X5862))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5862),X5861))),X5860) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X5862)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5861),X5860)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_852_diff__Suc__diff__eq2])]) ).
fof(i_0_1891,plain,
! [X6276,X6277] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6276),X6277))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6276),X6277)),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6276),X6277)),zero_zero_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6276),X6277)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1037_less__bin__lemma])]) ).
fof(i_0_1892,plain,
! [X6101,X6102,X6103,X6104,X6105,X6106,X6107] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6102),X6103))
| hBOOL(hAPP_nat_bool(X6101,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X6101,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6102),X6103))) )
& ( X6102 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6103),X6104)
| hBOOL(hAPP_nat_bool(X6101,X6104))
| ~ hBOOL(hAPP_nat_bool(X6101,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6102),X6103))) )
& ( X6106 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6107),esk178_3(X6105,X6106,X6107))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6106),X6107))
| hBOOL(hAPP_nat_bool(X6105,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6106),X6107))) )
& ( ~ hBOOL(hAPP_nat_bool(X6105,esk178_3(X6105,X6106,X6107)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6106),X6107))
| hBOOL(hAPP_nat_bool(X6105,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6106),X6107))) )
& ( X6106 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6107),esk178_3(X6105,X6106,X6107))
| ~ hBOOL(hAPP_nat_bool(X6105,zero_zero_nat))
| hBOOL(hAPP_nat_bool(X6105,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6106),X6107))) )
& ( ~ hBOOL(hAPP_nat_bool(X6105,esk178_3(X6105,X6106,X6107)))
| ~ hBOOL(hAPP_nat_bool(X6105,zero_zero_nat))
| hBOOL(hAPP_nat_bool(X6105,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6106),X6107))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1465])])])])])]) ).
fof(i_0_1893,plain,
! [X6093,X6094,X6095,X6096,X6097,X6098,X6099] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6094),X6095))
| hBOOL(hAPP_nat_bool(X6093,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X6093,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6094),X6095))) )
& ( X6094 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6095),X6096)
| hBOOL(hAPP_nat_bool(X6093,X6096))
| ~ hBOOL(hAPP_nat_bool(X6093,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6094),X6095))) )
& ( X6098 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6099),esk177_3(X6097,X6098,X6099))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6098),X6099))
| hBOOL(hAPP_nat_bool(X6097,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6098),X6099))) )
& ( ~ hBOOL(hAPP_nat_bool(X6097,esk177_3(X6097,X6098,X6099)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6098),X6099))
| hBOOL(hAPP_nat_bool(X6097,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6098),X6099))) )
& ( X6098 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6099),esk177_3(X6097,X6098,X6099))
| ~ hBOOL(hAPP_nat_bool(X6097,zero_zero_nat))
| hBOOL(hAPP_nat_bool(X6097,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6098),X6099))) )
& ( ~ hBOOL(hAPP_nat_bool(X6097,esk177_3(X6097,X6098,X6099)))
| ~ hBOOL(hAPP_nat_bool(X6097,zero_zero_nat))
| hBOOL(hAPP_nat_bool(X6097,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6098),X6099))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_961_nat__diff__split])])])])])]) ).
fof(i_0_1894,plain,
! [X5236,X5237] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5237))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5236),X5237))
| hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5237),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5236),bot_bot_fun_int_bool)))) = hAPP_f957591787ol_nat(finite_card_int,X5237) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_643_card__Suc__Diff1])]) ).
fof(i_0_1895,plain,
! [X5238,X5239] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5239))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5238),X5239))
| hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5239),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5238),bot_bot_fun_nat_bool)))) = hAPP_f22106695ol_nat(finite_card_nat,X5239) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_644_card__Suc__Diff1])]) ).
fof(i_0_1896,plain,
! [X5234,X5235] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5235))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5234),X5235))
| hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5235),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5234),bot_bot_fun_a_bool)))) = hAPP_fun_a_bool_nat(finite_card_a,X5235) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_642_card__Suc__Diff1])]) ).
fof(i_0_1897,plain,
! [X5240,X5241] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5241))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5240),X5241))
| hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5241),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5240),bot_bo844097828e_bool)))) = hAPP_f921600141ol_nat(finite_card_pname,X5241) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_645_card__Suc__Diff1])]) ).
fof(i_0_1898,plain,
! [X6314,X6315] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6314),one_one_int)),X6315))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6314),X6315)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6314),X6315))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6314),one_one_int)),X6315)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1054_add1__zle__eq])]) ).
fof(i_0_1899,plain,
! [X4844,X4845,X4846] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4845),X4846))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4844),X4845)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4844),X4846))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_466_insert__mono])]) ).
fof(i_0_1900,plain,
! [X4841,X4842,X4843] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4842),X4843))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4841),X4842)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4841),X4843))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_465_insert__mono])]) ).
fof(i_0_1901,plain,
! [X4838,X4839,X4840] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4839),X4840))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4838),X4839)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4838),X4840))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_464_insert__mono])]) ).
fof(i_0_1902,plain,
! [X5922,X5923,X5924] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5923),X5924))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5923),X5922)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5924),X5922))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_881_add__less__mono1])]) ).
fof(i_0_1903,plain,
! [X6169,X6170,X6171] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6170),X6171))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6170),X6169)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6171),X6169))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_988_mult__le__mono1])]) ).
fof(i_0_1904,plain,
! [X6166,X6167,X6168] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6167),X6168))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6166),X6167)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6166),X6168))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_987_mult__le__mono2])]) ).
fof(i_0_1905,plain,
! [X5795,X5796,X5797] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5796),X5797))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5796),X5795)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5797),X5795))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_828_add__le__mono1])]) ).
fof(i_0_1906,plain,
! [X5737,X5738,X5739] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5738),X5739))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5738),X5737)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5739),X5737))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_808_add__right__mono])]) ).
fof(i_0_1907,plain,
! [X5743,X5744,X5745] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5744),X5745))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5743),X5744)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5743),X5745))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_810_add__left__mono])]) ).
fof(i_0_1908,plain,
! [X3994,X3995,X3996] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3995),X3996))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3995),X3994)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3996),X3994))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_177_diff__le__mono])]) ).
fof(i_0_1909,plain,
! [X3997,X3998,X3999] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3998),X3999))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3997),X3999)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3997),X3998))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_178_diff__le__mono2])]) ).
fof(i_0_1910,plain,
! [X6305,X6306,X6307] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6306),X6307))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6306),X6305)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6307),X6305))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1051_zadd__strict__right__mono])]) ).
fof(i_0_1911,plain,
! [X5734,X5735,X5736] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5735),X5736))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5735),X5734)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5736),X5734))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_807_add__right__mono])]) ).
fof(i_0_1912,plain,
! [X6280,X6281,X6282] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6281),X6282))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6280),X6281)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6280),X6282))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1040_zadd__left__mono])]) ).
fof(i_0_1913,plain,
! [X5740,X5741,X5742] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5741),X5742))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5740),X5741)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5740),X5742))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_809_add__left__mono])]) ).
fof(i_0_1914,plain,
! [X6479,X6480,X6481] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X6479)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X6480)),X6481)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6479),X6480))),X6481),
inference(variable_rename,[status(thm)],[fact_1104_zadd__int__left]) ).
fof(i_0_1915,plain,
! [X5611,X5612] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5612))
| hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5611),X5612)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5612),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5611),bot_bot_fun_int_bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_768_card_Oinsert__remove])]) ).
fof(i_0_1916,plain,
! [X5613,X5614] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5614))
| hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5613),X5614)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5614),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5613),bot_bot_fun_nat_bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_769_card_Oinsert__remove])]) ).
fof(i_0_1917,plain,
! [X5609,X5610] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5610))
| hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5609),X5610)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5610),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5609),bot_bot_fun_a_bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_767_card_Oinsert__remove])]) ).
fof(i_0_1918,plain,
! [X5615,X5616] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5616))
| hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5615),X5616)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5616),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5615),bot_bo844097828e_bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_770_card_Oinsert__remove])]) ).
fof(i_0_1919,plain,
! [X6080,X6081] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6081))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6080))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6080),X6081)),X6080)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_953_diff__less])]) ).
fof(i_0_1920,plain,
! [X5244,X5245] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5245))
| hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5244),X5245)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5245),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5244),bot_bot_fun_int_bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_647_card__insert])]) ).
fof(i_0_1921,plain,
! [X5246,X5247] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5247))
| hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5246),X5247)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5247),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5246),bot_bot_fun_nat_bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_648_card__insert])]) ).
fof(i_0_1922,plain,
! [X5242,X5243] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5243))
| hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5242),X5243)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5243),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5242),bot_bot_fun_a_bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_646_card__insert])]) ).
fof(i_0_1923,plain,
! [X5248,X5249] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5249))
| hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5248),X5249)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5249),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5248),bot_bo844097828e_bool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_649_card__insert])]) ).
fof(i_0_1924,plain,
! [X5909,X5910] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5909),X5910)),X5909)),
inference(variable_rename,[status(thm)],[i_0_1466]) ).
fof(i_0_1925,plain,
! [X5911,X5912] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5911),X5912)),X5912)),
inference(variable_rename,[status(thm)],[i_0_1467]) ).
fof(i_0_1926,plain,
! [X3978,X3979,X3980] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X3978)),X3979)),hAPP_nat_nat(suc,X3980)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3978),X3979)),X3980),
inference(variable_rename,[status(thm)],[fact_171_Suc__diff__diff]) ).
fof(i_0_1927,plain,
! [X5052,X5053,X5054] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5052),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5053),X5054)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5052),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5053),bot_bot_fun_int_bool))),X5054),
inference(variable_rename,[status(thm)],[fact_557_Diff__insert2]) ).
fof(i_0_1928,plain,
! [X5049,X5050,X5051] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5049),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5050),X5051)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5049),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5050),bot_bot_fun_nat_bool))),X5051),
inference(variable_rename,[status(thm)],[fact_556_Diff__insert2]) ).
fof(i_0_1929,plain,
! [X5046,X5047,X5048] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5046),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5047),X5048)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5046),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5047),bot_bot_fun_a_bool))),X5048),
inference(variable_rename,[status(thm)],[fact_555_Diff__insert2]) ).
fof(i_0_1930,plain,
! [X3905,X3906] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X3905)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X3905),X3906)))) )
& ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X3906)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X3905),X3906)))) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X3905)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X3906)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X3905),X3906)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_134_finite__Collect__disjI])])]) ).
fof(i_0_1931,plain,
! [X3903,X3904] :
( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X3903)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X3903),X3904)))) )
& ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X3904)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X3903),X3904)))) )
& ( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X3903)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X3904)))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X3903),X3904)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_133_finite__Collect__disjI])])]) ).
fof(i_0_1932,plain,
! [X3907,X3908] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X3907)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X3907),X3908)))) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X3908)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X3907),X3908)))) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X3907)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X3908)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X3907),X3908)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_135_finite__Collect__disjI])])]) ).
fof(i_0_1933,plain,
! [X3909,X3910] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X3909)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X3909),X3910)))) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X3910)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X3909),X3910)))) )
& ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X3909)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X3910)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X3909),X3910)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_136_finite__Collect__disjI])])]) ).
fof(i_0_1934,plain,
! [X3911,X3912] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X3911)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X3911),X3912)))) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X3912)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X3911),X3912)))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X3911)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X3912)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X3911),X3912)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_137_finite__Collect__disjI])])]) ).
fof(i_0_1935,plain,
! [X3901,X3902] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X3901)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X3901),X3902)))) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X3902)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X3901),X3902)))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X3901)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X3902)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X3901),X3902)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_132_finite__Collect__disjI])])]) ).
fof(i_0_1936,plain,
! [X3826,X3827] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3827))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X3827)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3826),X3827)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_93_card__insert__le])]) ).
fof(i_0_1937,plain,
! [X3824,X3825] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3825))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X3825)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3824),X3825)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_92_card__insert__le])]) ).
fof(i_0_1938,plain,
! [X3820,X3821] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3821))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X3821)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X3820),X3821)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_90_card__insert__le])]) ).
fof(i_0_1939,plain,
! [X3818,X3819] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3819))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X3819)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X3818),X3819)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_89_card__insert__le])]) ).
fof(i_0_1940,plain,
! [X3816,X3817] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3817))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X3817)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X3816),X3817)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_88_card__insert__le])]) ).
fof(i_0_1941,plain,
! [X3814,X3815] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3815))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X3815)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X3814),X3815)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_87_card__insert__le])]) ).
fof(i_0_1942,plain,
! [X3828,X3829] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3829))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X3829)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3828),X3829)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_94_card__insert__le])]) ).
fof(i_0_1943,plain,
! [X3822,X3823] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3823))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X3823)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3822),X3823)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_91_card__insert__le])]) ).
cnf(i_0_1944,plain,
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1))),X3)
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1468]) ).
cnf(i_0_1945,plain,
( X1 = X2
| bit1(X1) != bit1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1469]) ).
fof(i_0_1946,plain,
! [X3986,X3987,X3988] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3987),X3988))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3987),X3986))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3988),X3987)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3986),X3987)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3988),X3986) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_174_Nat_Odiff__diff__eq])]) ).
fof(i_0_1947,plain,
! [X5857,X5858,X5859] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5858),X5859))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5857),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5859),X5858))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5857),X5858)),hAPP_nat_nat(suc,X5859)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_851_diff__Suc__diff__eq1])]) ).
fof(i_0_1948,plain,
! [X3802,X3803] :
( ~ is_fun1661590463l_bool(X3802)
| ~ is_fun1661590463l_bool(X3803)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3803))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3802),X3803))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X3803)),hAPP_f55526627ol_nat(finite1340463720e_bool,X3802)))
| X3802 = X3803 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_81_card__seteq])]) ).
fof(i_0_1949,plain,
! [X3804,X3805] :
( ~ is_fun949378684l_bool(X3804)
| ~ is_fun949378684l_bool(X3805)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3805))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3804),X3805))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X3805)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X3804)))
| X3804 = X3805 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_82_card__seteq])]) ).
fof(i_0_1950,plain,
! [X3806,X3807] :
( ~ is_fun_pname_bool(X3806)
| ~ is_fun_pname_bool(X3807)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3807))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3806),X3807))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X3807)),hAPP_f921600141ol_nat(finite_card_pname,X3806)))
| X3806 = X3807 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_83_card__seteq])]) ).
fof(i_0_1951,plain,
! [X3808,X3809] :
( ~ is_fun_a_bool(X3808)
| ~ is_fun_a_bool(X3809)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3809))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3808),X3809))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X3809)),hAPP_fun_a_bool_nat(finite_card_a,X3808)))
| X3808 = X3809 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_84_card__seteq])]) ).
fof(i_0_1952,plain,
! [X6172] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6172),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6172),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6172),X6172)))),
inference(variable_rename,[status(thm)],[fact_989_le__cube]) ).
fof(i_0_1953,plain,
! [X3800,X3801] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3801))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3800),X3801))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X3801)),hAPP_f696928925ol_nat(finite346522414t_bool,X3800)))
| X3800 = X3801 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_80_card__seteq])]) ).
fof(i_0_1954,plain,
! [X3798,X3799] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3799))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3798),X3799))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X3799)),hAPP_f521865025ol_nat(finite1876863882t_bool,X3798)))
| X3798 = X3799 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_79_card__seteq])]) ).
fof(i_0_1955,plain,
! [X3810,X3811] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3811))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3810),X3811))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X3811)),hAPP_f22106695ol_nat(finite_card_nat,X3810)))
| X3810 = X3811 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_85_card__seteq])]) ).
fof(i_0_1956,plain,
! [X3812,X3813] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3813))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3812),X3813))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X3813)),hAPP_f957591787ol_nat(finite_card_int,X3812)))
| X3812 = X3813 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_86_card__seteq])]) ).
fof(i_0_1957,plain,
! [X4823,X4824,X4825] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4825),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4824),X4823)))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4825),X4823))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4824),X4825)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4825),X4823))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4825),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4824),X4823)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4824),X4825)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1470])])]) ).
fof(i_0_1958,plain,
! [X4820,X4821,X4822] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4822),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4821),X4820)))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4822),X4820))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4821),X4822)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4822),X4820))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4822),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4821),X4820)))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4821),X4822)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1471])])]) ).
fof(i_0_1959,plain,
! [X4826,X4827,X4828] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4828),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4827),X4826)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4828),X4826))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4827),X4828)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4828),X4826))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4828),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4827),X4826)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4827),X4828)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1472])])]) ).
fof(i_0_1960,plain,
! [X4817,X4818,X4819] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4819),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4818),X4817)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4819),X4817))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4818),X4819)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4819),X4817))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4819),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4818),X4817)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4818),X4819)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1473])])]) ).
cnf(i_0_1961,plain,
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
| number_number_of_nat(bit1(X1)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),number_number_of_nat(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1474]) ).
fof(i_0_1962,plain,
! [X5954,X5955,X5956] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5955),X5956))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5955),X5954)),X5956)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_893_less__imp__diff__less])]) ).
fof(i_0_1963,plain,
! [X5852,X5853,X5854] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5853),X5854))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5854),X5852)),X5853) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5854),X5853)),X5852) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_848_diff__add__assoc2])]) ).
fof(i_0_1964,plain,
! [X5849,X5850,X5851] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5850),X5851))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5851),X5850)),X5849) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5851),X5849)),X5850) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_847_add__diff__assoc2])]) ).
fof(i_0_1965,plain,
! [X6076,X6077] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6076),X6077)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6076))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6077)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6076))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6076),X6077))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6077))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6076),X6077))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_951_add__gr__0])])]) ).
fof(i_0_1966,plain,
! [X6383,X6384,X6385] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6385))
| X6385 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6383),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6385),X6384))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6383),X6385))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X6384)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1073_self__quotient__aux1])]) ).
fof(i_0_1967,plain,
! [X6316,X6317] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6316),X6317))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6316),one_one_int)),X6317)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1055_zless__imp__add1__zle])]) ).
fof(i_0_1968,plain,
! [X4586,X4587] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4586),collect_a(X4587)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X4586))),X4587)),
inference(variable_rename,[status(thm)],[fact_373_insert__Collect]) ).
fof(i_0_1969,plain,
! [X6386,X6387,X6388] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6388))
| X6388 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6386),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6388),X6387))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6386))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6387),one_one_int)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1074_self__quotient__aux2])]) ).
fof(i_0_1970,plain,
! [X5533,X5534] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5534))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5533),X5534))
| hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5534),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5533),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,X5534)),one_one_nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_741_card__Diff__singleton])]) ).
fof(i_0_1971,plain,
! [X5525,X5526] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5525),X5526))
| hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5526),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5525),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,X5526)),one_one_nat)
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5526)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5525),X5526))
| hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5526),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5525),bot_bot_fun_int_bool))) = hAPP_f957591787ol_nat(finite_card_int,X5526)
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5526)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1475])])]) ).
fof(i_0_1972,plain,
! [X5535,X5536] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5536))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5535),X5536))
| hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5536),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5535),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,X5536)),one_one_nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_742_card__Diff__singleton])]) ).
fof(i_0_1973,plain,
! [X5527,X5528] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5527),X5528))
| hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5528),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5527),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,X5528)),one_one_nat)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5528)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5527),X5528))
| hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5528),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5527),bot_bot_fun_nat_bool))) = hAPP_f22106695ol_nat(finite_card_nat,X5528)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5528)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1476])])]) ).
fof(i_0_1974,plain,
! [X5531,X5532] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5532))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5531),X5532))
| hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5532),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5531),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,X5532)),one_one_nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_740_card__Diff__singleton])]) ).
fof(i_0_1975,plain,
! [X5523,X5524] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5523),X5524))
| hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5524),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5523),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,X5524)),one_one_nat)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5524)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5523),X5524))
| hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5524),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5523),bot_bot_fun_a_bool))) = hAPP_fun_a_bool_nat(finite_card_a,X5524)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5524)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1477])])]) ).
fof(i_0_1976,plain,
! [X5537,X5538] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5538))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5537),X5538))
| hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5538),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5537),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,X5538)),one_one_nat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_743_card__Diff__singleton])]) ).
fof(i_0_1977,plain,
! [X5529,X5530] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5529),X5530))
| hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5530),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5529),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,X5530)),one_one_nat)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5530)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5529),X5530))
| hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5530),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5529),bot_bo844097828e_bool))) = hAPP_f921600141ol_nat(finite_card_pname,X5530)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5530)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1478])])]) ).
fof(i_0_1978,plain,
! [X5474,X5475,X5476] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5474),X5475))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5474),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5475),X5476))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5474),X5476))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5474),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5475),X5476))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5474),X5475))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5474),X5476))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5474),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5475),X5476))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1479])])]) ).
fof(i_0_1979,plain,
! [X5426,X5427,X5428] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5426),X5427))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5426),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5427),X5428))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5426),X5428))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5426),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5427),X5428))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_705_DiffE])])]) ).
fof(i_0_1980,plain,
! [X5450,X5451,X5452] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5450),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5451),X5452)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5450),X5452)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1480])]) ).
fof(i_0_1981,plain,
! [X5471,X5472,X5473] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5471),X5472))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5471),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5472),X5473))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5471),X5473))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5471),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5472),X5473))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5471),X5472))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5471),X5473))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5471),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5472),X5473))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1481])])]) ).
fof(i_0_1982,plain,
! [X5423,X5424,X5425] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5423),X5424))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5423),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5424),X5425))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5423),X5425))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5423),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5424),X5425))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_704_DiffE])])]) ).
fof(i_0_1983,plain,
! [X5447,X5448,X5449] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5447),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5448),X5449)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5447),X5449)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1482])]) ).
fof(i_0_1984,plain,
! [X5480,X5481,X5482] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5480),X5481))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5480),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5481),X5482))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5480),X5482))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5480),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5481),X5482))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5480),X5481))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5480),X5482))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5480),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5481),X5482))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1483])])]) ).
fof(i_0_1985,plain,
! [X5432,X5433,X5434] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5432),X5433))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5432),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5433),X5434))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5432),X5434))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5432),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5433),X5434))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_707_DiffE])])]) ).
fof(i_0_1986,plain,
! [X5456,X5457,X5458] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5456),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5457),X5458)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5456),X5458)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1484])]) ).
fof(i_0_1987,plain,
! [X5477,X5478,X5479] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5477),X5478))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5477),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5478),X5479))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5477),X5479))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5477),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5478),X5479))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5477),X5478))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5477),X5479))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5477),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5478),X5479))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1485])])]) ).
fof(i_0_1988,plain,
! [X5429,X5430,X5431] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5429),X5430))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5429),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5430),X5431))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5429),X5431))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5429),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5430),X5431))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_706_DiffE])])]) ).
fof(i_0_1989,plain,
! [X5453,X5454,X5455] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5453),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5454),X5455)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5453),X5455)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1486])]) ).
fof(i_0_1990,plain,
! [X3760,X3761] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3761))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(X3760,X3761))),hAPP_f921600141ol_nat(finite_card_pname,X3761))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_60_card__image__le])]) ).
fof(i_0_1991,plain,
! [X3780,X3781] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3781))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(X3780,X3781))),hAPP_f22106695ol_nat(finite_card_nat,X3781))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_70_card__image__le])]) ).
fof(i_0_1992,plain,
! [X3770,X3771] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3771))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(X3770,X3771))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X3771))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_65_card__image__le])]) ).
fof(i_0_1993,plain,
! [X3768,X3769] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3769))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(X3768,X3769))),hAPP_f55526627ol_nat(finite1340463720e_bool,X3769))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_64_card__image__le])]) ).
fof(i_0_1994,plain,
! [X3766,X3767] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3767))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(X3766,X3767))),hAPP_f696928925ol_nat(finite346522414t_bool,X3767))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_63_card__image__le])]) ).
fof(i_0_1995,plain,
! [X3764,X3765] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3765))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(X3764,X3765))),hAPP_f521865025ol_nat(finite1876863882t_bool,X3765))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_62_card__image__le])]) ).
fof(i_0_1996,plain,
! [X3762,X3763] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3763))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(X3762,X3763))),hAPP_fun_a_bool_nat(finite_card_a,X3763))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_61_card__image__le])]) ).
fof(i_0_1997,plain,
! [X3748,X3749] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3749))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X3748,X3749))),hAPP_f921600141ol_nat(finite_card_pname,X3749))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_54_card__image__le])]) ).
fof(i_0_1998,plain,
! [X3758,X3759] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3759))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X3758,X3759))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X3759))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_59_card__image__le])]) ).
fof(i_0_1999,plain,
! [X3756,X3757] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3757))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X3756,X3757))),hAPP_f55526627ol_nat(finite1340463720e_bool,X3757))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_58_card__image__le])]) ).
fof(i_0_2000,plain,
! [X3754,X3755] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3755))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X3754,X3755))),hAPP_f696928925ol_nat(finite346522414t_bool,X3755))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_57_card__image__le])]) ).
fof(i_0_2001,plain,
! [X3752,X3753] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3753))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(X3752,X3753))),hAPP_f521865025ol_nat(finite1876863882t_bool,X3753))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_56_card__image__le])]) ).
fof(i_0_2002,plain,
! [X3750,X3751] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3751))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X3750,X3751))),hAPP_fun_a_bool_nat(finite_card_a,X3751))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_55_card__image__le])]) ).
fof(i_0_2003,plain,
! [X3742,X3743] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3743))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X3742,X3743))),hAPP_f696928925ol_nat(finite346522414t_bool,X3743))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_51_card__image__le])]) ).
fof(i_0_2004,plain,
! [X3740,X3741] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3741))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(X3740,X3741))),hAPP_f521865025ol_nat(finite1876863882t_bool,X3741))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_50_card__image__le])]) ).
fof(i_0_2005,plain,
! [X3744,X3745] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3745))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X3744,X3745))),hAPP_f55526627ol_nat(finite1340463720e_bool,X3745))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_52_card__image__le])]) ).
fof(i_0_2006,plain,
! [X3746,X3747] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3747))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X3746,X3747))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X3747))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_53_card__image__le])]) ).
fof(i_0_2007,plain,
! [X3778,X3779] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3779))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X3778,X3779))),hAPP_f921600141ol_nat(finite_card_pname,X3779))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_69_card__image__le])]) ).
fof(i_0_2008,plain,
! [X3738,X3739] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3739))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X3738,X3739))),hAPP_fun_a_bool_nat(finite_card_a,X3739))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_49_card__image__le])]) ).
fof(i_0_2009,plain,
! [X3774,X3775] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3775))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X3774,X3775))),hAPP_f22106695ol_nat(finite_card_nat,X3775))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_67_card__image__le])]) ).
fof(i_0_2010,plain,
! [X3776,X3777] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3777))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(X3776,X3777))),hAPP_f957591787ol_nat(finite_card_int,X3777))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_68_card__image__le])]) ).
fof(i_0_2011,plain,
! [X3736,X3737] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3737))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X3736,X3737))),hAPP_f921600141ol_nat(finite_card_pname,X3737))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_48_card__image__le])]) ).
fof(i_0_2012,plain,
! [X3772,X3773] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3773))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X3772,X3773))),hAPP_fun_a_bool_nat(finite_card_a,X3773))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_66_card__image__le])]) ).
cnf(i_0_2013,plain,
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
| hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(X1))),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1487]) ).
cnf(i_0_2014,plain,
succ(X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int),
inference(split_conjunct,[status(thm)],[i_0_1488]) ).
fof(i_0_2015,plain,
! [X6119,X6120,X6122] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk179_2(X6119,X6120)),X6119))
| ~ hBOOL(hAPP_nat_bool(X6120,X6119))
| hBOOL(hAPP_nat_bool(X6120,zero_zero_nat)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6122),esk179_2(X6119,X6120)))
| ~ hBOOL(hAPP_nat_bool(X6120,X6122))
| ~ hBOOL(hAPP_nat_bool(X6120,X6119))
| hBOOL(hAPP_nat_bool(X6120,zero_zero_nat)) )
& ( hBOOL(hAPP_nat_bool(X6120,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk179_2(X6119,X6120)),one_one_nat)))
| ~ hBOOL(hAPP_nat_bool(X6120,X6119))
| hBOOL(hAPP_nat_bool(X6120,zero_zero_nat)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1489])])])])]) ).
fof(i_0_2016,plain,
! [X4616,X4617,X4618] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4616),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4617),X4618)))
| X4616 = X4617
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4616),X4618))
| ~ is_pname(X4616)
| ~ is_pname(X4617) )
& ( X4616 != X4617
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4616),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4617),X4618)))
| ~ is_pname(X4616)
| ~ is_pname(X4617) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4616),X4618))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4616),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4617),X4618)))
| ~ is_pname(X4616)
| ~ is_pname(X4617) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_387_insert__iff])])]) ).
fof(i_0_2017,plain,
! [X4407,X4408,X4409] :
( ~ is_pname(X4407)
| ~ is_pname(X4408)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4407),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4408),X4409)))
| X4407 = X4408
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4407),X4409)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_298_insertE])]) ).
fof(i_0_2018,plain,
! [X4607,X4608,X4609] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4607),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4608),X4609)))
| X4607 = X4608
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4607),X4609))
| ~ is_a(X4607)
| ~ is_a(X4608) )
& ( X4607 != X4608
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4607),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4608),X4609)))
| ~ is_a(X4607)
| ~ is_a(X4608) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4607),X4609))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4607),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4608),X4609)))
| ~ is_a(X4607)
| ~ is_a(X4608) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_384_insert__iff])])]) ).
fof(i_0_2019,plain,
! [X4398,X4399,X4400] :
( ~ is_a(X4398)
| ~ is_a(X4399)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4398),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4399),X4400)))
| X4398 = X4399
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4398),X4400)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_295_insertE])]) ).
fof(i_0_2020,plain,
! [X6200,X6201] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6200))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6200),X6201))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6201))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6200),X6201))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6200))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6201))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6200),X6201))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1002_nat__0__less__mult__iff])])]) ).
fof(i_0_2021,plain,
! [X6532,X6533] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6533))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6532))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X6533),X6532))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1128_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])]) ).
fof(i_0_2022,plain,
! [X6422,X6423] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6423))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6422))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6423),X6422))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1083_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).
fof(i_0_2023,plain,
! [X6424,X6425] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6425))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6424))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6425),X6424))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1085_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).
fof(i_0_2024,plain,
! [X6264,X6265,X6266] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6264),X6265)),X6266) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6264),X6266)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6265),X6266)),
inference(variable_rename,[status(thm)],[fact_1029_zadd__zmult__distrib]) ).
fof(i_0_2025,plain,
! [X6253,X6254,X6255] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6253),X6254)),X6255) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6253),X6255)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6254),X6255)),
inference(variable_rename,[status(thm)],[fact_1025_zdiff__zmult__distrib]) ).
fof(i_0_2026,plain,
! [X6156,X6157,X6158] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6156),X6157)),X6158) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6156),X6158)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6157),X6158)),
inference(variable_rename,[status(thm)],[fact_984_add__mult__distrib]) ).
fof(i_0_2027,plain,
! [X6174,X6175,X6176] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6174),X6175)),X6176) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6174),X6176)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6175),X6176)),
inference(variable_rename,[status(thm)],[fact_991_diff__mult__distrib]) ).
fof(i_0_2028,plain,
! [X4930,X4931] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X4930)),X4931))
| hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X4930)),X4931)) )
& ( ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X4930)),X4931))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X4930)),X4931)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_489_less__eq__nat_Osimps_I2_J])]) ).
fof(i_0_2029,plain,
! [X4613,X4614,X4615] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4613),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4614),X4615)))
| X4613 = X4614
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4613),X4615)) )
& ( X4613 != X4614
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4613),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4614),X4615))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4613),X4615))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4613),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4614),X4615))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_386_insert__iff])])]) ).
fof(i_0_2030,plain,
! [X4404,X4405,X4406] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4404),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4405),X4406)))
| X4404 = X4405
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4404),X4406)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_297_insertE])]) ).
fof(i_0_2031,plain,
! [X4610,X4611,X4612] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4610),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4611),X4612)))
| X4610 = X4611
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4610),X4612)) )
& ( X4610 != X4611
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4610),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4611),X4612))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4610),X4612))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4610),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4611),X4612))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_385_insert__iff])])]) ).
fof(i_0_2032,plain,
! [X4401,X4402,X4403] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4401),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4402),X4403)))
| X4401 = X4402
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4401),X4403)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_296_insertE])]) ).
fof(i_0_2033,plain,
! [X6228,X6229] :
( ( X6229 != zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6229),X6228) = zero_zero_nat )
& ( X6229 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6229),X6228) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6228),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6229),one_one_nat)),X6228)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1014_mult__eq__if])]) ).
fof(i_0_2034,plain,
! [X5462,X5463,X5464] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5462),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5463),X5464)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5462),X5463)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_717_DiffD1])]) ).
fof(i_0_2035,plain,
! [X5459,X5460,X5461] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5459),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5460),X5461)))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5459),X5460)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_716_DiffD1])]) ).
fof(i_0_2036,plain,
! [X5468,X5469,X5470] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5468),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5469),X5470)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5468),X5469)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_719_DiffD1])]) ).
fof(i_0_2037,plain,
! [X5465,X5466,X5467] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5465),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5466),X5467)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5465),X5466)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_718_DiffD1])]) ).
fof(i_0_2038,plain,
! [X5438,X5439,X5440] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5439),X5440))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5439),X5438))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5439),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5440),X5438))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1490])]) ).
fof(i_0_2039,plain,
! [X5435,X5436,X5437] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5436),X5437))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5436),X5435))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5436),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5437),X5435))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1491])]) ).
fof(i_0_2040,plain,
! [X5444,X5445,X5446] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5445),X5446))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5445),X5444))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5445),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5446),X5444))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1492])]) ).
fof(i_0_2041,plain,
! [X5441,X5442,X5443] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5442),X5443))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5442),X5441))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5442),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5443),X5441))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1493])]) ).
fof(i_0_2042,plain,
! [X5489,X5490] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5489),X5490) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X5489)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X5490)))),
inference(variable_rename,[status(thm)],[fact_727_set__diff__eq]) ).
fof(i_0_2043,plain,
! [X5487,X5488] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5487),X5488) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5487)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5488)))),
inference(variable_rename,[status(thm)],[fact_726_set__diff__eq]) ).
fof(i_0_2044,plain,
! [X6318,X6319] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6318),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6319),one_one_int)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6318),X6319))
| X6318 = X6319 )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6318),X6319))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6318),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6319),one_one_int))) )
& ( X6318 != X6319
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6318),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6319),one_one_int))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1056_zless__add1__eq])])]) ).
cnf(i_0_2045,plain,
( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X1)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X2))
| ~ hBOOL(hAPP_int_bool(X1,esk191_2(X2,X1)))
| ~ hBOOL(hAPP_int_bool(X2,esk191_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1494]) ).
fof(i_0_2046,plain,
! [X6549,X6550] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X6549),X6550))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X6549)),image_nat_int(semiri1621563631at_int,X6550))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X6549)),image_nat_int(semiri1621563631at_int,X6550)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X6549),X6550)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1137_transfer__nat__int__set__relations_I2_J])]) ).
fof(i_0_2047,plain,
! [X6543,X6544] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6543),X6544))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X6543)),image_nat_int(semiri1621563631at_int,X6544))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X6543)),image_nat_int(semiri1621563631at_int,X6544)))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X6543),X6544)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1133_transfer__nat__int__set__relations_I4_J])]) ).
fof(i_0_2048,plain,
! [X6545,X6546] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6545),X6546))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X6545)),image_nat_int(semiri1621563631at_int,X6546))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X6545)),image_nat_int(semiri1621563631at_int,X6546)))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X6545),X6546)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1134_transfer__nat__int__set__relations_I5_J])]) ).
fof(i_0_2049,plain,
! [X5907,X5908] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X5907)),hAPP_nat_nat(suc,X5908)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5907),X5908)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_875_Suc__less__SucD])]) ).
fof(i_0_2050,plain,
! [X5890,X5891] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X5890)),hAPP_nat_nat(suc,X5891)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5890),X5891)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5890),X5891))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X5890)),hAPP_nat_nat(suc,X5891))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_867_Suc__less__eq])]) ).
fof(i_0_2051,plain,
! [X6494,X6495] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X6494)),hAPP_nat_int(semiri1621563631at_int,X6495)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6494),X6495)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6494),X6495))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X6494)),hAPP_nat_int(semiri1621563631at_int,X6495))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1109_transfer__int__nat__relations_I2_J])]) ).
fof(i_0_2052,plain,
! [X6473,X6474] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X6473)),hAPP_nat_int(semiri1621563631at_int,X6474)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6473),X6474)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6473),X6474))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X6473)),hAPP_nat_int(semiri1621563631at_int,X6474))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1101_zless__int])]) ).
fof(i_0_2053,plain,
! [X3971,X3972] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X3971)),hAPP_nat_nat(suc,X3972)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3971),X3972)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3971),X3972))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X3971)),hAPP_nat_nat(suc,X3972))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_167_Suc__le__mono])]) ).
fof(i_0_2054,plain,
! [X6496,X6497] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X6496)),hAPP_nat_int(semiri1621563631at_int,X6497)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6496),X6497)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6496),X6497))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X6496)),hAPP_nat_int(semiri1621563631at_int,X6497))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1110_transfer__int__nat__relations_I3_J])]) ).
fof(i_0_2055,plain,
! [X6475,X6476] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X6475)),hAPP_nat_int(semiri1621563631at_int,X6476)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6475),X6476)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6475),X6476))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X6475)),hAPP_nat_int(semiri1621563631at_int,X6476))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1102_zle__int])]) ).
fof(i_0_2056,plain,
! [X6078,X6079] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6078),X6079)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6079),X6078)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6079),X6078))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6078),X6079))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_952_zero__less__diff])]) ).
fof(i_0_2057,plain,
! [X6299,X6300] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6299),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6300),one_one_int)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6299),X6300)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6299),X6300))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6299),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6300),one_one_int))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1048_zle__diff1__eq])]) ).
fof(i_0_2058,plain,
! [X6312,X6313] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6312),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6313),one_one_int)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6312),X6313)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6312),X6313))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6312),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6313),one_one_int))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1053_zle__add1__eq__le])]) ).
fof(i_0_2059,plain,
! [X5846,X5847,X5848] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5847),X5848))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5846),X5848)),X5847) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5846),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5848),X5847)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_846_diff__add__assoc])]) ).
fof(i_0_2060,plain,
! [X5835,X5836,X5837] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5836),X5837))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5835),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5837),X5836)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5835),X5837)),X5836) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_842_add__diff__assoc])]) ).
fof(i_0_2061,plain,
! [X5824,X5825,X5826] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5825),X5826))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5824),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5826),X5825)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5824),X5825)),X5826) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_838_diff__diff__right])]) ).
fof(i_0_2062,plain,
! [X5993,X5994] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5993),X5994)),hAPP_nat_nat(suc,X5993))),
inference(variable_rename,[status(thm)],[fact_908_diff__less__Suc]) ).
fof(i_0_2063,plain,
! [X5969,X5970] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5969),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5969),X5970)))),
inference(variable_rename,[status(thm)],[fact_898_less__add__Suc1]) ).
fof(i_0_2064,plain,
! [X5971,X5972] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5971),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5972),X5971)))),
inference(variable_rename,[status(thm)],[fact_899_less__add__Suc2]) ).
fof(i_0_2065,plain,
! [X5900,X5901,X5902] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5901),X5902))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5902),X5900))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X5901)),X5900)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_872_less__trans__Suc])]) ).
fof(i_0_2066,plain,
! [X6117,X6118] :
( ( X6118 != zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6118),X6117) = X6117 )
& ( X6118 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6118),X6117) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6118),one_one_nat)),X6117)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_968_add__eq__if])]) ).
fof(i_0_2067,plain,
! [X6030,X6031] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6030),esk174_2(X6030,X6031)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X6030)),X6031)) )
& ( X6031 = hAPP_nat_nat(suc,esk174_2(X6030,X6031))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X6030)),X6031)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_920_Suc__lessE])])])]) ).
fof(i_0_2068,plain,
! [X3866,X3867] :
( ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X3867)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X3867),X3866)))) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X3866)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X3867),X3866)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_113_finite__Collect__conjI])])]) ).
fof(i_0_2069,plain,
! [X3864,X3865] :
( ( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X3865)))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X3865),X3864)))) )
& ( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X3864)))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X3865),X3864)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_112_finite__Collect__conjI])])]) ).
fof(i_0_2070,plain,
! [X3868,X3869] :
( ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X3869)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X3869),X3868)))) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X3868)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X3869),X3868)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_114_finite__Collect__conjI])])]) ).
fof(i_0_2071,plain,
! [X3870,X3871] :
( ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X3871)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X3871),X3870)))) )
& ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X3870)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X3871),X3870)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_115_finite__Collect__conjI])])]) ).
fof(i_0_2072,plain,
! [X3872,X3873] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X3873)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X3873),X3872)))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X3872)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X3873),X3872)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_116_finite__Collect__conjI])])]) ).
fof(i_0_2073,plain,
! [X3862,X3863] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X3863)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X3863),X3862)))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X3862)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X3863),X3862)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_111_finite__Collect__conjI])])]) ).
fof(i_0_2074,plain,
! [X3975,X3976] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3975),X3976))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X3976)),X3975)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X3976)),X3975))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3975),X3976)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1495])]) ).
cnf(i_0_2075,plain,
( number_number_of_nat(bit1(X1)) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1474]) ).
fof(i_0_2076,plain,
! [X5276,X5277] :
( ~ is_fun_a_bool(X5276)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5276),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5277),bot_bot_fun_a_bool)))
| X5276 = bot_bot_fun_a_bool
| X5276 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5277),bot_bot_fun_a_bool) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_660_subset__singletonD])]) ).
fof(i_0_2077,plain,
! [X3796,X3797] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3797))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3796),X3797))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X3796)),hAPP_f957591787ol_nat(finite_card_int,X3797))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_78_card__mono])]) ).
fof(i_0_2078,plain,
! [X3794,X3795] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3795))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3794),X3795))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X3794)),hAPP_f22106695ol_nat(finite_card_nat,X3795))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_77_card__mono])]) ).
fof(i_0_2079,plain,
! [X3788,X3789] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3789))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3788),X3789))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X3788)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X3789))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_74_card__mono])]) ).
fof(i_0_2080,plain,
! [X3786,X3787] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3787))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3786),X3787))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X3786)),hAPP_f55526627ol_nat(finite1340463720e_bool,X3787))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_73_card__mono])]) ).
fof(i_0_2081,plain,
! [X3784,X3785] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3785))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3784),X3785))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X3784)),hAPP_f696928925ol_nat(finite346522414t_bool,X3785))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_72_card__mono])]) ).
fof(i_0_2082,plain,
! [X3782,X3783] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3783))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3782),X3783))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X3782)),hAPP_f521865025ol_nat(finite1876863882t_bool,X3783))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_71_card__mono])]) ).
fof(i_0_2083,plain,
! [X3792,X3793] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3793))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3792),X3793))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X3792)),hAPP_fun_a_bool_nat(finite_card_a,X3793))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_76_card__mono])]) ).
fof(i_0_2084,plain,
! [X3790,X3791] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3791))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3790),X3791))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X3790)),hAPP_f921600141ol_nat(finite_card_pname,X3791))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_75_card__mono])]) ).
fof(i_0_2085,plain,
! [X5030,X5031] :
( ~ is_fun_pname_bool(X5031)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5030),X5031))
| hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5030),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5031),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5030),bot_bo844097828e_bool))) = X5031 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_547_insert__Diff])]) ).
fof(i_0_2086,plain,
! [X5024,X5025] :
( ~ is_fun_a_bool(X5025)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5024),X5025))
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5024),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5025),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5024),bot_bot_fun_a_bool))) = X5025 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_544_insert__Diff])]) ).
fof(i_0_2087,plain,
! [X5278,X5279] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5278),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5279),bot_bot_fun_nat_bool)))
| X5278 = bot_bot_fun_nat_bool
| X5278 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5279),bot_bot_fun_nat_bool) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_661_subset__singletonD])]) ).
fof(i_0_2088,plain,
! [X5280,X5281] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5280),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5281),bot_bot_fun_int_bool)))
| X5280 = bot_bot_fun_int_bool
| X5280 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5281),bot_bot_fun_int_bool) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_662_subset__singletonD])]) ).
fof(i_0_2089,plain,
! [X6066,X6067,X6069,X6070,X6071] :
( ( X6066 = hAPP_nat_nat(suc,esk176_2(X6066,X6067))
| X6066 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6066),hAPP_nat_nat(suc,X6067))) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk176_2(X6066,X6067)),X6067))
| X6066 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6066),hAPP_nat_nat(suc,X6067))) )
& ( X6069 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6069),hAPP_nat_nat(suc,X6070))) )
& ( X6069 != hAPP_nat_nat(suc,X6071)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6071),X6070))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6069),hAPP_nat_nat(suc,X6070))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_948_less__Suc__eq__0__disj])])])])])]) ).
fof(i_0_2090,plain,
! [X5026,X5027] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5026),X5027))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5026),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5027),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5026),bot_bot_fun_int_bool))) = X5027 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_545_insert__Diff])]) ).
fof(i_0_2091,plain,
! [X5028,X5029] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5028),X5029))
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5028),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5029),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5028),bot_bot_fun_nat_bool))) = X5029 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_546_insert__Diff])]) ).
fof(i_0_2092,plain,
! [X5159,X5160,X5161,X5162] :
( ( X5159 = X5162
| X5159 = X5161
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5159),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5160),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5161),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5162),bot_bot_fun_a_bool))
| ~ is_a(X5159)
| ~ is_a(X5160)
| ~ is_a(X5161)
| ~ is_a(X5162) )
& ( X5160 = X5161
| X5159 = X5161
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5159),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5160),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5161),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5162),bot_bot_fun_a_bool))
| ~ is_a(X5159)
| ~ is_a(X5160)
| ~ is_a(X5161)
| ~ is_a(X5162) )
& ( X5159 = X5162
| X5160 = X5162
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5159),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5160),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5161),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5162),bot_bot_fun_a_bool))
| ~ is_a(X5159)
| ~ is_a(X5160)
| ~ is_a(X5161)
| ~ is_a(X5162) )
& ( X5160 = X5161
| X5160 = X5162
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5159),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5160),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5161),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5162),bot_bot_fun_a_bool))
| ~ is_a(X5159)
| ~ is_a(X5160)
| ~ is_a(X5161)
| ~ is_a(X5162) )
& ( X5159 != X5161
| X5160 != X5162
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5159),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5160),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5161),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5162),bot_bot_fun_a_bool))
| ~ is_a(X5159)
| ~ is_a(X5160)
| ~ is_a(X5161)
| ~ is_a(X5162) )
& ( X5159 != X5162
| X5160 != X5161
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5159),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5160),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5161),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5162),bot_bot_fun_a_bool))
| ~ is_a(X5159)
| ~ is_a(X5160)
| ~ is_a(X5161)
| ~ is_a(X5162) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_596_doubleton__eq__iff])])]) ).
fof(i_0_2093,plain,
! [X5109,X5110,X5111] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5110),X5111))
| hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5110),X5109)),X5111) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5109),X5111) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5110),X5111))
| hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5110),X5109)),X5111) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5110),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5109),X5111)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1496])]) ).
fof(i_0_2094,plain,
! [X5112,X5113,X5114] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5113),X5114))
| hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5113),X5112)),X5114) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5112),X5114) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5113),X5114))
| hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5113),X5112)),X5114) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5113),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5112),X5114)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1497])]) ).
fof(i_0_2095,plain,
! [X5115,X5116,X5117] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5116),X5117))
| hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5116),X5115)),X5117) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5115),X5117) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5116),X5117))
| hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5116),X5115)),X5117) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5116),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5115),X5117)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1498])]) ).
fof(i_0_2096,plain,
! [X5106,X5107,X5108] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5107),X5108))
| hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5107),X5106)),X5108) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5106),X5108) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5107),X5108))
| hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5107),X5106)),X5108) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5107),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5106),X5108)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1499])]) ).
fof(i_0_2097,plain,
! [X5141,X5142] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5141),X5142)),X5141)),
inference(variable_rename,[status(thm)],[fact_587_Diff__subset]) ).
fof(i_0_2098,plain,
! [X5139,X5140] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5139),X5140)),X5139)),
inference(variable_rename,[status(thm)],[fact_586_Diff__subset]) ).
fof(i_0_2099,plain,
! [X5143,X5144] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5143),X5144)),X5143)),
inference(variable_rename,[status(thm)],[fact_588_Diff__subset]) ).
fof(i_0_2100,plain,
! [X4000,X4001] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X4000),X4001)),X4000)),
inference(variable_rename,[status(thm)],[fact_179_diff__le__self]) ).
fof(i_0_2101,plain,
! [X6259,X6260,X6261] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6259),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6260),X6261)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6259),X6260)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6259),X6261)),
inference(variable_rename,[status(thm)],[fact_1027_zadd__zmult__distrib2]) ).
fof(i_0_2102,plain,
! [X6256,X6257,X6258] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6256),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6257),X6258)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6256),X6257)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6256),X6258)),
inference(variable_rename,[status(thm)],[fact_1026_zdiff__zmult__distrib2]) ).
fof(i_0_2103,plain,
! [X6159,X6160,X6161] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6159),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6160),X6161)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6159),X6160)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6159),X6161)),
inference(variable_rename,[status(thm)],[fact_985_add__mult__distrib2]) ).
fof(i_0_2104,plain,
! [X6177,X6178,X6179] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6177),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6178),X6179)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6177),X6178)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6177),X6179)),
inference(variable_rename,[status(thm)],[fact_992_diff__mult__distrib2]) ).
fof(i_0_2105,plain,
! [X3898,X3899,X3900] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3898),X3899)),X3900) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3898),X3900)),X3899),
inference(variable_rename,[status(thm)],[fact_131_diff__commute]) ).
fof(i_0_2106,plain,
! [X4891,X4892] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk76_2(X4891,X4892)),X4892))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4892),X4891)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk76_2(X4891,X4892)),X4891))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4892),X4891)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_478_subsetI])])])]) ).
fof(i_0_2107,plain,
! [X4888,X4889] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk75_2(X4888,X4889)),X4889))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4889),X4888)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk75_2(X4888,X4889)),X4888))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4889),X4888)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_477_subsetI])])])]) ).
fof(i_0_2108,plain,
! [X4897,X4898] :
( ( is_pname(esk78_2(X4897,X4898))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4898),X4897)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk78_2(X4897,X4898)),X4898))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4898),X4897)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk78_2(X4897,X4898)),X4897))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4898),X4897)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_480_subsetI])])])]) ).
fof(i_0_2109,plain,
! [X4894,X4895] :
( ( is_a(esk77_2(X4894,X4895))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4895),X4894)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk77_2(X4894,X4895)),X4895))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4895),X4894)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk77_2(X4894,X4895)),X4894))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4895),X4894)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_479_subsetI])])])]) ).
fof(i_0_2110,plain,
! [X3989,X3990,X3991] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3991),X3990) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3989),X3990)
| X3991 = X3989
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3990),X3989))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3990),X3991)) )
& ( X3991 != X3989
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3991),X3990) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3989),X3990)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3990),X3989))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3990),X3991)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_175_eq__diff__iff])])]) ).
fof(i_0_2111,plain,
! [X5061,X5062,X5063] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5061),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5062),X5063)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5061),X5063)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5062),bot_bot_fun_int_bool)),
inference(variable_rename,[status(thm)],[fact_560_Diff__insert]) ).
fof(i_0_2112,plain,
! [X5058,X5059,X5060] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5058),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5059),X5060)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5058),X5060)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5059),bot_bot_fun_nat_bool)),
inference(variable_rename,[status(thm)],[fact_559_Diff__insert]) ).
fof(i_0_2113,plain,
! [X5055,X5056,X5057] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5055),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5056),X5057)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5055),X5057)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5056),bot_bot_fun_a_bool)),
inference(variable_rename,[status(thm)],[fact_558_Diff__insert]) ).
fof(i_0_2114,plain,
! [X5124,X5125,X5126] :
( ~ is_fun_a_bool(X5125)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5125),X5126))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5126),X5124))
| hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5126),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5124),X5125)) = X5125 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_582_double__diff])]) ).
fof(i_0_2115,plain,
! [X6139,X6140] :
( ( hBOOL(hAPP_nat_bool(X6140,esk186_2(X6139,X6140)))
| hBOOL(hAPP_nat_bool(X6140,X6139))
| ~ hBOOL(hAPP_nat_bool(X6140,zero_zero_nat)) )
& ( ~ hBOOL(hAPP_nat_bool(X6140,hAPP_nat_nat(suc,esk186_2(X6139,X6140))))
| hBOOL(hAPP_nat_bool(X6140,X6139))
| ~ hBOOL(hAPP_nat_bool(X6140,zero_zero_nat)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_976_nat__induct])])])]) ).
fof(i_0_2116,plain,
! [X5302,X5303] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5303))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5303),X5302))
| hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5302),X5303)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,X5302)),hAPP_f957591787ol_nat(finite_card_int,X5303)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_670_card__Diff__subset])]) ).
fof(i_0_2117,plain,
! [X5304,X5305] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5305))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5305),X5304))
| hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5304),X5305)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,X5304)),hAPP_f22106695ol_nat(finite_card_nat,X5305)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_671_card__Diff__subset])]) ).
fof(i_0_2118,plain,
! [X5306,X5307] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5307))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5307),X5306))
| hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5306),X5307)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,X5306)),hAPP_fun_a_bool_nat(finite_card_a,X5307)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_672_card__Diff__subset])]) ).
fof(i_0_2119,plain,
! [X5308,X5309] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5309))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5309),X5308))
| hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5308),X5309)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,X5308)),hAPP_f921600141ol_nat(finite_card_pname,X5309)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_673_card__Diff__subset])]) ).
fof(i_0_2120,plain,
! [X5177,X5178] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5177),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5178),bot_bo844097828e_bool)))
| X5177 = X5178
| ~ is_pname(X5177)
| ~ is_pname(X5178) )
& ( X5177 != X5178
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5177),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5178),bot_bo844097828e_bool)))
| ~ is_pname(X5177)
| ~ is_pname(X5178) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_602_singleton__iff])])]) ).
fof(i_0_2121,plain,
! [X5157,X5158] :
( ~ is_pname(X5157)
| ~ is_pname(X5158)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5157),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5158),bot_bo844097828e_bool)))
| X5157 = X5158 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_595_singletonE])]) ).
fof(i_0_2122,plain,
! [X5171,X5172] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5171),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5172),bot_bot_fun_a_bool)))
| X5171 = X5172
| ~ is_a(X5171)
| ~ is_a(X5172) )
& ( X5171 != X5172
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5171),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5172),bot_bot_fun_a_bool)))
| ~ is_a(X5171)
| ~ is_a(X5172) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_599_singleton__iff])])]) ).
fof(i_0_2123,plain,
! [X5151,X5152] :
( ~ is_a(X5151)
| ~ is_a(X5152)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5151),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5152),bot_bot_fun_a_bool)))
| X5151 = X5152 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_592_singletonE])]) ).
fof(i_0_2124,plain,
! [X4741,X4742,X4743] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4742),X4743))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X4741,X4742)),image_nat_int(X4741,X4743))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_433_imageI])]) ).
fof(i_0_2125,plain,
! [X4874,X4875,X4876] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4875),X4876))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X4874,X4875)),image_nat_int(X4874,X4876))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_473_image__mono])]) ).
fof(i_0_2126,plain,
! [X4877,X4878,X4879] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4878),X4879))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X4877,X4878)),image_pname_a(X4877,X4879))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_474_image__mono])]) ).
fof(i_0_2127,plain,
! [X4744,X4745,X4746] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4745),X4746))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X4744,X4745)),image_pname_a(X4744,X4746))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_434_imageI])]) ).
fof(i_0_2128,plain,
! [X4793,X4794,X4795] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4794),X4795))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X4794,X4793)),hAPP_nat_bool(X4795,X4793))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_448_le__funE])]) ).
fof(i_0_2129,plain,
! [X4784,X4785,X4786] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4785),X4786))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X4785,X4784)),hAPP_nat_bool(X4786,X4784))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_445_le__funD])]) ).
fof(i_0_2130,plain,
! [X4790,X4791,X4792] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4791),X4792))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X4791,X4790)),hAPP_int_bool(X4792,X4790))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_447_le__funE])]) ).
fof(i_0_2131,plain,
! [X4781,X4782,X4783] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4782),X4783))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X4782,X4781)),hAPP_int_bool(X4783,X4781))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_444_le__funD])]) ).
fof(i_0_2132,plain,
! [X4796,X4797,X4798] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4797),X4798))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X4797,X4796)),hAPP_a_bool(X4798,X4796))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_449_le__funE])]) ).
fof(i_0_2133,plain,
! [X4787,X4788,X4789] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4788),X4789))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X4788,X4787)),hAPP_a_bool(X4789,X4787))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_446_le__funD])]) ).
fof(i_0_2134,plain,
! [X5625,X5626,X5627,X5628] :
( ~ is_fun_pname_bool(X5625)
| ~ hBOOL(finite89670078_pname(X5627,X5628))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5626))
| X5625 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5625),X5626))
| hAPP_pname_pname(hAPP_p1170154830_pname(X5627,hAPP_f1297739591_pname(X5628,X5625)),hAPP_f1297739591_pname(X5628,X5626)) = hAPP_f1297739591_pname(X5628,X5626) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_773_folding__one__idem_Osubset__idem])]) ).
fof(i_0_2135,plain,
! [X5629,X5630,X5631,X5632] :
( ~ is_fun_a_bool(X5629)
| ~ hBOOL(finite1819937229idem_a(X5631,X5632))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5630))
| X5629 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5629),X5630))
| hAPP_a_a(hAPP_a_fun_a_a(X5631,hAPP_fun_a_bool_a(X5632,X5629)),hAPP_fun_a_bool_a(X5632,X5630)) = hAPP_fun_a_bool_a(X5632,X5630) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_774_folding__one__idem_Osubset__idem])]) ).
fof(i_0_2136,plain,
! [X5118,X5119,X5120] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5119),X5120))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5120),X5118))
| hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5120),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5118),X5119)) = X5119 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_580_double__diff])]) ).
fof(i_0_2137,plain,
! [X5121,X5122,X5123] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5122),X5123))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5123),X5121))
| hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5123),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5121),X5122)) = X5122 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_581_double__diff])]) ).
fof(i_0_2138,plain,
! [X5621,X5622,X5623,X5624] :
( ~ hBOOL(finite795500164em_nat(X5623,X5624))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5622))
| X5621 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5621),X5622))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(X5623,hAPP_f22106695ol_nat(X5624,X5621)),hAPP_f22106695ol_nat(X5624,X5622)) = hAPP_f22106695ol_nat(X5624,X5622) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_772_folding__one__idem_Osubset__idem])]) ).
fof(i_0_2139,plain,
! [X5617,X5618,X5619,X5620] :
( ~ hBOOL(finite1432773856em_int(X5619,X5620))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5618))
| X5617 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5617),X5618))
| hAPP_int_int(hAPP_int_fun_int_int(X5619,hAPP_f1594865479ol_int(X5620,X5617)),hAPP_f1594865479ol_int(X5620,X5618)) = hAPP_f1594865479ol_int(X5620,X5618) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_771_folding__one__idem_Osubset__idem])]) ).
fof(i_0_2140,plain,
! [X5905,X5906] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X5905)),X5906))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5905),X5906)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_874_Suc__lessD])]) ).
fof(i_0_2141,plain,
! [X5991,X5992] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X5991)),X5992))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5991),X5992)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_907_Suc__le__lessD])]) ).
fof(i_0_2142,plain,
! [X5983,X5984] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X5983)),X5984))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5983),X5984)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5983),X5984))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X5983)),X5984)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_903_Suc__le__eq])]) ).
fof(i_0_2143,plain,
! [X5979,X5980] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5979),X5980))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X5979)),X5980)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X5979)),X5980))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5979),X5980)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_901_less__eq__Suc__le])]) ).
fof(i_0_2144,plain,
! [X3965,X3966] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X3965)),X3966))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3965),X3966)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_164_Suc__leD])]) ).
fof(i_0_2145,plain,
! [X4640,X4641,X4642] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4641),X4642))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4641),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4640),X4642))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_395_insertI2])]) ).
fof(i_0_2146,plain,
! [X4392,X4393,X4394] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4393),X4394))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4393),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4392),X4394))) )
& ( X4393 != X4392
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4393),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4392),X4394))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1500])])]) ).
fof(i_0_2147,plain,
! [X4835,X4836,X4837] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4836),X4837))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4836),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4835),X4837))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_463_subset__insertI2])]) ).
fof(i_0_2148,plain,
! [X4637,X4638,X4639] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4638),X4639))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4638),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4637),X4639))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_394_insertI2])]) ).
fof(i_0_2149,plain,
! [X4389,X4390,X4391] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4390),X4391))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4390),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4389),X4391))) )
& ( X4390 != X4389
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4390),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4389),X4391))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1501])])]) ).
fof(i_0_2150,plain,
! [X4832,X4833,X4834] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4833),X4834))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4833),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4832),X4834))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_462_subset__insertI2])]) ).
fof(i_0_2151,plain,
! [X4643,X4644,X4645] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4644),X4645))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4644),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4643),X4645))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_396_insertI2])]) ).
fof(i_0_2152,plain,
! [X4395,X4396,X4397] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4396),X4397))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4396),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4395),X4397))) )
& ( X4396 != X4395
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4396),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4395),X4397))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1502])])]) ).
fof(i_0_2153,plain,
! [X4829,X4830,X4831] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4830),X4831))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4830),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4829),X4831))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_461_subset__insertI2])]) ).
fof(i_0_2154,plain,
! [X4634,X4635,X4636] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4635),X4636))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4635),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4634),X4636))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_393_insertI2])]) ).
fof(i_0_2155,plain,
! [X4386,X4387,X4388] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4387),X4388))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4387),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4386),X4388))) )
& ( X4387 != X4386
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4387),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4386),X4388))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1503])])]) ).
fof(i_0_2156,plain,
! [X5936,X5937,X5938] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5937),X5938))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5937),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5938),X5936))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_885_termination__basic__simps_I1_J])]) ).
fof(i_0_2157,plain,
! [X5916,X5917,X5918] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5917),X5918))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5917),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5918),X5916))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_879_trans__less__add1])]) ).
fof(i_0_2158,plain,
! [X5939,X5940,X5941] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5940),X5941))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5940),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5939),X5941))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_886_termination__basic__simps_I2_J])]) ).
fof(i_0_2159,plain,
! [X5919,X5920,X5921] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5920),X5921))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5920),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5919),X5921))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_880_trans__less__add2])]) ).
fof(i_0_2160,plain,
! [X5866,X5867,X5868] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5867),X5868))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5867),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5868),X5866))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_854_termination__basic__simps_I3_J])]) ).
fof(i_0_2161,plain,
! [X5789,X5790,X5791] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5790),X5791))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5790),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5791),X5789))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_826_trans__le__add1])]) ).
fof(i_0_2162,plain,
! [X5863,X5864,X5865] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5864),X5865))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5864),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5863),X5865))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_853_termination__basic__simps_I4_J])]) ).
fof(i_0_2163,plain,
! [X5792,X5793,X5794] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5793),X5794))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5793),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5792),X5794))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_827_trans__le__add2])]) ).
fof(i_0_2164,plain,
! [X5090,X5091] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5090),X5091)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5090))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5091)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5090))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5090),X5091)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5091)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_570_finite__Diff2])])]) ).
fof(i_0_2165,plain,
! [X5088,X5089] :
( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5088),X5089)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5088))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5089)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5088))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5088),X5089)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5089)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_569_finite__Diff2])])]) ).
fof(i_0_2166,plain,
! [X5092,X5093] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5092),X5093)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5092))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5093)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5092))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5092),X5093)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5093)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_571_finite__Diff2])])]) ).
fof(i_0_2167,plain,
! [X5175,X5176] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5175),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5176),bot_bot_fun_nat_bool)))
| X5175 = X5176 )
& ( X5175 != X5176
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5175),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5176),bot_bot_fun_nat_bool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_601_singleton__iff])]) ).
fof(i_0_2168,plain,
! [X5155,X5156] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5155),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5156),bot_bot_fun_nat_bool)))
| X5155 = X5156 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_594_singletonE])]) ).
fof(i_0_2169,plain,
! [X5173,X5174] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5173),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5174),bot_bot_fun_int_bool)))
| X5173 = X5174 )
& ( X5173 != X5174
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5173),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5174),bot_bot_fun_int_bool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_600_singleton__iff])]) ).
fof(i_0_2170,plain,
! [X5153,X5154] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5153),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5154),bot_bot_fun_int_bool)))
| X5153 = X5154 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_593_singletonE])]) ).
fof(i_0_2171,plain,
! [X5097,X5098,X5099] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5098),X5099))
| hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5098),X5097)),X5099) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5097),X5099) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_573_insert__Diff1])]) ).
fof(i_0_2172,plain,
! [X5100,X5101,X5102] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5101),X5102))
| hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5101),X5100)),X5102) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5100),X5102) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_574_insert__Diff1])]) ).
fof(i_0_2173,plain,
! [X5103,X5104,X5105] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5104),X5105))
| hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5104),X5103)),X5105) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X5103),X5105) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_575_insert__Diff1])]) ).
fof(i_0_2174,plain,
! [X5094,X5095,X5096] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5095),X5096))
| hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5095),X5094)),X5096) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5094),X5096) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_572_insert__Diff1])]) ).
fof(i_0_2175,plain,
! [X5167,X5168,X5169,X5170] :
( ( X5167 = X5170
| X5167 = X5169
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5167),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5168),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5169),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5170),bot_bot_fun_int_bool)) )
& ( X5168 = X5169
| X5167 = X5169
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5167),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5168),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5169),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5170),bot_bot_fun_int_bool)) )
& ( X5167 = X5170
| X5168 = X5170
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5167),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5168),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5169),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5170),bot_bot_fun_int_bool)) )
& ( X5168 = X5169
| X5168 = X5170
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5167),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5168),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5169),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5170),bot_bot_fun_int_bool)) )
& ( X5167 != X5169
| X5168 != X5170
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5167),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5168),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5169),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5170),bot_bot_fun_int_bool)) )
& ( X5167 != X5170
| X5168 != X5169
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5167),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5168),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5169),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5170),bot_bot_fun_int_bool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_598_doubleton__eq__iff])])]) ).
fof(i_0_2176,plain,
! [X5163,X5164,X5165,X5166] :
( ( X5163 = X5166
| X5163 = X5165
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5163),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5164),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5165),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5166),bot_bot_fun_nat_bool)) )
& ( X5164 = X5165
| X5163 = X5165
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5163),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5164),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5165),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5166),bot_bot_fun_nat_bool)) )
& ( X5163 = X5166
| X5164 = X5166
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5163),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5164),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5165),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5166),bot_bot_fun_nat_bool)) )
& ( X5164 = X5165
| X5164 = X5166
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5163),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5164),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5165),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5166),bot_bot_fun_nat_bool)) )
& ( X5163 != X5165
| X5164 != X5166
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5163),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5164),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5165),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5166),bot_bot_fun_nat_bool)) )
& ( X5163 != X5166
| X5164 != X5165
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5163),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5164),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5165),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5166),bot_bot_fun_nat_bool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_597_doubleton__eq__iff])])]) ).
cnf(i_0_2177,plain,
number_number_of_nat(bit1(pls)) = hAPP_nat_nat(suc,zero_zero_nat),
inference(split_conjunct,[status(thm)],[fact_1170_numeral__1__eq__Suc__0]) ).
fof(i_0_2178,plain,
! [X5038,X5039] :
( ~ is_fun_pname_bool(X5039)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5038),X5039))
| hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5038),X5039)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5038),bot_bo844097828e_bool)) = X5039 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1504])]) ).
fof(i_0_2179,plain,
! [X5032,X5033] :
( ~ is_fun_a_bool(X5033)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5032),X5033))
| hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5032),X5033)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5032),bot_bot_fun_a_bool)) = X5033 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1505])]) ).
fof(i_0_2180,plain,
! [X5870,X5871] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5870),X5871))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X5870)),hAPP_nat_nat(suc,X5871))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_856_Suc__mono])]) ).
fof(i_0_2181,plain,
! [X6519,X6520,X6522,X6523,X6524] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6519),X6520))
| X6520 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6519),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,esk209_2(X6519,X6520)))) )
& ( X6523 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6522),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X6524)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6522),X6523)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1123_zless__iff__Suc__zadd])])])])]) ).
fof(i_0_2182,plain,
! [X5577,X5578,X5579,X5580] :
( ~ is_fun_pname_bool(X5578)
| ~ hBOOL(finite1282449217_pname(X5579,X5580))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5578))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5577),X5578))
| X5578 = bot_bo844097828e_bool
| hAPP_f1297739591_pname(X5580,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5577),X5578)) = hAPP_pname_pname(hAPP_p1170154830_pname(X5579,X5577),hAPP_f1297739591_pname(X5580,X5578)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1506])]) ).
fof(i_0_2183,plain,
! [X5565,X5566,X5567,X5568] :
( ~ is_fun_a_bool(X5566)
| ~ hBOOL(finite_folding_one_a(X5567,X5568))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5566))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5565),X5566))
| X5566 = bot_bot_fun_a_bool
| hAPP_fun_a_bool_a(X5568,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5565),X5566)) = hAPP_a_a(hAPP_a_fun_a_a(X5567,X5565),hAPP_fun_a_bool_a(X5568,X5566)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1507])]) ).
fof(i_0_2184,plain,
! [X5034,X5035] :
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5034),X5035))
| hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5034),X5035)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5034),bot_bot_fun_int_bool)) = X5035 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1508])]) ).
fof(i_0_2185,plain,
! [X5036,X5037] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5036),X5037))
| hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5036),X5037)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5036),bot_bot_fun_nat_bool)) = X5037 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1509])]) ).
fof(i_0_2186,plain,
! [X6123,X6124,X6126] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk180_2(X6123,X6124)),X6123))
| ~ hBOOL(hAPP_nat_bool(X6124,X6123))
| hBOOL(hAPP_nat_bool(X6124,zero_zero_nat)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6126),esk180_2(X6123,X6124)))
| ~ hBOOL(hAPP_nat_bool(X6124,X6126))
| ~ hBOOL(hAPP_nat_bool(X6124,X6123))
| hBOOL(hAPP_nat_bool(X6124,zero_zero_nat)) )
& ( hBOOL(hAPP_nat_bool(X6124,esk180_2(X6123,X6124)))
| ~ hBOOL(hAPP_nat_bool(X6124,X6123))
| hBOOL(hAPP_nat_bool(X6124,zero_zero_nat)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1510])])])])]) ).
cnf(i_0_2187,plain,
number_number_of_nat(bit1(pls)) = one_one_nat,
inference(split_conjunct,[status(thm)],[fact_1174_nat__numeral__1__eq__1]) ).
cnf(i_0_2188,plain,
one_one_nat = number_number_of_nat(bit1(pls)),
inference(split_conjunct,[status(thm)],[fact_1173_Numeral1__eq1__nat]) ).
fof(i_0_2189,plain,
! [X5573,X5574,X5575,X5576] :
( ~ hBOOL(finite988810631ne_nat(X5575,X5576))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5574))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5573),X5574))
| X5574 = bot_bot_fun_nat_bool
| hAPP_f22106695ol_nat(X5576,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5573),X5574)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X5575,X5573),hAPP_f22106695ol_nat(X5576,X5574)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1511])]) ).
fof(i_0_2190,plain,
! [X5569,X5570,X5571,X5572] :
( ~ hBOOL(finite1626084323ne_int(X5571,X5572))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5570))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5569),X5570))
| X5570 = bot_bot_fun_int_bool
| hAPP_f1594865479ol_int(X5572,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5569),X5570)) = hAPP_int_int(hAPP_int_fun_int_int(X5571,X5569),hAPP_f1594865479ol_int(X5572,X5570)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1512])]) ).
fof(i_0_2191,plain,
! [X4619,X4620,X4621] :
( ( ~ hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4619),X4620),X4621))
| X4619 = X4621
| hBOOL(hAPP_a_bool(X4620,X4621))
| ~ is_a(X4619)
| ~ is_a(X4621) )
& ( X4619 != X4621
| hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4619),X4620),X4621))
| ~ is_a(X4619)
| ~ is_a(X4621) )
& ( ~ hBOOL(hAPP_a_bool(X4620,X4621))
| hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4619),X4620),X4621))
| ~ is_a(X4619)
| ~ is_a(X4621) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_388_insert__code])])]) ).
cnf(i_0_2192,plain,
( hBOOL(hAPP_int_bool(X1,esk191_2(X2,X1)))
| hBOOL(hAPP_int_bool(X2,esk191_2(X2,X1)))
| collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X1)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1494]) ).
fof(i_0_2193,plain,
! [X4690,X4691,X4692] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4691),X4692))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4692),X4690))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4691),X4690)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_418_set__rev__mp])]) ).
fof(i_0_2194,plain,
! [X4702,X4703,X4704] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4703),X4704))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4702),X4703))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4702),X4704)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_422_set__mp])]) ).
fof(i_0_2195,plain,
! [X4678,X4679,X4680] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4679),X4680))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4678),X4679))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4678),X4680)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_414_in__mono])]) ).
fof(i_0_2196,plain,
! [X4377,X4378,X4379] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4378),X4379))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4377),X4378))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4377),X4379)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_288_subsetD])]) ).
fof(i_0_2197,plain,
! [X4714,X4715,X4716] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4715),X4716))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4716),X4714))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4715),X4714)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_426_subset__trans])]) ).
fof(i_0_2198,plain,
! [X4529,X4530,X4531] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4530),X4531))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4531),X4529))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4530),X4529)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_349_order__trans])]) ).
fof(i_0_2199,plain,
! [X4554,X4555,X4556] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4555),X4556))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4554),X4555))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4554),X4556)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_359_xt1_I6_J])]) ).
fof(i_0_2200,plain,
! [X4687,X4688,X4689] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4688),X4689))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4689),X4687))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4688),X4687)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_417_set__rev__mp])]) ).
fof(i_0_2201,plain,
! [X4699,X4700,X4701] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4700),X4701))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4699),X4700))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4699),X4701)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_421_set__mp])]) ).
fof(i_0_2202,plain,
! [X4675,X4676,X4677] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4676),X4677))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4675),X4676))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4675),X4677)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_413_in__mono])]) ).
fof(i_0_2203,plain,
! [X4374,X4375,X4376] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4375),X4376))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4374),X4375))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4374),X4376)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_287_subsetD])]) ).
fof(i_0_2204,plain,
! [X4711,X4712,X4713] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4712),X4713))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4713),X4711))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4712),X4711)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_425_subset__trans])]) ).
fof(i_0_2205,plain,
! [X4526,X4527,X4528] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4527),X4528))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4528),X4526))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4527),X4526)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_348_order__trans])]) ).
fof(i_0_2206,plain,
! [X4551,X4552,X4553] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4552),X4553))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4551),X4552))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4551),X4553)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_358_xt1_I6_J])]) ).
fof(i_0_2207,plain,
! [X4696,X4697,X4698] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4697),X4698))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4698),X4696))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4697),X4696)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_420_set__rev__mp])]) ).
fof(i_0_2208,plain,
! [X4708,X4709,X4710] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4709),X4710))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4708),X4709))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4708),X4710)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_424_set__mp])]) ).
fof(i_0_2209,plain,
! [X4684,X4685,X4686] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4685),X4686))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4684),X4685))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4684),X4686)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_416_in__mono])]) ).
fof(i_0_2210,plain,
! [X4383,X4384,X4385] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4384),X4385))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4383),X4384))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4383),X4385)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_290_subsetD])]) ).
fof(i_0_2211,plain,
! [X4717,X4718,X4719] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4718),X4719))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4719),X4717))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4718),X4717)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_427_subset__trans])]) ).
fof(i_0_2212,plain,
! [X4538,X4539,X4540] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4539),X4540))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4540),X4538))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4539),X4538)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_352_order__trans])]) ).
fof(i_0_2213,plain,
! [X4563,X4564,X4565] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4564),X4565))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4563),X4564))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4563),X4565)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_362_xt1_I6_J])]) ).
fof(i_0_2214,plain,
! [X4693,X4694,X4695] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4694),X4695))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4695),X4693))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4694),X4693)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_419_set__rev__mp])]) ).
fof(i_0_2215,plain,
! [X4705,X4706,X4707] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4706),X4707))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4705),X4706))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4705),X4707)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_423_set__mp])]) ).
fof(i_0_2216,plain,
! [X4681,X4682,X4683] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4682),X4683))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4681),X4682))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4681),X4683)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_415_in__mono])]) ).
fof(i_0_2217,plain,
! [X4380,X4381,X4382] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4381),X4382))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4380),X4381))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4380),X4382)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_289_subsetD])]) ).
fof(i_0_2218,plain,
! [X4535,X4536,X4537] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4536),X4537))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4537),X4535))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4536),X4535)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_351_order__trans])]) ).
fof(i_0_2219,plain,
! [X3890,X3891,X3892] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3891),X3892))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3892),X3890))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3891),X3890)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_127_le__trans])]) ).
fof(i_0_2220,plain,
! [X4560,X4561,X4562] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4561),X4562))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4560),X4561))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4560),X4562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_361_xt1_I6_J])]) ).
fof(i_0_2221,plain,
! [X6294,X6295,X6296] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6295),X6296))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6296),X6294))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6295),X6294)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1046_zle__trans])]) ).
fof(i_0_2222,plain,
! [X4532,X4533,X4534] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4533),X4534))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4534),X4532))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4533),X4532)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_350_order__trans])]) ).
fof(i_0_2223,plain,
! [X4557,X4558,X4559] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4558),X4559))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4557),X4558))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4557),X4559)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_360_xt1_I6_J])]) ).
fof(i_0_2224,plain,
! [X5989,X5990] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5990),hAPP_nat_nat(suc,X5989)))
| X5990 = X5989
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5989),X5990)) )
& ( X5990 != X5989
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5990),hAPP_nat_nat(suc,X5989)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5989),X5990)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_906_le__less__Suc__eq])])]) ).
fof(i_0_2225,plain,
! [X5929,X5930,X5931,X5932] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5931),X5932))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5929),X5932) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5931),X5930)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5929),X5930)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_883_less__add__eq__less])]) ).
fof(i_0_2226,plain,
! [X4926,X4927,X4928,X4929] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4926),X4927))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4928),X4929))
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X4926),X4927) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X4928),X4929) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4928),X4929))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4926),X4927))
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X4926),X4927) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X4928),X4929) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_488_diff__eq__diff__less__eq])])]) ).
fof(i_0_2227,plain,
! [X5886,X5887] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5886),X5887))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5887),hAPP_nat_nat(suc,X5886))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5887),hAPP_nat_nat(suc,X5886)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5886),X5887)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1513])]) ).
fof(i_0_2228,plain,
! [X6278] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6278))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X6278))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1038_le__imp__0__less])]) ).
fof(i_0_2229,plain,
! [X5960,X5962,X5963,X5964] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5960))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5962),X5960))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5962),esk163_1(X5960))) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk164_2(X5963,X5964)),X5963))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5963)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk164_2(X5963,X5964)),X5964))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5963)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_895_finite__nat__set__iff__bounded])])])])])]) ).
fof(i_0_2230,plain,
! [X4917,X4919,X4920,X4921] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4917))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4919),X4917))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4919),esk84_1(X4917))) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk85_2(X4920,X4921)),X4920))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4920)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk85_2(X4920,X4921)),X4921))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4920)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_486_finite__nat__set__iff__bounded__le])])])])])]) ).
fof(i_0_2231,plain,
! [X6019,X6020] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk170_2(X6019,X6020)),X6020))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6020)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk170_2(X6019,X6020)),X6019))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6020)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_917_bounded__nat__set__is__finite])])])]) ).
fof(i_0_2232,plain,
! [X6526,X6527] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6526),X6527))
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X6527)),hAPP_nat_int(semiri1621563631at_int,X6526)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6527),X6526)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1125_zdiff__int])]) ).
fof(i_0_2233,plain,
! [X4761,X4762] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4761),X4762) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X4761)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X4762))),
inference(variable_rename,[status(thm)],[fact_440_insert__compr__raw]) ).
fof(i_0_2234,plain,
! [X4584,X4585] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4584),X4585) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X4584)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X4585))),
inference(variable_rename,[status(thm)],[fact_372_insert__compr]) ).
fof(i_0_2235,plain,
! [X4755,X4756] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4755),X4756) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X4755)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X4756))),
inference(variable_rename,[status(thm)],[fact_437_insert__compr__raw]) ).
fof(i_0_2236,plain,
! [X4578,X4579] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4578),X4579) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X4578)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X4579))),
inference(variable_rename,[status(thm)],[fact_369_insert__compr]) ).
fof(i_0_2237,plain,
! [X4414,X4415] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X4414)),X4415))
| X4415 = hAPP_nat_nat(suc,esk65_2(X4414,X4415)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_300_Suc__le__D])])]) ).
fof(i_0_2238,plain,
! [X5898,X5899] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5898),X5899))
| hAPP_nat_nat(suc,X5898) = X5899
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X5898)),X5899)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_871_Suc__lessI])]) ).
fof(i_0_2239,plain,
! [X5841,X5842] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5841),X5842))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5842),X5841)),X5841) = X5842 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_844_le__add__diff__inverse2])]) ).
fof(i_0_2240,plain,
! [X6512,X6514,X6515,X6517] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk207_1(X6512)))
| hBOOL(hAPP_int_bool(X6512,hAPP_nat_int(semiri1621563631at_int,X6514))) )
& ( ~ hBOOL(hAPP_int_bool(X6512,esk207_1(X6512)))
| hBOOL(hAPP_int_bool(X6512,hAPP_nat_int(semiri1621563631at_int,X6514))) )
& ( ~ hBOOL(hAPP_int_bool(X6515,hAPP_nat_int(semiri1621563631at_int,esk208_1(X6515))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6517))
| hBOOL(hAPP_int_bool(X6515,X6517)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1120_transfer__int__nat__quantifiers_I1_J])])])])])]) ).
cnf(i_0_2241,plain,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X2))))),
inference(split_conjunct,[status(thm)],[i_0_1514]) ).
fof(i_0_2242,plain,
! [X3919,X3920] :
( ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X3919),X3920)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3920)) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3920))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X3919),X3920))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_141_finite__insert])]) ).
fof(i_0_2243,plain,
! [X3917,X3918] :
( ( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X3917),X3918)))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3918)) )
& ( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3918))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X3917),X3918))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_140_finite__insert])]) ).
fof(i_0_2244,plain,
! [X3921,X3922] :
( ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X3921),X3922)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3922)) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3922))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X3921),X3922))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_142_finite__insert])]) ).
fof(i_0_2245,plain,
! [X3923,X3924] :
( ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X3923),X3924)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3924)) )
& ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3924))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X3923),X3924))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_143_finite__insert])]) ).
cnf(i_0_2246,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1515]) ).
cnf(i_0_2247,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X2),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1515]) ).
fof(i_0_2248,plain,
! [X3927,X3928] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3927),X3928)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3928)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3928))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3927),X3928))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_145_finite__insert])]) ).
cnf(i_0_2249,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1516]) ).
cnf(i_0_2250,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X2),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1516]) ).
fof(i_0_2251,plain,
! [X3929,X3930] :
( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3929),X3930)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3930)) )
& ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3930))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3929),X3930))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_146_finite__insert])]) ).
fof(i_0_2252,plain,
! [X3925,X3926] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3925),X3926)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3926)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3926))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3925),X3926))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_144_finite__insert])]) ).
fof(i_0_2253,plain,
! [X3931,X3932] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3931),X3932)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3932)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3932))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3931),X3932))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_147_finite__insert])]) ).
fof(i_0_2254,plain,
! [X5818,X5819,X5820] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5818),X5819)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5818),X5820)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5819),X5820),
inference(variable_rename,[status(thm)],[fact_836_diff__cancel]) ).
fof(i_0_2255,plain,
! [X5821,X5822,X5823] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5821),X5822)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5823),X5822)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5821),X5823),
inference(variable_rename,[status(thm)],[fact_837_diff__cancel2]) ).
fof(i_0_2256,plain,
! [X6248,X6249,X6250] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6248),X6249)),X6250) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6248),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6249),X6250)),
inference(variable_rename,[status(thm)],[fact_1023_zmult__assoc]) ).
fof(i_0_2257,plain,
! [X6283,X6284,X6285] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6283),X6284)),X6285) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6283),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6284),X6285)),
inference(variable_rename,[status(thm)],[fact_1041_zadd__assoc]) ).
fof(i_0_2258,plain,
! [X5672,X5673,X5674] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5672),X5673)),X5674) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5672),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5673),X5674)),
inference(variable_rename,[status(thm)],[fact_786_ab__semigroup__add__class_Oadd__ac_I1_J]) ).
fof(i_0_2259,plain,
! [X6237,X6238,X6239] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6237),X6238)),X6239) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6237),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6238),X6239)),
inference(variable_rename,[status(thm)],[fact_1017_nat__mult__assoc]) ).
fof(i_0_2260,plain,
! [X5713,X5714,X5715] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5713),X5714)),X5715) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5713),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5714),X5715)),
inference(variable_rename,[status(thm)],[fact_800_nat__add__assoc]) ).
fof(i_0_2261,plain,
! [X5675,X5676,X5677] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5675),X5676)),X5677) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5675),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5676),X5677)),
inference(variable_rename,[status(thm)],[fact_787_ab__semigroup__add__class_Oadd__ac_I1_J]) ).
fof(i_0_2262,plain,
! [X5815,X5816,X5817] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5815),X5816)),X5817) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5815),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5816),X5817)),
inference(variable_rename,[status(thm)],[fact_835_diff__diff__left]) ).
fof(i_0_2263,plain,
! [X5987,X5988] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5987),X5988))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X5987)),X5988)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_905_Suc__leI])]) ).
fof(i_0_2264,plain,
! [X5216,X5217] :
( ( ~ hBOOL(hAPP_a_bool(X5216,X5217))
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X5217)),X5216)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5217),bot_bot_fun_a_bool) )
& ( hBOOL(hAPP_a_bool(X5216,X5217))
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X5217)),X5216)) = bot_bot_fun_a_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1517])]) ).
fof(i_0_2265,plain,
! [X3878,X3879] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3878),X3879))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X3879)),X3878) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3879),X3878)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_119_Suc__diff__le])]) ).
fof(i_0_2266,plain,
! [X4631,X4632,X4633] :
( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4632),X4633) != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4632),X4631)
| X4633 = X4631
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4632),X4631))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4632),X4633))
| ~ is_fun_pname_bool(X4631)
| ~ is_fun_pname_bool(X4633) )
& ( X4633 != X4631
| hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4632),X4633) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4632),X4631)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4632),X4631))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4632),X4633))
| ~ is_fun_pname_bool(X4631)
| ~ is_fun_pname_bool(X4633) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1518])])]) ).
fof(i_0_2267,plain,
! [X4622,X4623,X4624] :
( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4623),X4624) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4623),X4622)
| X4624 = X4622
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4623),X4622))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4623),X4624))
| ~ is_fun_a_bool(X4622)
| ~ is_fun_a_bool(X4624) )
& ( X4624 != X4622
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4623),X4624) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4623),X4622)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4623),X4622))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4623),X4624))
| ~ is_fun_a_bool(X4622)
| ~ is_fun_a_bool(X4624) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1519])])]) ).
fof(i_0_2268,plain,
! [X5044,X5045] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5044),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X5045),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5044),bot_bot_fun_int_bool))) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5044),X5045),
inference(variable_rename,[status(thm)],[fact_554_insert__Diff__single]) ).
fof(i_0_2269,plain,
! [X5042,X5043] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5042),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X5043),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5042),bot_bot_fun_nat_bool))) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5042),X5043),
inference(variable_rename,[status(thm)],[fact_553_insert__Diff__single]) ).
fof(i_0_2270,plain,
! [X5040,X5041] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5040),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X5041),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5040),bot_bot_fun_a_bool))) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5040),X5041),
inference(variable_rename,[status(thm)],[fact_552_insert__Diff__single]) ).
fof(i_0_2271,plain,
! [X3973,X3974] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3973),hAPP_nat_nat(suc,X3974)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3973),X3974))
| X3973 = hAPP_nat_nat(suc,X3974) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3973),X3974))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3973),hAPP_nat_nat(suc,X3974))) )
& ( X3973 != hAPP_nat_nat(suc,X3974)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3973),hAPP_nat_nat(suc,X3974))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_168_le__Suc__eq])])]) ).
fof(i_0_2272,plain,
! [X3967,X3968] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3967),hAPP_nat_nat(suc,X3968)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3967),X3968))
| X3967 = hAPP_nat_nat(suc,X3968) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1520])]) ).
cnf(i_0_2273,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk191_2(X1,X2)))
| collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X2)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1494]) ).
fof(i_0_2274,plain,
! [X4038,X4039,X4040] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4040))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4038),image_26036933t_bool(X4039,X4040)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4038)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_192_finite__surj])]) ).
fof(i_0_2275,plain,
! [X4056,X4057,X4058] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4058))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4056),image_892525857t_bool(X4057,X4058)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4056)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_198_finite__surj])]) ).
fof(i_0_2276,plain,
! [X4020,X4021,X4022] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4022))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X4020),image_2129980159t_bool(X4021,X4022)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4020)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_186_finite__surj])]) ).
fof(i_0_2277,plain,
! [X4035,X4036,X4037] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4037))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4035),image_1556378401t_bool(X4036,X4037)))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4035)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_191_finite__surj])]) ).
fof(i_0_2278,plain,
! [X4053,X4054,X4055] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4055))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4053),image_275383677t_bool(X4054,X4055)))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4053)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_197_finite__surj])]) ).
fof(i_0_2279,plain,
! [X4017,X4018,X4019] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4019))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X4017),image_1512837979t_bool(X4018,X4019)))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4017)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_185_finite__surj])]) ).
fof(i_0_2280,plain,
! [X4041,X4042,X4043] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4043))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4041),image_1655916159e_bool(X4042,X4043)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4041)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_193_finite__surj])]) ).
fof(i_0_2281,plain,
! [X4059,X4060,X4061] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4061))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4059),image_637364955e_bool(X4060,X4061)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4059)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_199_finite__surj])]) ).
fof(i_0_2282,plain,
! [X4023,X4024,X4025] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4025))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X4023),image_47868345e_bool(X4024,X4025)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4023)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_187_finite__surj])]) ).
fof(i_0_2283,plain,
! [X4044,X4045,X4046] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4046))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4044),image_nat_fun_a_bool(X4045,X4046)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4044)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_194_finite__surj])]) ).
fof(i_0_2284,plain,
! [X4062,X4063,X4064] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4064))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4062),image_int_fun_a_bool(X4063,X4064)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4062)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_200_finite__surj])]) ).
fof(i_0_2285,plain,
! [X4026,X4027,X4028] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4028))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X4026),image_112932426a_bool(X4027,X4028)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4026)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_188_finite__surj])]) ).
fof(i_0_2286,plain,
! [X4089,X4090,X4091] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4091))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4089),image_496248727ol_nat(X4090,X4091)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4089)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_209_finite__surj])]) ).
fof(i_0_2287,plain,
! [X4086,X4087,X4088] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4088))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4086),image_1431733819ol_nat(X4087,X4088)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4086)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_208_finite__surj])]) ).
fof(i_0_2288,plain,
! [X4092,X4093,X4094] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4094))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4092),image_1551609309ol_nat(X4093,X4094)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4092)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_210_finite__surj])]) ).
fof(i_0_2289,plain,
! [X4095,X4096,X4097] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4097))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4095),image_fun_a_bool_nat(X4096,X4097)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4095)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_211_finite__surj])]) ).
fof(i_0_2290,plain,
! [X4083,X4084,X4085] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4085))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4083),image_a_nat(X4084,X4085)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4083)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_207_finite__surj])]) ).
fof(i_0_2291,plain,
! [X4104,X4105,X4106] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4106))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4104),image_1133522419ol_int(X4105,X4106)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_214_finite__surj])]) ).
fof(i_0_2292,plain,
! [X4101,X4102,X4103] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4103))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4101),image_2069007511ol_int(X4102,X4103)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4101)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_213_finite__surj])]) ).
fof(i_0_2293,plain,
! [X4107,X4108,X4109] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4109))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4107),image_41399353ol_int(X4108,X4109)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_215_finite__surj])]) ).
fof(i_0_2294,plain,
! [X4110,X4111,X4112] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4112))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4110),image_fun_a_bool_int(X4111,X4112)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4110)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_216_finite__surj])]) ).
fof(i_0_2295,plain,
! [X4116,X4117,X4118] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4118))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4116),image_nat_int(X4117,X4118)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4116)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_218_finite__surj])]) ).
fof(i_0_2296,plain,
! [X4098,X4099,X4100] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4100))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4098),image_a_int(X4099,X4100)))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4098)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_212_finite__surj])]) ).
fof(i_0_2297,plain,
! [X4074,X4075,X4076] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4076))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4074),image_1921560913_pname(X4075,X4076)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4074)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_204_finite__surj])]) ).
fof(i_0_2298,plain,
! [X4071,X4072,X4073] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4073))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4071),image_62782965_pname(X4072,X4073)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4071)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_203_finite__surj])]) ).
fof(i_0_2299,plain,
! [X4077,X4078,X4079] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4079))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4077),image_1283814551_pname(X4078,X4079)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4077)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_205_finite__surj])]) ).
fof(i_0_2300,plain,
! [X4080,X4081,X4082] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4082))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4080),image_1854862208_pname(X4081,X4082)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4080)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_206_finite__surj])]) ).
fof(i_0_2301,plain,
! [X4047,X4048,X4049] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4049))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4047),image_nat_pname(X4048,X4049)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4047)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_195_finite__surj])]) ).
fof(i_0_2302,plain,
! [X4065,X4066,X4067] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4067))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4065),image_int_pname(X4066,X4067)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4065)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_201_finite__surj])]) ).
fof(i_0_2303,plain,
! [X4029,X4030,X4031] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4031))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4029),image_pname_pname(X4030,X4031)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4029)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_189_finite__surj])]) ).
fof(i_0_2304,plain,
! [X4068,X4069,X4070] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4070))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X4068),image_a_pname(X4069,X4070)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4068)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_202_finite__surj])]) ).
fof(i_0_2305,plain,
! [X4008,X4009,X4010] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X4010))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4008),image_fun_nat_bool_a(X4009,X4010)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4008)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_182_finite__surj])]) ).
fof(i_0_2306,plain,
! [X4005,X4006,X4007] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X4007))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4005),image_fun_int_bool_a(X4006,X4007)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4005)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_181_finite__surj])]) ).
fof(i_0_2307,plain,
! [X4011,X4012,X4013] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X4013))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4011),image_876012084bool_a(X4012,X4013)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4011)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_183_finite__surj])]) ).
fof(i_0_2308,plain,
! [X4014,X4015,X4016] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X4016))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4014),image_fun_a_bool_a(X4015,X4016)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4014)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_184_finite__surj])]) ).
fof(i_0_2309,plain,
! [X4032,X4033,X4034] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4034))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4032),image_nat_a(X4033,X4034)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4032)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_190_finite__surj])]) ).
fof(i_0_2310,plain,
! [X4050,X4051,X4052] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4052))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4050),image_int_a(X4051,X4052)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4050)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_196_finite__surj])]) ).
fof(i_0_2311,plain,
! [X4113,X4114,X4115] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4115))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4113),image_pname_a(X4114,X4115)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_217_finite__surj])]) ).
fof(i_0_2312,plain,
! [X4002,X4003,X4004] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4004))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4002),image_a_a(X4003,X4004)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4002)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_180_finite__surj])]) ).
fof(i_0_2313,plain,
! [X4360,X4361,X4362,X4363] :
( X4361 != hAPP_nat_int(X4362,X4363)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4363),X4360))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4361),image_nat_int(X4362,X4360))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_282_image__eqI])]) ).
fof(i_0_2314,plain,
! [X4747,X4748,X4749,X4750] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4749),X4750))
| X4747 != hAPP_nat_int(X4748,X4749)
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4747),image_nat_int(X4748,X4750))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_435_rev__image__eqI])]) ).
fof(i_0_2315,plain,
! [X4364,X4365,X4366,X4367] :
( X4365 != hAPP_pname_a(X4366,X4367)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4367),X4364))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4365),image_pname_a(X4366,X4364))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_283_image__eqI])]) ).
fof(i_0_2316,plain,
! [X4751,X4752,X4753,X4754] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4753),X4754))
| X4751 != hAPP_pname_a(X4752,X4753)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4751),image_pname_a(X4752,X4754))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_436_rev__image__eqI])]) ).
fof(i_0_2317,plain,
! [X4628,X4629,X4630] :
( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4629),X4630) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4629),X4628)
| X4630 = X4628
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4629),X4628))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4629),X4630)) )
& ( X4630 != X4628
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4629),X4630) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4629),X4628)
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4629),X4628))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4629),X4630)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1521])])]) ).
fof(i_0_2318,plain,
! [X4625,X4626,X4627] :
( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4626),X4627) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4626),X4625)
| X4627 = X4625
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4626),X4625))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4626),X4627)) )
& ( X4627 != X4625
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4626),X4627) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4626),X4625)
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4626),X4625))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4626),X4627)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1522])])]) ).
fof(i_0_2319,plain,
! [X5903,X5904] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5903),hAPP_nat_nat(suc,X5904)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5903),X5904))
| X5903 = X5904 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1523])]) ).
fof(i_0_2320,plain,
! [X5894,X5895] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5894),X5895))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5894),hAPP_nat_nat(suc,X5895)))
| X5895 = X5894 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1524])]) ).
fof(i_0_2321,plain,
! [X5892,X5893] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5892),hAPP_nat_nat(suc,X5893)))
| X5892 = X5893
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5892),X5893)) )
& ( X5892 != X5893
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5892),hAPP_nat_nat(suc,X5893)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5892),X5893)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1525])])]) ).
fof(i_0_2322,plain,
! [X5888,X5889] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5888),hAPP_nat_nat(suc,X5889)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5888),X5889))
| X5888 = X5889 )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5888),X5889))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5888),hAPP_nat_nat(suc,X5889))) )
& ( X5888 != X5889
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5888),hAPP_nat_nat(suc,X5889))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_866_less__Suc__eq])])]) ).
fof(i_0_2323,plain,
! [X5981,X5982] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5981),hAPP_nat_nat(suc,X5982)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5981),X5982)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5981),X5982))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5981),hAPP_nat_nat(suc,X5982))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_902_less__Suc__eq__le])]) ).
cnf(i_0_2324,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),X3)
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1468]) ).
cnf(i_0_2325,plain,
bit1(X1) != pls,
inference(split_conjunct,[status(thm)],[i_0_1526]) ).
fof(i_0_2326,plain,
! [X6272] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X6272)),X6272) != zero_zero_int,
inference(variable_rename,[status(thm)],[fact_1032_odd__nonzero]) ).
cnf(i_0_2327,plain,
pls != bit1(X1),
inference(split_conjunct,[status(thm)],[i_0_1527]) ).
fof(i_0_2328,plain,
! [X3977] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X3977)),X3977)),
inference(variable_rename,[status(thm)],[i_0_1528]) ).
fof(i_0_2329,plain,
! [X6153,X6154,X6155] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X6153)),X6154) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X6153)),X6155)
| X6154 = X6155 )
& ( X6154 != X6155
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X6153)),X6154) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X6153)),X6155) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_983_Suc__mult__cancel1])]) ).
fof(i_0_2330,plain,
! [X6027,X6028] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6027),esk173_2(X6027,X6028)))
| X6028 = hAPP_nat_nat(suc,X6027)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6027),X6028)) )
& ( X6028 = hAPP_nat_nat(suc,esk173_2(X6027,X6028))
| X6028 = hAPP_nat_nat(suc,X6027)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6027),X6028)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_919_lessE])])])]) ).
fof(i_0_2331,plain,
! [X6518] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X6518)),zero_zero_int))
| X6518 = zero_zero_nat )
& ( X6518 != zero_zero_nat
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X6518)),zero_zero_int)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1121_int__le__0__conv])]) ).
fof(i_0_2332,plain,
! [X3842,X3843] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3842),X3843))
| hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3842),X3843)) = hAPP_f957591787ol_nat(finite_card_int,X3843)
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3843)) )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3842),X3843))
| hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3842),X3843)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,X3843))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3843)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1529])])]) ).
fof(i_0_2333,plain,
! [X3840,X3841] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3840),X3841))
| hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3840),X3841)) = hAPP_f22106695ol_nat(finite_card_nat,X3841)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3841)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3840),X3841))
| hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3840),X3841)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X3841))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3841)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1530])])]) ).
fof(i_0_2334,plain,
! [X3836,X3837] :
( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X3836),X3837))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X3836),X3837)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X3837)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3837)) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X3836),X3837))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X3836),X3837)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X3837))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3837)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1531])])]) ).
fof(i_0_2335,plain,
! [X3834,X3835] :
( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X3834),X3835))
| hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X3834),X3835)) = hAPP_f55526627ol_nat(finite1340463720e_bool,X3835)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3835)) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X3834),X3835))
| hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X3834),X3835)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X3835))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3835)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1532])])]) ).
fof(i_0_2336,plain,
! [X3832,X3833] :
( ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X3832),X3833))
| hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X3832),X3833)) = hAPP_f696928925ol_nat(finite346522414t_bool,X3833)
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3833)) )
& ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X3832),X3833))
| hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X3832),X3833)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X3833))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3833)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1533])])]) ).
fof(i_0_2337,plain,
! [X3830,X3831] :
( ( ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X3830),X3831))
| hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X3830),X3831)) = hAPP_f521865025ol_nat(finite1876863882t_bool,X3831)
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3831)) )
& ( hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X3830),X3831))
| hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X3830),X3831)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X3831))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3831)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1534])])]) ).
fof(i_0_2338,plain,
! [X3844,X3845] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3844),X3845))
| hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3844),X3845)) = hAPP_fun_a_bool_nat(finite_card_a,X3845)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3845)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3844),X3845))
| hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3844),X3845)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X3845))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3845)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1535])])]) ).
fof(i_0_2339,plain,
! [X3838,X3839] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3838),X3839))
| hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3838),X3839)) = hAPP_f921600141ol_nat(finite_card_pname,X3839)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3839)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3838),X3839))
| hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3838),X3839)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X3839))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3839)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1536])])]) ).
fof(i_0_2340,plain,
! [X6471] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X6471)),zero_zero_int)),
inference(variable_rename,[status(thm)],[i_0_1537]) ).
fof(i_0_2341,plain,
! [X6506,X6507,X6509,X6510] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6507))
| ~ hBOOL(hAPP_int_bool(X6506,X6507))
| hBOOL(hAPP_int_bool(X6506,hAPP_nat_int(semiri1621563631at_int,esk205_1(X6506)))) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk206_1(X6509)))
| ~ hBOOL(hAPP_int_bool(X6509,hAPP_nat_int(semiri1621563631at_int,X6510))) )
& ( hBOOL(hAPP_int_bool(X6509,esk206_1(X6509)))
| ~ hBOOL(hAPP_int_bool(X6509,hAPP_nat_int(semiri1621563631at_int,X6510))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1119_transfer__int__nat__quantifiers_I2_J])])])])])]) ).
cnf(i_0_2342,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1515]) ).
cnf(i_0_2343,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1516]) ).
fof(i_0_2344,plain,
! [X6016,X6017] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6016),X6017))
| X6017 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6016),esk169_2(X6016,X6017))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_916_less__imp__Suc__add])])]) ).
fof(i_0_2345,plain,
! [X5973,X5974,X5976,X5977,X5978] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5973),X5974))
| X5974 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5973),esk165_2(X5973,X5974))) )
& ( X5977 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5976),X5978))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5976),X5977)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_900_less__iff__Suc__add])])])])]) ).
fof(i_0_2346,plain,
! [X4661,X4662] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4661),X4662))
| X4661 != X4662
| ~ is_fun_a_bool(X4661)
| ~ is_fun_a_bool(X4662) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4662),X4661))
| X4661 != X4662
| ~ is_fun_a_bool(X4661)
| ~ is_fun_a_bool(X4662) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4661),X4662))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4662),X4661))
| X4661 = X4662
| ~ is_fun_a_bool(X4661)
| ~ is_fun_a_bool(X4662) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_406_set__eq__subset])])]) ).
fof(i_0_2347,plain,
! [X4549,X4550] :
( ~ is_fun_a_bool(X4549)
| ~ is_fun_a_bool(X4550)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4549),X4550))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4550),X4549))
| X4550 = X4549 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_357_xt1_I5_J])]) ).
fof(i_0_2348,plain,
! [X4524,X4525] :
( ~ is_fun_a_bool(X4524)
| ~ is_fun_a_bool(X4525)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4524),X4525))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4525),X4524))
| X4524 = X4525 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_347_order__antisym])]) ).
fof(i_0_2349,plain,
! [X4454,X4455] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4455),X4454))
| X4455 = X4454
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4454),X4455))
| ~ is_fun_a_bool(X4454)
| ~ is_fun_a_bool(X4455) )
& ( X4455 != X4454
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4455),X4454))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4454),X4455))
| ~ is_fun_a_bool(X4454)
| ~ is_fun_a_bool(X4455) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_322_order__antisym__conv])])]) ).
fof(i_0_2350,plain,
! [X4434,X4435] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4434),X4435))
| X4434 != X4435
| ~ is_fun_a_bool(X4434)
| ~ is_fun_a_bool(X4435) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4435),X4434))
| X4434 != X4435
| ~ is_fun_a_bool(X4434)
| ~ is_fun_a_bool(X4435) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4434),X4435))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4435),X4434))
| X4434 = X4435
| ~ is_fun_a_bool(X4434)
| ~ is_fun_a_bool(X4435) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_312_order__eq__iff])])]) ).
fof(i_0_2351,plain,
! [X4372,X4373] :
( ~ is_fun_a_bool(X4372)
| ~ is_fun_a_bool(X4373)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4372),X4373))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4373),X4372))
| X4372 = X4373 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_286_equalityI])]) ).
fof(i_0_2352,plain,
! [X6528] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X6528)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6528)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6528))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X6528))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1126_zero__less__int__conv])]) ).
fof(i_0_2353,plain,
! [X5645,X5646,X5647,X5648] :
( ~ is_fun_pname_bool(X5646)
| ~ hBOOL(finite89670078_pname(X5647,X5648))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5646))
| X5646 = bot_bo844097828e_bool
| hAPP_f1297739591_pname(X5648,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5645),X5646)) = hAPP_pname_pname(hAPP_p1170154830_pname(X5647,X5645),hAPP_f1297739591_pname(X5648,X5646)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_778_folding__one__idem_Oinsert__idem])]) ).
fof(i_0_2354,plain,
! [X5633,X5634,X5635,X5636] :
( ~ is_fun_a_bool(X5634)
| ~ hBOOL(finite1819937229idem_a(X5635,X5636))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5634))
| X5634 = bot_bot_fun_a_bool
| hAPP_fun_a_bool_a(X5636,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5633),X5634)) = hAPP_a_a(hAPP_a_fun_a_a(X5635,X5633),hAPP_fun_a_bool_a(X5636,X5634)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_775_folding__one__idem_Oinsert__idem])]) ).
fof(i_0_2355,plain,
! [X5222,X5223] :
( ( ~ hBOOL(hAPP_a_bool(X5222,X5223))
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X5223)),X5222)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5223),bot_bot_fun_a_bool) )
& ( hBOOL(hAPP_a_bool(X5222,X5223))
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X5223)),X5222)) = bot_bot_fun_a_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1538])]) ).
fof(i_0_2356,plain,
! [X4853,X4854,X4855] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4854),X4855))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X4853,X4854)),image_nat_int(X4853,X4855)) = image_nat_int(X4853,X4855) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_469_insert__image])]) ).
fof(i_0_2357,plain,
! [X4856,X4857,X4858] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4857),X4858))
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X4856,X4857)),image_pname_a(X4856,X4858)) = image_pname_a(X4856,X4858) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_470_insert__image])]) ).
cnf(i_0_2358,plain,
hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),collect_int(X2)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X1))),X2)),
inference(split_conjunct,[status(thm)],[i_0_1539]) ).
cnf(i_0_2359,plain,
hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),collect_nat(X2)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2)),
inference(split_conjunct,[status(thm)],[i_0_1540]) ).
fof(i_0_2360,plain,
! [X5641,X5642,X5643,X5644] :
( ~ hBOOL(finite795500164em_nat(X5643,X5644))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5642))
| X5642 = bot_bot_fun_nat_bool
| hAPP_f22106695ol_nat(X5644,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5641),X5642)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X5643,X5641),hAPP_f22106695ol_nat(X5644,X5642)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_777_folding__one__idem_Oinsert__idem])]) ).
fof(i_0_2361,plain,
! [X5637,X5638,X5639,X5640] :
( ~ hBOOL(finite1432773856em_int(X5639,X5640))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5638))
| X5638 = bot_bot_fun_int_bool
| hAPP_f1594865479ol_int(X5640,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5637),X5638)) = hAPP_int_int(hAPP_int_fun_int_int(X5639,X5637),hAPP_f1594865479ol_int(X5640,X5638)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_776_folding__one__idem_Oinsert__idem])]) ).
fof(i_0_2362,plain,
! [X4659,X4660] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4659),X4660))
| X4659 != X4660 )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4660),X4659))
| X4659 != X4660 )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4659),X4660))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4660),X4659))
| X4659 = X4660 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_405_set__eq__subset])])]) ).
fof(i_0_2363,plain,
! [X4543,X4544] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4543),X4544))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4544),X4543))
| X4544 = X4543 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_354_xt1_I5_J])]) ).
fof(i_0_2364,plain,
! [X4518,X4519] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4518),X4519))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4519),X4518))
| X4518 = X4519 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_344_order__antisym])]) ).
fof(i_0_2365,plain,
! [X4448,X4449] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4449),X4448))
| X4449 = X4448
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4448),X4449)) )
& ( X4449 != X4448
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4449),X4448))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4448),X4449)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_319_order__antisym__conv])])]) ).
fof(i_0_2366,plain,
! [X4428,X4429] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4428),X4429))
| X4428 != X4429 )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4429),X4428))
| X4428 != X4429 )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4428),X4429))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4429),X4428))
| X4428 = X4429 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_309_order__eq__iff])])]) ).
fof(i_0_2367,plain,
! [X4370,X4371] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4370),X4371))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4371),X4370))
| X4370 = X4371 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_285_equalityI])]) ).
fof(i_0_2368,plain,
! [X4657,X4658] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4657),X4658))
| X4657 != X4658 )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4658),X4657))
| X4657 != X4658 )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4657),X4658))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4658),X4657))
| X4657 = X4658 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_404_set__eq__subset])])]) ).
fof(i_0_2369,plain,
! [X4541,X4542] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4541),X4542))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4542),X4541))
| X4542 = X4541 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_353_xt1_I5_J])]) ).
fof(i_0_2370,plain,
! [X4516,X4517] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4516),X4517))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4517),X4516))
| X4516 = X4517 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_343_order__antisym])]) ).
fof(i_0_2371,plain,
! [X4446,X4447] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4447),X4446))
| X4447 = X4446
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4446),X4447)) )
& ( X4447 != X4446
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4447),X4446))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4446),X4447)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_318_order__antisym__conv])])]) ).
fof(i_0_2372,plain,
! [X4426,X4427] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4426),X4427))
| X4426 != X4427 )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4427),X4426))
| X4426 != X4427 )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4426),X4427))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4427),X4426))
| X4426 = X4427 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_308_order__eq__iff])])]) ).
fof(i_0_2373,plain,
! [X4368,X4369] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4368),X4369))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4369),X4368))
| X4368 = X4369 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_284_equalityI])]) ).
fof(i_0_2374,plain,
! [X4547,X4548] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4547),X4548))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4548),X4547))
| X4548 = X4547 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_356_xt1_I5_J])]) ).
fof(i_0_2375,plain,
! [X4522,X4523] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4522),X4523))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4523),X4522))
| X4522 = X4523 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_346_order__antisym])]) ).
fof(i_0_2376,plain,
! [X4452,X4453] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4453),X4452))
| X4453 = X4452
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4452),X4453)) )
& ( X4453 != X4452
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4453),X4452))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4452),X4453)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_321_order__antisym__conv])])]) ).
fof(i_0_2377,plain,
! [X4432,X4433] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4432),X4433))
| X4432 != X4433 )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4433),X4432))
| X4432 != X4433 )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4432),X4433))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4433),X4432))
| X4432 = X4433 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_311_order__eq__iff])])]) ).
fof(i_0_2378,plain,
! [X3888,X3889] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3888),X3889))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3889),X3888))
| X3888 = X3889 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_126_le__antisym])]) ).
fof(i_0_2379,plain,
! [X6297,X6298] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6297),X6298))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6298),X6297))
| X6297 = X6298 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1047_zle__antisym])]) ).
fof(i_0_2380,plain,
! [X4545,X4546] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4545),X4546))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4546),X4545))
| X4546 = X4545 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_355_xt1_I5_J])]) ).
fof(i_0_2381,plain,
! [X4520,X4521] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4520),X4521))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4521),X4520))
| X4520 = X4521 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_345_order__antisym])]) ).
fof(i_0_2382,plain,
! [X4450,X4451] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4451),X4450))
| X4451 = X4450
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4450),X4451)) )
& ( X4451 != X4450
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4451),X4450))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4450),X4451)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_320_order__antisym__conv])])]) ).
fof(i_0_2383,plain,
! [X4430,X4431] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4430),X4431))
| X4430 != X4431 )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4431),X4430))
| X4430 != X4431 )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4430),X4431))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4431),X4430))
| X4430 = X4431 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_310_order__eq__iff])])]) ).
fof(i_0_2384,plain,
! [X6127,X6128] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk181_2(X6127,X6128)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6127),X6128)) )
& ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6127),esk181_2(X6127,X6128)) = X6128
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6127),X6128)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_971_less__imp__add__positive])])])]) ).
fof(i_0_2385,plain,
! [X5896,X5897] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5896),X5897))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5896),hAPP_nat_nat(suc,X5897))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_870_less__SucI])]) ).
fof(i_0_2386,plain,
! [X5985,X5986] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5985),X5986))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5985),hAPP_nat_nat(suc,X5986))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_904_le__imp__less__Suc])]) ).
fof(i_0_2387,plain,
! [X3969,X3970] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3969),X3970))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3969),hAPP_nat_nat(suc,X3970))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_166_le__SucI])]) ).
fof(i_0_2388,hypothesis,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
inference(fof_simplification,[status(thm)],[conj_5]) ).
fof(i_0_2389,plain,
! [X6142] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X6142)))
| number_number_of_nat(X6142) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,number_number_of_nat(X6142)),one_one_nat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_977_expand__Suc])]) ).
fof(i_0_2390,plain,
! [X3858,X3859] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3859))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3858),X3859))
| hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3858),X3859)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,X3859)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1541])]) ).
fof(i_0_2391,plain,
! [X3856,X3857] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3857))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3856),X3857))
| hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3856),X3857)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X3857)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1542])]) ).
fof(i_0_2392,plain,
! [X3852,X3853] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3853))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X3852),X3853))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X3852),X3853)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X3853)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1543])]) ).
fof(i_0_2393,plain,
! [X3850,X3851] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3851))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X3850),X3851))
| hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X3850),X3851)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X3851)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1544])]) ).
fof(i_0_2394,plain,
! [X3848,X3849] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3849))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X3848),X3849))
| hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X3848),X3849)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X3849)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1545])]) ).
fof(i_0_2395,plain,
! [X3846,X3847] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3847))
| hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X3846),X3847))
| hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X3846),X3847)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X3847)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1546])]) ).
fof(i_0_2396,plain,
! [X3860,X3861] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3861))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3860),X3861))
| hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3860),X3861)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X3861)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1547])]) ).
fof(i_0_2397,plain,
! [X3854,X3855] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3855))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3854),X3855))
| hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3854),X3855)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X3855)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1548])]) ).
cnf(i_0_2398,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),X3)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1468]) ).
fof(i_0_2399,plain,
! [X5883,X5884,X5885] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5885),X5884))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| X5884 = X5885
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5884),X5885)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| X5884 = X5885
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5884),X5885)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5885),X5884))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5884),X5885)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5884),X5885)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5885),X5884))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| X5884 = X5885
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| X5884 = X5885
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5885),X5884))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X5883,X5885),X5884)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_864_nat__less__cases])])]) ).
fof(i_0_2400,plain,
! [X6090] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6090))
| hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6090),hAPP_nat_nat(suc,zero_zero_nat))) = X6090 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_959_Suc__pred])]) ).
fof(i_0_2401,plain,
! [X5542,X5543] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5542),hAPP_nat_nat(suc,X5543)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5542),one_one_nat)),X5543),
inference(variable_rename,[status(thm)],[fact_747_diff__Suc__eq__diff__pred]) ).
fof(i_0_2402,plain,
! [X6482,X6483,X6485,X6486,X6487] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6482),X6483))
| X6483 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6482),hAPP_nat_int(semiri1621563631at_int,esk204_2(X6482,X6483))) )
& ( X6486 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6485),hAPP_nat_int(semiri1621563631at_int,X6487))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6485),X6486)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1105_zle__iff__zadd])])])])]) ).
fof(i_0_2403,plain,
! [X5285,X5286,X5287] :
( ( ~ hBOOL(hAPP_nat_bool(nat_case_bool(X5285,X5286),hAPP_nat_nat(suc,X5287)))
| hBOOL(hAPP_nat_bool(X5286,X5287)) )
& ( ~ hBOOL(hAPP_nat_bool(X5286,X5287))
| hBOOL(hAPP_nat_bool(nat_case_bool(X5285,X5286),hAPP_nat_nat(suc,X5287))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_664_nat__case__Suc])]) ).
fof(i_0_2404,plain,
! [X5833,X5834] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5833),X5834))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5833),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5834),X5833)) = X5834 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_841_le__add__diff__inverse])]) ).
fof(i_0_2405,plain,
! [X3992,X3993] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3992),X3993))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3993),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3993),X3992)) = X3992 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_176_diff__diff__cancel])]) ).
fof(i_0_2406,plain,
! [X6327,X6328,X6329] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6329),X6327) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6329),X6328)
| X6327 = X6328
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6329)) )
& ( X6327 != X6328
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6329),X6327) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6329),X6328)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6329)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1059_nat__mult__eq__cancel1])])]) ).
cnf(i_0_2407,plain,
hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X2)))),
inference(split_conjunct,[status(thm)],[i_0_1549]) ).
cnf(i_0_2408,plain,
hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2)))),
inference(split_conjunct,[status(thm)],[i_0_1550]) ).
fof(i_0_2409,plain,
! [X4574,X4575] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4574),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4574),X4575))),
inference(variable_rename,[status(thm)],[fact_367_insertI1]) ).
fof(i_0_2410,plain,
! [X4803,X4804] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4803),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4804),X4803))),
inference(variable_rename,[status(thm)],[fact_452_subset__insertI]) ).
fof(i_0_2411,plain,
! [X4572,X4573] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4572),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4572),X4573))),
inference(variable_rename,[status(thm)],[fact_366_insertI1]) ).
fof(i_0_2412,plain,
! [X4801,X4802] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4801),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4802),X4801))),
inference(variable_rename,[status(thm)],[fact_451_subset__insertI]) ).
fof(i_0_2413,plain,
! [X4576,X4577] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4576),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4576),X4577))),
inference(variable_rename,[status(thm)],[fact_368_insertI1]) ).
fof(i_0_2414,plain,
! [X4799,X4800] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4799),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4800),X4799))),
inference(variable_rename,[status(thm)],[fact_450_subset__insertI]) ).
fof(i_0_2415,plain,
! [X4570,X4571] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4570),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4570),X4571))),
inference(variable_rename,[status(thm)],[fact_365_insertI1]) ).
fof(i_0_2416,plain,
! [X6173] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6173),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6173),X6173))),
inference(variable_rename,[status(thm)],[fact_990_le__square]) ).
fof(i_0_2417,plain,
! [X5778,X5779] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5778),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5778),X5779))),
inference(variable_rename,[status(thm)],[fact_823_le__add1]) ).
fof(i_0_2418,plain,
! [X5776,X5777] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5776),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5777),X5776))),
inference(variable_rename,[status(thm)],[fact_822_le__add2]) ).
fof(i_0_2419,plain,
! [X5843,X5844,X5845] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5845),X5844) != X5843
| X5845 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5843),X5844)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5844),X5845)) )
& ( X5845 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5843),X5844)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5845),X5844) = X5843
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5844),X5845)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_845_le__imp__diff__is__add])])]) ).
fof(i_0_2420,plain,
! [X6286,X6287,X6288] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6286),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6287),X6288)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6287),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6286),X6288)),
inference(variable_rename,[status(thm)],[fact_1042_zadd__left__commute]) ).
fof(i_0_2421,plain,
! [X5710,X5711,X5712] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5710),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5711),X5712)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5711),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5710),X5712)),
inference(variable_rename,[status(thm)],[fact_799_nat__add__left__commute]) ).
fof(i_0_2422,plain,
! [X4604,X4605,X4606] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4604),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4605),X4606)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4605),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4604),X4606)),
inference(variable_rename,[status(thm)],[fact_383_insert__commute]) ).
fof(i_0_2423,plain,
! [X3722,X3723] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3723))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X3722),X3723))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_41_finite_OinsertI])]) ).
fof(i_0_2424,plain,
! [X3720,X3721] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3721))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X3720),X3721))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_40_finite_OinsertI])]) ).
fof(i_0_2425,plain,
! [X3724,X3725] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3725))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X3724),X3725))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_42_finite_OinsertI])]) ).
fof(i_0_2426,plain,
! [X3726,X3727] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3727))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X3726),X3727))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_43_finite_OinsertI])]) ).
cnf(i_0_2427,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1551]) ).
cnf(i_0_2428,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X2),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1551]) ).
fof(i_0_2429,plain,
! [X4938,X4939] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4939))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4939),X4938))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_495_finite__Diff])]) ).
fof(i_0_2430,plain,
! [X3730,X3731] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3731))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3730),X3731))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_45_finite_OinsertI])]) ).
cnf(i_0_2431,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X2))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1552]) ).
cnf(i_0_2432,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X2),X1))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1552]) ).
fof(i_0_2433,plain,
! [X4936,X4937] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X4937))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4937),X4936))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_494_finite__Diff])]) ).
fof(i_0_2434,plain,
! [X3732,X3733] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3733))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3732),X3733))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_46_finite_OinsertI])]) ).
fof(i_0_2435,plain,
! [X4940,X4941] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4941))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X4941),X4940))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_496_finite__Diff])]) ).
fof(i_0_2436,plain,
! [X3728,X3729] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3729))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3728),X3729))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_44_finite_OinsertI])]) ).
fof(i_0_2437,plain,
! [X3734,X3735] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3735))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3734),X3735))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_47_finite_OinsertI])]) ).
fof(i_0_2438,plain,
! [X3651] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3651))
| hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X3651)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2_finite__Collect__subsets])]) ).
fof(i_0_2439,plain,
! [X3650] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3650))
| hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),X3650)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1_finite__Collect__subsets])]) ).
fof(i_0_2440,plain,
! [X3652] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3652))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X3652)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_3_finite__Collect__subsets])]) ).
fof(i_0_2441,plain,
! [X3653] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3653))
| hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X3653)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_finite__Collect__subsets])]) ).
fof(i_0_2442,plain,
! [X3656] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3656))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X3656)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_7_finite__Collect__subsets])]) ).
fof(i_0_2443,plain,
! [X3657] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3657))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),X3657)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_8_finite__Collect__subsets])]) ).
fof(i_0_2444,plain,
! [X3655] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3655))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X3655)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_6_finite__Collect__subsets])]) ).
fof(i_0_2445,plain,
! [X3654] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3654))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X3654)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_finite__Collect__subsets])]) ).
fof(i_0_2446,plain,
! [X4847,X4848,X4849] : image_nat_int(X4847,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4848),X4849)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X4847,X4848)),image_nat_int(X4847,X4849)),
inference(variable_rename,[status(thm)],[fact_467_image__insert]) ).
fof(i_0_2447,plain,
! [X4850,X4851,X4852] : image_pname_a(X4850,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4851),X4852)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X4850,X4851)),image_pname_a(X4850,X4852)),
inference(variable_rename,[status(thm)],[fact_468_image__insert]) ).
fof(i_0_2448,plain,
! [X5948,X5949] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5948),X5949))
| X5948 = X5949
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5948),X5949)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_890_le__neq__implies__less])]) ).
fof(i_0_2449,plain,
! [X5944,X5945] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5944),X5945))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5944),X5945))
| X5944 = X5945 )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5944),X5945))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5944),X5945)) )
& ( X5944 != X5945
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5944),X5945)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_888_le__eq__less__or__eq])])]) ).
fof(i_0_2450,plain,
! [X5942,X5943] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5942),X5943))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5942),X5943)) )
& ( X5942 != X5943
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5942),X5943)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5942),X5943))
| X5942 = X5943
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5942),X5943)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_887_nat__less__le])])]) ).
fof(i_0_2451,plain,
! [X6303,X6304] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6303),X6304))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6303),X6304)) )
& ( X6303 != X6304
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6303),X6304)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6303),X6304))
| X6303 = X6304
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6303),X6304)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1050_zless__le])])]) ).
fof(i_0_2452,plain,
! [X5952,X5953] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5952),X5953))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5952),X5953)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_892_termination__basic__simps_I5_J])]) ).
fof(i_0_2453,plain,
! [X5950,X5951] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5950),X5951))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5950),X5951)) )
& ( X5950 != X5951
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5950),X5951)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_891_less__or__eq__imp__le])])]) ).
fof(i_0_2454,plain,
! [X5946,X5947] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5946),X5947))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5946),X5947)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_889_less__imp__le__nat])]) ).
fof(i_0_2455,plain,
! [X6537,X6538] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6537),X6538))
| hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X6538),X6537) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6538),X6537) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1130_tsub__eq])]) ).
fof(i_0_2456,plain,
! [X6468,X6469] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6468),X6469))
| hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X6469),X6468) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6469),X6468) )
& ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6468),X6469))
| hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X6469),X6468) = zero_zero_int ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1553])]) ).
cnf(i_0_2457,plain,
succ(pls) = bit1(pls),
inference(split_conjunct,[status(thm)],[fact_1166_succ__Pls]) ).
fof(i_0_2458,plain,
! [X6539] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk210_1(X6539)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6539)) )
& ( X6539 = hAPP_nat_int(semiri1621563631at_int,esk210_1(X6539))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6539)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1131_zero__less__imp__eq__int])])])]) ).
fof(i_0_2459,plain,
! [X6115] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6115))
| hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6115),one_one_nat)) = X6115 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_966_Suc__diff__1])]) ).
fof(i_0_2460,plain,
! [X6116] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6116))
| X6116 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6116),one_one_nat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_967_Suc__pred_H])]) ).
fof(i_0_2461,plain,
! [X6207,X6208] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X6207)),X6208) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6208),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6207),X6208)),
inference(variable_rename,[status(thm)],[fact_1005_mult__Suc]) ).
fof(i_0_2462,plain,
! [X3935,X3936] :
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3935),X3936))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3936))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3935)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_149_finite__subset])]) ).
fof(i_0_2463,plain,
! [X3951,X3952] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3952))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3951),X3952))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3951)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_157_rev__finite__subset])]) ).
fof(i_0_2464,plain,
! [X3933,X3934] :
( ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3933),X3934))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3934))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3933)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_148_finite__subset])]) ).
fof(i_0_2465,plain,
! [X3949,X3950] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3950))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3949),X3950))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3949)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_156_rev__finite__subset])]) ).
fof(i_0_2466,plain,
! [X3937,X3938] :
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3937),X3938))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3938))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3937)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_150_finite__subset])]) ).
fof(i_0_2467,plain,
! [X3953,X3954] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3954))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3953),X3954))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3953)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_158_rev__finite__subset])]) ).
fof(i_0_2468,plain,
! [X3939,X3940] :
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3939),X3940))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3940))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3939)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_151_finite__subset])]) ).
fof(i_0_2469,plain,
! [X3955,X3956] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3956))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3955),X3956))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3955)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_159_rev__finite__subset])]) ).
fof(i_0_2470,plain,
! [X3945,X3946] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3945),X3946))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3946))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3945)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_154_finite__subset])]) ).
fof(i_0_2471,plain,
! [X3961,X3962] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3962))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3961),X3962))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3961)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_162_rev__finite__subset])]) ).
fof(i_0_2472,plain,
! [X3947,X3948] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3947),X3948))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3948))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3947)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_155_finite__subset])]) ).
fof(i_0_2473,plain,
! [X3963,X3964] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3964))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3963),X3964))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3963)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_163_rev__finite__subset])]) ).
fof(i_0_2474,plain,
! [X3943,X3944] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3943),X3944))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3944))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3943)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_153_finite__subset])]) ).
fof(i_0_2475,plain,
! [X3959,X3960] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3960))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3959),X3960))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3959)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_161_rev__finite__subset])]) ).
fof(i_0_2476,plain,
! [X3941,X3942] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3941),X3942))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3942))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3941)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_152_finite__subset])]) ).
fof(i_0_2477,plain,
! [X3957,X3958] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3958))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3957),X3958))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3957)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_160_rev__finite__subset])]) ).
fof(i_0_2478,plain,
! [X6498,X6499] : hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X6498)),hAPP_nat_int(semiri1621563631at_int,X6499)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6498),X6499)),
inference(variable_rename,[status(thm)],[fact_1111_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).
fof(i_0_2479,plain,
! [X6492,X6493] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X6492)),hAPP_nat_int(semiri1621563631at_int,X6493)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6492),X6493)),
inference(variable_rename,[status(thm)],[fact_1108_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).
fof(i_0_2480,plain,
! [X6488,X6489] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X6488)),hAPP_nat_int(semiri1621563631at_int,X6489)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6488),X6489)),
inference(variable_rename,[status(thm)],[fact_1106_zmult__int]) ).
fof(i_0_2481,plain,
! [X6500,X6501] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X6500)),hAPP_nat_int(semiri1621563631at_int,X6501)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6500),X6501)),
inference(variable_rename,[status(thm)],[fact_1112_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).
fof(i_0_2482,plain,
! [X6477,X6478] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X6477)),hAPP_nat_int(semiri1621563631at_int,X6478)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6477),X6478)),
inference(variable_rename,[status(thm)],[fact_1103_zadd__int]) ).
fof(i_0_2483,plain,
! [X6490,X6491] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6490),X6491)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X6490)),hAPP_nat_int(semiri1621563631at_int,X6491)),
inference(variable_rename,[status(thm)],[fact_1107_int__mult]) ).
fof(i_0_2484,plain,
! [X5417,X5420,X5421] :
( ( is_pname(esk140_1(X5417))
| X5417 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X5417) )
& ( is_fun_pname_bool(esk141_1(X5417))
| X5417 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X5417) )
& ( X5417 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk140_1(X5417)),esk141_1(X5417))
| X5417 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X5417) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk140_1(X5417)),esk141_1(X5417)))
| X5417 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X5417) )
& ( ~ is_pname(X5420)
| ~ is_fun_pname_bool(X5421)
| X5417 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5420),X5421)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5420),X5421))
| X5417 != bot_bo844097828e_bool
| ~ is_fun_pname_bool(X5417) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1554])])])])]) ).
fof(i_0_2485,plain,
! [X5400,X5403,X5404] :
( ( is_a(esk134_1(X5400))
| X5400 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X5400) )
& ( is_fun_a_bool(esk135_1(X5400))
| X5400 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X5400) )
& ( X5400 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk134_1(X5400)),esk135_1(X5400))
| X5400 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X5400) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk134_1(X5400)),esk135_1(X5400)))
| X5400 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X5400) )
& ( ~ is_a(X5403)
| ~ is_fun_a_bool(X5404)
| X5400 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5403),X5404)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5403),X5404))
| X5400 != bot_bot_fun_a_bool
| ~ is_fun_a_bool(X5400) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1555])])])])]) ).
cnf(i_0_2486,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X1)) = number_number_of_nat(succ(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1556]) ).
fof(i_0_2487,plain,
! [X5998,X5999] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5998),X5999))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5999),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X5998),X5999)) = X5998 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1557])]) ).
cnf(i_0_2488,plain,
( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X2)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1487]) ).
cnf(i_0_2489,plain,
( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X2)),X1)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1558]) ).
cnf(i_0_2490,plain,
( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),X1)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1559]) ).
fof(i_0_2491,plain,
! [X5780,X5781,X5783,X5784,X5785] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5780),X5781))
| X5781 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5780),esk162_2(X5780,X5781)) )
& ( X5784 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5783),X5785)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5783),X5784)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_824_le__iff__add])])])])]) ).
fof(i_0_2492,plain,
! [X6065] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6065),hAPP_nat_nat(suc,zero_zero_nat)))
| X6065 = zero_zero_nat )
& ( X6065 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6065),hAPP_nat_nat(suc,zero_zero_nat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_947_less__Suc0])]) ).
fof(i_0_2493,plain,
! [X5766,X5767] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X5766),X5767)),X5767) = X5766,
inference(variable_rename,[status(thm)],[fact_817_diff__add__cancel]) ).
fof(i_0_2494,plain,
! [X5768,X5769] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5768),X5769)),X5769) = X5768,
inference(variable_rename,[status(thm)],[fact_818_add__diff__cancel]) ).
fof(i_0_2495,plain,
! [X5813,X5814] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5813),X5814)),X5813) = X5814,
inference(variable_rename,[status(thm)],[fact_834_diff__add__inverse]) ).
fof(i_0_2496,plain,
! [X5811,X5812] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5811),X5812)),X5812) = X5811,
inference(variable_rename,[status(thm)],[fact_833_diff__add__inverse2]) ).
fof(i_0_2497,plain,
! [X6275] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X6275))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6275)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6275))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X6275)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1036_int__one__le__iff__zero__less])]) ).
fof(i_0_2498,plain,
! [X5411,X5414,X5415,X5416] :
( ( X5411 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk138_1(X5411)),esk139_1(X5411))
| X5411 = bot_bot_fun_nat_bool )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk138_1(X5411)),esk139_1(X5411)))
| X5411 = bot_bot_fun_nat_bool )
& ( X5414 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5415),X5416)
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5415),X5416))
| X5414 != bot_bot_fun_nat_bool ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1560])])])])])]) ).
fof(i_0_2499,plain,
! [X5405,X5408,X5409,X5410] :
( ( X5405 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk136_1(X5405)),esk137_1(X5405))
| X5405 = bot_bot_fun_int_bool )
& ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk136_1(X5405)),esk137_1(X5405)))
| X5405 = bot_bot_fun_int_bool )
& ( X5408 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5409),X5410)
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5409),X5410))
| X5408 != bot_bot_fun_int_bool ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1561])])])])])]) ).
fof(i_0_2500,plain,
! [X6134,X6135] :
( ( hBOOL(hAPP_nat_bool(X6134,hAPP_nat_nat(suc,esk184_1(X6134))))
| hBOOL(hAPP_nat_bool(X6134,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X6134,X6135)) )
& ( ~ hBOOL(hAPP_nat_bool(X6134,esk184_1(X6134)))
| hBOOL(hAPP_nat_bool(X6134,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X6134,X6135)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_974_zero__induct])])])])])]) ).
fof(i_0_2501,plain,
! [X5288,X5289,X5290] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5289),X5290))
| image_nat_int(cOMBK_int_nat(X5288),X5290) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5288),bot_bot_fun_int_bool) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_665_image__constant])]) ).
fof(i_0_2502,plain,
! [X5291,X5292,X5293] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5292),X5293))
| image_pname_a(cOMBK_a_pname(X5291),X5293) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5291),bot_bot_fun_a_bool) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_666_image__constant])]) ).
fof(i_0_2503,plain,
! [X6270,X6271] :
( ( X6271 = one_one_int
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6271),X6270) != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6271)) )
& ( X6270 = one_one_int
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6271),X6270) != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6271)) )
& ( X6271 != one_one_int
| X6270 != one_one_int
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6271),X6270) = one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X6271)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1031_pos__zmult__eq__1__iff])])]) ).
cnf(i_0_2504,plain,
hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X2))),
inference(split_conjunct,[status(thm)],[i_0_1562]) ).
cnf(i_0_2505,plain,
hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X2))),
inference(split_conjunct,[status(thm)],[i_0_1563]) ).
cnf(i_0_2506,plain,
hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))),
inference(split_conjunct,[status(thm)],[i_0_1564]) ).
cnf(i_0_2507,plain,
hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))),
inference(split_conjunct,[status(thm)],[i_0_1565]) ).
cnf(i_0_2508,plain,
( number_number_of_nat(X2) = number_number_of_nat(X1)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
| number_number_of_int(X2) != zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X1)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[i_0_1566]) ).
fof(i_0_2509,plain,
! [X6205,X6206] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6205),hAPP_nat_nat(suc,X6206)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6205),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6205),X6206)),
inference(variable_rename,[status(thm)],[fact_1004_mult__Suc__right]) ).
fof(i_0_2510,plain,
! [X5772,X5773] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X5772)),X5773) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5772),X5773)),
inference(variable_rename,[status(thm)],[fact_820_add__Suc]) ).
cnf(i_0_2511,plain,
( number_number_of_nat(X1) = number_number_of_nat(X2)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X2)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[i_0_1566]) ).
cnf(i_0_2512,plain,
( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X2)),X1)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1567]) ).
cnf(i_0_2513,plain,
( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X2)),X1)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1568]) ).
fof(i_0_2514,plain,
! [X6088,X6089] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6088),hAPP_nat_nat(suc,X6089)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6088),X6089)),
inference(variable_rename,[status(thm)],[fact_958_diff__Suc]) ).
fof(i_0_2515,plain,
! [X4652,X4653] :
( ~ is_fun_pname_bool(X4653)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4652),X4653))
| hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4652),X4653) = X4653 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_400_insert__absorb])]) ).
fof(i_0_2516,plain,
! [X4646,X4647] :
( ~ is_fun_a_bool(X4647)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4646),X4647))
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4646),X4647) = X4647 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_397_insert__absorb])]) ).
fof(i_0_2517,plain,
! [X3648,X3649] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3648),X3649))
| hBOOL(hAPP_fun_a_bool_bool(p(X3649),X3648)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_assms_I1_J])]) ).
fof(i_0_2518,plain,
! [X5422] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5422),u))
| hBOOL(wt(the_com(body(X5422)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_703_assms_I4_J])]) ).
cnf(i_0_2519,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(split_conjunct,[status(thm)],[fact_1175_one__is__num__one]) ).
fof(i_0_2520,plain,
! [X4648,X4649] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4648),X4649))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4648),X4649) = X4649 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_398_insert__absorb])]) ).
fof(i_0_2521,plain,
! [X4650,X4651] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4650),X4651))
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4650),X4651) = X4651 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_399_insert__absorb])]) ).
fof(i_0_2522,plain,
! [X6086,X6087] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6086),X6087))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6086),X6087) = zero_zero_nat ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_956_diff__is__0__eq_H])]) ).
fof(i_0_2523,plain,
! [X6084,X6085] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6084),X6085) != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6084),X6085)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6084),X6085))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6084),X6085) = zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_955_diff__is__0__eq])]) ).
fof(i_0_2524,plain,
! [X6568] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X6568)),one_one_int))
| X6568 = zero_zero_int )
& ( X6568 != zero_zero_int
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X6568)),one_one_int)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1145_zabs__less__one__iff])]) ).
fof(i_0_2525,plain,
! [X5876,X5877] :
( X5876 = X5877
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5876),X5877))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5877),X5876)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1569])]) ).
fof(i_0_2526,plain,
! [X5874,X5875] :
( ( X5874 = X5875
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5874),X5875))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5875),X5874)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5874),X5875))
| X5874 != X5875 )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5875),X5874))
| X5874 != X5875 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_859_nat__neq__iff])])]) ).
fof(i_0_2527,plain,
! [X6301,X6302] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6301),X6302))
| X6301 = X6302
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6302),X6301)) ),
inference(variable_rename,[status(thm)],[fact_1049_zless__linear]) ).
fof(i_0_2528,plain,
! [X5671] : hAPP_f1594865479ol_int(the_elem_int,X5671) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,X5671),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))),
inference(variable_rename,[status(thm)],[fact_785_the__elem__def]) ).
fof(i_0_2529,plain,
! [X5670] : hAPP_f22106695ol_nat(the_elem_nat,X5670) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X5670),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))),
inference(variable_rename,[status(thm)],[fact_784_the__elem__def]) ).
fof(i_0_2530,plain,
! [X5669] : hAPP_fun_a_bool_a(the_elem_a,X5669) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,X5669),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))),
inference(variable_rename,[status(thm)],[fact_783_the__elem__def]) ).
fof(i_0_2531,plain,
! [X6570] :
( ( hBOOL(hAPP_int_bool(nat_neg,X6570))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6570)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6570))
| ~ hBOOL(hAPP_int_bool(nat_neg,X6570)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1570])]) ).
fof(i_0_2532,plain,
! [X4568,X4569] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4568),X4569))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4569),X4568)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1571])]) ).
fof(i_0_2533,plain,
! [X4424,X4425] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4424),X4425))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4425),X4424)) ),
inference(variable_rename,[status(thm)],[fact_307_linorder__linear]) ).
fof(i_0_2534,plain,
! [X3895,X3896] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3895),X3896))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3896),X3895)) ),
inference(variable_rename,[status(thm)],[fact_129_nat__le__linear]) ).
fof(i_0_2535,plain,
! [X6292,X6293] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6292),X6293))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6293),X6292)) ),
inference(variable_rename,[status(thm)],[fact_1045_zle__linear]) ).
fof(i_0_2536,plain,
! [X4566,X4567] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4566),X4567))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4567),X4566)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1572])]) ).
fof(i_0_2537,plain,
! [X4422,X4423] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4422),X4423))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4423),X4422)) ),
inference(variable_rename,[status(thm)],[fact_306_linorder__linear]) ).
fof(i_0_2538,plain,
! [X5389,X5392,X5393] :
( ( is_fun_pname_bool(esk131_1(X5389))
| X5389 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5389))
| ~ is_fun_pname_bool(X5389) )
& ( is_pname(esk132_1(X5389))
| X5389 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5389))
| ~ is_fun_pname_bool(X5389) )
& ( X5389 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk132_1(X5389)),esk131_1(X5389))
| X5389 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5389))
| ~ is_fun_pname_bool(X5389) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk131_1(X5389)))
| X5389 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5389))
| ~ is_fun_pname_bool(X5389) )
& ( X5389 != bot_bo844097828e_bool
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5389))
| ~ is_fun_pname_bool(X5389) )
& ( ~ is_fun_pname_bool(X5392)
| ~ is_pname(X5393)
| X5389 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X5393),X5392)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5392))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5389))
| ~ is_fun_pname_bool(X5389) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_694_finite_Osimps])])])])])]) ).
fof(i_0_2539,plain,
! [X5372,X5375,X5376] :
( ( is_fun_a_bool(esk125_1(X5372))
| X5372 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5372))
| ~ is_fun_a_bool(X5372) )
& ( is_a(esk126_1(X5372))
| X5372 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5372))
| ~ is_fun_a_bool(X5372) )
& ( X5372 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk126_1(X5372)),esk125_1(X5372))
| X5372 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5372))
| ~ is_fun_a_bool(X5372) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk125_1(X5372)))
| X5372 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5372))
| ~ is_fun_a_bool(X5372) )
& ( X5372 != bot_bot_fun_a_bool
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5372))
| ~ is_fun_a_bool(X5372) )
& ( ~ is_fun_a_bool(X5375)
| ~ is_a(X5376)
| X5372 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5376),X5375)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5375))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5372))
| ~ is_fun_a_bool(X5372) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_691_finite_Osimps])])])])])]) ).
fof(i_0_2540,plain,
! [X4594,X4595] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4594),X4595))
| hBOOL(hAPP_nat_bool(X4595,X4594)) )
& ( ~ hBOOL(hAPP_nat_bool(X4595,X4594))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4594),X4595)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_377_mem__def])]) ).
fof(i_0_2541,plain,
! [X4592,X4593] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4592),X4593))
| hBOOL(hAPP_int_bool(X4593,X4592)) )
& ( ~ hBOOL(hAPP_int_bool(X4593,X4592))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4592),X4593)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_376_mem__def])]) ).
fof(i_0_2542,plain,
! [X4598,X4599] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4598),X4599))
| hBOOL(hAPP_pname_bool(X4599,X4598)) )
& ( ~ hBOOL(hAPP_pname_bool(X4599,X4598))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4598),X4599)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_379_mem__def])]) ).
fof(i_0_2543,plain,
! [X4596,X4597] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4596),X4597))
| hBOOL(hAPP_a_bool(X4597,X4596)) )
& ( ~ hBOOL(hAPP_a_bool(X4597,X4596))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4596),X4597)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_378_mem__def])]) ).
fof(i_0_2544,plain,
! [X4602,X4603] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4602),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4602),X4603)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4602),X4603),
inference(variable_rename,[status(thm)],[fact_382_insert__absorb2]) ).
fof(i_0_2545,plain,
! [X5770,X5771] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5770),hAPP_nat_nat(suc,X5771)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5770),X5771)),
inference(variable_rename,[status(thm)],[fact_819_add__Suc__right]) ).
fof(i_0_2546,plain,
! [X6562] : X6562 = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,esk214_1(X6562))),hAPP_nat_int(semiri1621563631at_int,esk215_1(X6562))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1143_int__diff__cases])])]) ).
fof(i_0_2547,plain,
! [X3981,X3982] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X3981)),hAPP_nat_nat(suc,X3982)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3981),X3982),
inference(variable_rename,[status(thm)],[fact_172_diff__Suc__Suc]) ).
fof(i_0_2548,plain,
! [X5774,X5775] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X5774)),X5775) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5774),hAPP_nat_nat(suc,X5775)),
inference(variable_rename,[status(thm)],[fact_821_add__Suc__shift]) ).
fof(i_0_2549,plain,
! [X6569] :
( ( ~ hBOOL(hAPP_int_bool(nat_neg,X6569))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6569),zero_zero_int)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6569),zero_zero_int))
| hBOOL(hAPP_int_bool(nat_neg,X6569)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1146_neg__def])]) ).
fof(i_0_2550,plain,
! [X6503] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6503))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X6503))) )
& ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X6503)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X6503)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1114_transfer__nat__int__set__relations_I1_J])]) ).
fof(i_0_2551,plain,
! [X5544,X5545,X5546] :
( ~ is_a(X5544)
| ~ hBOOL(finite_folding_one_a(X5545,X5546))
| hAPP_fun_a_bool_a(X5546,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5544),bot_bot_fun_a_bool)) = X5544 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_748_folding__one_Osingleton])]) ).
fof(i_0_2552,plain,
! [X5015,X5017] :
( ( is_pname(esk100_1(X5015))
| X5015 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X5015) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk100_1(X5015)),X5015))
| X5015 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X5015) )
& ( X5015 != bot_bo844097828e_bool
| ~ is_pname(X5017)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5017),X5015))
| ~ is_fun_pname_bool(X5015) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1573])])])])]) ).
fof(i_0_2553,plain,
! [X5012,X5014] :
( ( is_a(esk99_1(X5012))
| X5012 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X5012) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk99_1(X5012)),X5012))
| X5012 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X5012) )
& ( X5012 != bot_bot_fun_a_bool
| ~ is_a(X5014)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X5014),X5012))
| ~ is_fun_a_bool(X5012) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1574])])])])]) ).
fof(i_0_2554,plain,
! [X5001,X5002] :
( ( ~ is_pname(X5002)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X5002),X5001))
| X5001 != bot_bo844097828e_bool
| ~ is_fun_pname_bool(X5001) )
& ( is_pname(esk96_1(X5001))
| X5001 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X5001) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk96_1(X5001)),X5001))
| X5001 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X5001) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_530_ex__in__conv])])])])]) ).
fof(i_0_2555,plain,
! [X4998,X4999] :
( ( ~ is_a(X4999)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4999),X4998))
| X4998 != bot_bot_fun_a_bool
| ~ is_fun_a_bool(X4998) )
& ( is_a(esk95_1(X4998))
| X4998 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X4998) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk95_1(X4998)),X4998))
| X4998 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X4998) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_529_ex__in__conv])])])])]) ).
fof(i_0_2556,plain,
! [X6669,X6670] :
( ~ is_pname(X6669)
| ~ is_pname(X6670)
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X6669),X6670))
| X6669 = X6670 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1575])]) ).
fof(i_0_2557,plain,
! [X6651,X6652] :
( ~ is_a(X6651)
| ~ is_a(X6652)
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X6651),X6652))
| X6651 = X6652 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1576])]) ).
fof(i_0_2558,plain,
! [X6710,X6711] :
( ~ is_fun_pname_bool(X6710)
| ~ is_fun_pname_bool(X6711)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X6710),X6711))
| X6710 = X6711 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1577])]) ).
fof(i_0_2559,plain,
! [X6686,X6687] :
( ~ is_fun_a_bool(X6686)
| ~ is_fun_a_bool(X6687)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X6686),X6687))
| X6686 = X6687 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1578])]) ).
fof(i_0_2560,plain,
! [X6551,X6552,X6553] :
( ( ~ hBOOL(X6553)
| hAPP_nat_int(semiri1621563631at_int,X6551) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X6553),X6551),X6552)) )
& ( hBOOL(X6553)
| hAPP_nat_int(semiri1621563631at_int,X6552) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X6553),X6551),X6552)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1579])]) ).
cnf(i_0_2561,plain,
( hBOOL(hAPP_int_bool(X1,X2))
| collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X2)),X1)) = bot_bot_fun_int_bool ),
inference(split_conjunct,[status(thm)],[i_0_1558]) ).
cnf(i_0_2562,plain,
( hBOOL(hAPP_nat_bool(X1,X2))
| collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),X1)) = bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_1559]) ).
fof(i_0_2563,plain,
! [X5550,X5551,X5552] :
( ~ hBOOL(finite1626084323ne_int(X5551,X5552))
| hAPP_f1594865479ol_int(X5552,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5550),bot_bot_fun_int_bool)) = X5550 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_750_folding__one_Osingleton])]) ).
fof(i_0_2564,plain,
! [X5547,X5548,X5549] :
( ~ hBOOL(finite988810631ne_nat(X5548,X5549))
| hAPP_f22106695ol_nat(X5549,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5547),bot_bot_fun_nat_bool)) = X5547 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_749_folding__one_Osingleton])]) ).
fof(i_0_2565,plain,
! [X6649,X6650] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X6649),X6650))
| ~ hBOOL(X6649)
| hBOOL(X6650) ),
inference(variable_rename,[status(thm)],[i_0_1580]) ).
fof(i_0_2566,plain,
! [X5383,X5386,X5387,X5388] :
( ( X5383 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk130_1(X5383)),esk129_1(X5383))
| X5383 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5383)) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk129_1(X5383)))
| X5383 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5383)) )
& ( X5386 != bot_bot_fun_nat_bool
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5386)) )
& ( X5386 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5388),X5387)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5387))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5386)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_693_finite_Osimps])])])])])]) ).
fof(i_0_2567,plain,
! [X5377,X5380,X5381,X5382] :
( ( X5377 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk128_1(X5377)),esk127_1(X5377))
| X5377 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5377)) )
& ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk127_1(X5377)))
| X5377 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5377)) )
& ( X5380 != bot_bot_fun_int_bool
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5380)) )
& ( X5380 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5382),X5381)
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5381))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X5380)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_692_finite_Osimps])])])])])]) ).
fof(i_0_2568,plain,
! [X6560] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6560))
| X6560 = hAPP_nat_int(semiri1621563631at_int,esk213_1(X6560)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1142_zero__le__imp__eq__int])])]) ).
fof(i_0_2569,plain,
! [X6558] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6558))
| X6558 = hAPP_nat_int(semiri1621563631at_int,esk212_1(X6558)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1141_nonneg__eq__int])])]) ).
fof(i_0_2570,plain,
! [X6556] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6556))
| X6556 = hAPP_nat_int(semiri1621563631at_int,esk211_1(X6556)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1140_nonneg__int__cases])])]) ).
fof(i_0_2571,plain,
! [X6130] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6130))
| X6130 = hAPP_nat_nat(suc,esk182_1(X6130)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_972_gr0__implies__Suc])])]) ).
fof(i_0_2572,plain,
! [X6061,X6063,X6064] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6061))
| X6061 = hAPP_nat_nat(suc,esk175_1(X6061)) )
& ( X6063 != hAPP_nat_nat(suc,X6064)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6063)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_946_gr0__conv__Suc])])])])]) ).
cnf(i_0_2573,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
| number_number_of_nat(X1) != number_number_of_nat(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1566]) ).
fof(i_0_2574,plain,
! [X6642,X6643] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X6642),X6643))
| hBOOL(X6642)
| hBOOL(X6643) ),
inference(variable_rename,[status(thm)],[i_0_1581]) ).
fof(i_0_2575,plain,
! [X5145,X5146] :
( ~ is_a(X5145)
| ~ is_a(X5146)
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5145),bot_bot_fun_a_bool) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5146),bot_bot_fun_a_bool)
| X5145 = X5146 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_589_singleton__inject])]) ).
fof(i_0_2576,plain,
! [X6634,X6635] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X6634),X6635))
| hBOOL(X6634) ),
inference(variable_rename,[status(thm)],[i_0_1582]) ).
fof(i_0_2577,plain,
! [X6636,X6637] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X6636),X6637))
| hBOOL(X6637) ),
inference(variable_rename,[status(thm)],[i_0_1583]) ).
fof(i_0_2578,plain,
! [X6571,X6572] :
( abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6571),X6572)) != one_one_int
| abs_abs_int(X6571) = one_one_int ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1150_abs__zmult__eq__1])]) ).
fof(i_0_2579,plain,
! [X5211] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5211),bot_bot_fun_a_bool))
| X5211 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X5211) )
& ( X5211 != bot_bot_fun_a_bool
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5211),bot_bot_fun_a_bool))
| ~ is_fun_a_bool(X5211) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_625_bot__unique])])]) ).
fof(i_0_2580,plain,
! [X5207] :
( ~ is_fun_a_bool(X5207)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5207),bot_bot_fun_a_bool))
| X5207 = bot_bot_fun_a_bool ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_621_le__bot])]) ).
fof(i_0_2581,plain,
! [X5193] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5193),bot_bot_fun_a_bool))
| X5193 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X5193) )
& ( X5193 != bot_bot_fun_a_bool
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5193),bot_bot_fun_a_bool))
| ~ is_fun_a_bool(X5193) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_611_subset__empty])])]) ).
fof(i_0_2582,plain,
! [X5881,X5882] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5881),X5882))
| X5881 != X5882 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_863_less__not__refl3])]) ).
fof(i_0_2583,plain,
! [X5879,X5880] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5879),X5880))
| X5880 != X5879 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_862_less__not__refl2])]) ).
fof(i_0_2584,plain,
! [X3680,X3681] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3681))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X3680,X3681))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_20_finite__imageI])]) ).
fof(i_0_2585,plain,
! [X3670,X3671] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3671))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X3670,X3671))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_15_finite__imageI])]) ).
fof(i_0_2586,plain,
! [X3660,X3661] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3661))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X3660,X3661))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_10_finite__imageI])]) ).
fof(i_0_2587,plain,
! [X3678,X3679] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3679))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X3678,X3679))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_19_finite__imageI])]) ).
fof(i_0_2588,plain,
! [X3668,X3669] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3669))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X3668,X3669))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_14_finite__imageI])]) ).
fof(i_0_2589,plain,
! [X3658,X3659] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3659))
| hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(X3658,X3659))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_9_finite__imageI])]) ).
fof(i_0_2590,plain,
! [X3672,X3673] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3673))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X3672,X3673))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_16_finite__imageI])]) ).
fof(i_0_2591,plain,
! [X3682,X3683] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3683))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X3682,X3683))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_21_finite__imageI])]) ).
fof(i_0_2592,plain,
! [X3662,X3663] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3663))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X3662,X3663))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_11_finite__imageI])]) ).
fof(i_0_2593,plain,
! [X3674,X3675] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3675))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X3674,X3675))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_17_finite__imageI])]) ).
fof(i_0_2594,plain,
! [X3684,X3685] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3685))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X3684,X3685))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_finite__imageI])]) ).
fof(i_0_2595,plain,
! [X3664,X3665] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3665))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X3664,X3665))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_12_finite__imageI])]) ).
fof(i_0_2596,plain,
! [X3704,X3705] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3705))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X3704,X3705))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_32_finite__imageI])]) ).
fof(i_0_2597,plain,
! [X3702,X3703] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3703))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X3702,X3703))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_31_finite__imageI])]) ).
fof(i_0_2598,plain,
! [X3700,X3701] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3701))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X3700,X3701))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_30_finite__imageI])]) ).
fof(i_0_2599,plain,
! [X3698,X3699] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3699))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(X3698,X3699))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_29_finite__imageI])]) ).
fof(i_0_2600,plain,
! [X3696,X3697] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3697))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X3696,X3697))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_28_finite__imageI])]) ).
fof(i_0_2601,plain,
! [X3718,X3719] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3719))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X3718,X3719))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_39_finite__imageI])]) ).
fof(i_0_2602,plain,
! [X3714,X3715] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3715))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(X3714,X3715))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_37_finite__imageI])]) ).
fof(i_0_2603,plain,
! [X3712,X3713] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3713))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(X3712,X3713))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_36_finite__imageI])]) ).
fof(i_0_2604,plain,
! [X3710,X3711] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3711))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(X3710,X3711))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_35_finite__imageI])]) ).
fof(i_0_2605,plain,
! [X3708,X3709] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3709))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(X3708,X3709))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_34_finite__imageI])]) ).
fof(i_0_2606,plain,
! [X3706,X3707] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3707))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(X3706,X3707))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_33_finite__imageI])]) ).
fof(i_0_2607,plain,
! [X3690,X3691] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3691))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X3690,X3691))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_25_finite__imageI])]) ).
fof(i_0_2608,plain,
! [X3688,X3689] :
( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3689))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(X3688,X3689))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_24_finite__imageI])]) ).
fof(i_0_2609,plain,
! [X3692,X3693] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3693))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X3692,X3693))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_26_finite__imageI])]) ).
fof(i_0_2610,plain,
! [X3694,X3695] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3695))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X3694,X3695))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_27_finite__imageI])]) ).
fof(i_0_2611,plain,
! [X3686,X3687] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3687))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X3686,X3687))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_23_finite__imageI])]) ).
fof(i_0_2612,plain,
! [X3666,X3667] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3667))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X3666,X3667))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_13_finite__imageI])]) ).
fof(i_0_2613,plain,
! [X3676,X3677] :
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3677))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X3676,X3677))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_18_finite__imageI])]) ).
fof(i_0_2614,plain,
! [X3716,X3717] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3717))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X3716,X3717))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_38_finite__imageI])]) ).
fof(i_0_2615,plain,
! [X5008,X5010,X5011] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk98_1(X5008)),X5008))
| X5008 = bot_bot_fun_nat_bool )
& ( X5010 != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X5011),X5010)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1584])])])])]) ).
fof(i_0_2616,plain,
! [X4947,X4948] :
( X4948 != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4947),X4948)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1585])]) ).
fof(i_0_2617,plain,
! [X5004,X5006,X5007] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk97_1(X5004)),X5004))
| X5004 = bot_bot_fun_int_bool )
& ( X5006 != bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X5007),X5006)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1586])])])])]) ).
fof(i_0_2618,plain,
! [X4945,X4946] :
( X4946 != bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4945),X4946)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1587])]) ).
fof(i_0_2619,plain,
! [X4951,X4952] :
( X4952 != bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4951),X4952)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1588])]) ).
fof(i_0_2620,plain,
! [X4949,X4950] :
( X4950 != bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4949),X4950)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1589])]) ).
fof(i_0_2621,plain,
! [X6050,X6051] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6050),X6051))
| X6051 != zero_zero_nat ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_936_gr__implies__not0])]) ).
fof(i_0_2622,plain,
! [X4994,X4995,X4996] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4995),X4994))
| X4994 != bot_bot_fun_nat_bool )
& ( X4996 = bot_bot_fun_nat_bool
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk94_1(X4996)),X4996)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_528_ex__in__conv])])])])]) ).
fof(i_0_2623,plain,
! [X4990,X4991,X4992] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4991),X4990))
| X4990 != bot_bot_fun_int_bool )
& ( X4992 = bot_bot_fun_int_bool
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk93_1(X4992)),X4992)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_527_ex__in__conv])])])])]) ).
fof(i_0_2624,plain,
! [X5298,X5299,X5300,X5301] :
( ( X5298 != X5299
| X5300 = X5301
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X5298),X5299) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X5300),X5301) )
& ( X5300 != X5301
| X5298 = X5299
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X5298),X5299) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X5300),X5301) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_669_diff__eq__diff__eq])])]) ).
fof(i_0_2625,plain,
! [X6706,X6707] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X6706),X6707))
| X6706 = X6707 ),
inference(variable_rename,[status(thm)],[i_0_1590]) ).
fof(i_0_2626,plain,
! [X6702,X6703] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X6702),X6703))
| X6702 = X6703 ),
inference(variable_rename,[status(thm)],[i_0_1591]) ).
fof(i_0_2627,plain,
! [X6665,X6666] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X6665),X6666))
| X6665 = X6666 ),
inference(variable_rename,[status(thm)],[i_0_1592]) ).
fof(i_0_2628,plain,
! [X6661,X6662] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X6661),X6662))
| X6661 = X6662 ),
inference(variable_rename,[status(thm)],[i_0_1593]) ).
fof(i_0_2629,plain,
! [X5869] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5869),hAPP_nat_nat(suc,X5869))),
inference(variable_rename,[status(thm)],[fact_855_lessI]) ).
fof(i_0_2630,plain,
! [X6150,X6151,X6152] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6150),X6151) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6152),X6151)
| X6150 = X6152
| X6151 = zero_zero_nat )
& ( X6150 != X6152
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6150),X6151) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6152),X6151) )
& ( X6151 != zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6150),X6151) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6152),X6151) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_982_mult__cancel2])])]) ).
fof(i_0_2631,plain,
! [X6320,X6321,X6322] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6320),X6321) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6320),X6322)
| X6320 = zero_zero_nat
| X6321 = X6322 )
& ( X6320 != zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6320),X6321) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6320),X6322) )
& ( X6321 != X6322
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6320),X6321) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6320),X6322) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1057_nat__mult__eq__cancel__disj])])]) ).
fof(i_0_2632,plain,
! [X6147,X6148,X6149] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6147),X6148) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6147),X6149)
| X6148 = X6149
| X6147 = zero_zero_nat )
& ( X6148 != X6149
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6147),X6148) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6147),X6149) )
& ( X6147 != zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6147),X6148) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6147),X6149) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_981_mult__cancel1])])]) ).
fof(i_0_2633,plain,
! [X5878] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5878),X5878)),
inference(variable_rename,[status(thm)],[i_0_1594]) ).
fof(i_0_2634,plain,
! [X5873] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X5873),X5873)),
inference(variable_rename,[status(thm)],[i_0_1595]) ).
fof(i_0_2635,plain,
! [X6038,X6039] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6038),X6039) != zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6039),X6038) != zero_zero_nat
| X6038 = X6039 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_926_diffs0__imp__equal])]) ).
cnf(i_0_2636,plain,
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
| hAPP_nat_nat(suc,number_number_of_nat(X1)) = number_number_of_nat(succ(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1596]) ).
fof(i_0_2637,plain,
! [X5702,X5703,X5704] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5702),X5703) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5704),X5703)
| X5702 = X5704 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_796_add__right__imp__eq])]) ).
fof(i_0_2638,plain,
! [X5684,X5685,X5686] :
( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5684),X5685) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5686),X5685)
| X5684 = X5686 )
& ( X5684 != X5686
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5684),X5685) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5686),X5685) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_790_add__right__cancel])]) ).
fof(i_0_2639,plain,
! [X5719,X5720,X5721] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5719),X5720) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5721),X5720)
| X5719 = X5721 )
& ( X5719 != X5721
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5719),X5720) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5721),X5720) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_802_nat__add__right__cancel])]) ).
fof(i_0_2640,plain,
! [X5705,X5706,X5707] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5705),X5706) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5707),X5706)
| X5705 = X5707 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_797_add__right__imp__eq])]) ).
fof(i_0_2641,plain,
! [X5687,X5688,X5689] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5687),X5688) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5689),X5688)
| X5687 = X5689 )
& ( X5687 != X5689
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5687),X5688) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5689),X5688) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_791_add__right__cancel])]) ).
fof(i_0_2642,plain,
! [X5696,X5697,X5698] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5696),X5697) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5696),X5698)
| X5697 = X5698 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_794_add__imp__eq])]) ).
fof(i_0_2643,plain,
! [X5690,X5691,X5692] :
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5690),X5691) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5690),X5692)
| X5691 = X5692 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_792_add__left__imp__eq])]) ).
fof(i_0_2644,plain,
! [X5678,X5679,X5680] :
( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5678),X5679) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5678),X5680)
| X5679 = X5680 )
& ( X5679 != X5680
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5678),X5679) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X5678),X5680) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_788_add__left__cancel])]) ).
fof(i_0_2645,plain,
! [X5716,X5717,X5718] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5716),X5717) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5716),X5718)
| X5717 = X5718 )
& ( X5717 != X5718
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5716),X5717) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5716),X5718) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_801_nat__add__left__cancel])]) ).
fof(i_0_2646,plain,
! [X5699,X5700,X5701] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5699),X5700) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5699),X5701)
| X5700 = X5701 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_795_add__imp__eq])]) ).
fof(i_0_2647,plain,
! [X5693,X5694,X5695] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5693),X5694) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5693),X5695)
| X5694 = X5695 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_793_add__left__imp__eq])]) ).
fof(i_0_2648,plain,
! [X5681,X5682,X5683] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5681),X5682) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5681),X5683)
| X5682 = X5683 )
& ( X5682 != X5683
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5681),X5682) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5681),X5683) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_789_add__left__cancel])]) ).
fof(i_0_2649,plain,
! [X6036] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6036),zero_zero_nat))
| X6036 = zero_zero_nat )
& ( X6036 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X6036),zero_zero_nat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_924_le__0__eq])]) ).
fof(i_0_2650,plain,
! [X5210] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5210),bot_bot_nat))
| X5210 = bot_bot_nat )
& ( X5210 != bot_bot_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5210),bot_bot_nat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_624_bot__unique])]) ).
fof(i_0_2651,plain,
! [X5206] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X5206),bot_bot_nat))
| X5206 = bot_bot_nat ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_620_le__bot])]) ).
fof(i_0_2652,plain,
! [X5208] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5208),bot_bot_fun_nat_bool))
| X5208 = bot_bot_fun_nat_bool )
& ( X5208 != bot_bot_fun_nat_bool
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5208),bot_bot_fun_nat_bool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_622_bot__unique])]) ).
fof(i_0_2653,plain,
! [X5204] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5204),bot_bot_fun_nat_bool))
| X5204 = bot_bot_fun_nat_bool ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_618_le__bot])]) ).
fof(i_0_2654,plain,
! [X5191] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5191),bot_bot_fun_nat_bool))
| X5191 = bot_bot_fun_nat_bool )
& ( X5191 != bot_bot_fun_nat_bool
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5191),bot_bot_fun_nat_bool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_609_subset__empty])]) ).
fof(i_0_2655,plain,
! [X5209] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5209),bot_bot_fun_int_bool))
| X5209 = bot_bot_fun_int_bool )
& ( X5209 != bot_bot_fun_int_bool
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5209),bot_bot_fun_int_bool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_623_bot__unique])]) ).
fof(i_0_2656,plain,
! [X5205] :
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5205),bot_bot_fun_int_bool))
| X5205 = bot_bot_fun_int_bool ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_619_le__bot])]) ).
fof(i_0_2657,plain,
! [X5192] :
( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5192),bot_bot_fun_int_bool))
| X5192 = bot_bot_fun_int_bool )
& ( X5192 != bot_bot_fun_int_bool
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X5192),bot_bot_fun_int_bool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_610_subset__empty])]) ).
fof(i_0_2658,plain,
! [X6035] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X6035))),
inference(variable_rename,[status(thm)],[fact_923_zero__less__Suc]) ).
fof(i_0_2659,plain,
! [X6505] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X6505))),
inference(variable_rename,[status(thm)],[fact_1118_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).
fof(i_0_2660,plain,
! [X6470] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X6470))),
inference(variable_rename,[status(thm)],[fact_1096_zero__zle__int]) ).
fof(i_0_2661,plain,
! [X4972] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4972),bot_bot_fun_nat_bool)),
inference(variable_rename,[status(thm)],[i_0_1597]) ).
fof(i_0_2662,plain,
! [X4933] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4933),bot_bot_fun_nat_bool)),
inference(variable_rename,[status(thm)],[i_0_1598]) ).
fof(i_0_2663,plain,
! [X4971] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4971),bot_bot_fun_int_bool)),
inference(variable_rename,[status(thm)],[i_0_1599]) ).
fof(i_0_2664,plain,
! [X4932] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4932),bot_bot_fun_int_bool)),
inference(variable_rename,[status(thm)],[i_0_1600]) ).
fof(i_0_2665,plain,
! [X4974] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4974),bot_bo844097828e_bool)),
inference(variable_rename,[status(thm)],[i_0_1601]) ).
fof(i_0_2666,plain,
! [X4935] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4935),bot_bo844097828e_bool)),
inference(variable_rename,[status(thm)],[i_0_1602]) ).
fof(i_0_2667,plain,
! [X4973] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4973),bot_bot_fun_a_bool)),
inference(variable_rename,[status(thm)],[i_0_1603]) ).
fof(i_0_2668,plain,
! [X4934] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4934),bot_bot_fun_a_bool)),
inference(variable_rename,[status(thm)],[i_0_1604]) ).
fof(i_0_2669,plain,
! [X6054] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6054),zero_zero_nat)),
inference(variable_rename,[status(thm)],[i_0_1605]) ).
fof(i_0_2670,plain,
! [X6052] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6052),zero_zero_nat)),
inference(variable_rename,[status(thm)],[i_0_1606]) ).
fof(i_0_2671,plain,
! [X6033] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X6033),zero_zero_nat)),
inference(variable_rename,[status(thm)],[i_0_1607]) ).
fof(i_0_2672,plain,
! [X6573] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,X6573))),
inference(variable_rename,[status(thm)],[i_0_1608]) ).
fof(i_0_2673,plain,
! [X5149,X5150] :
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5149),bot_bot_fun_int_bool) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5150),bot_bot_fun_int_bool)
| X5149 = X5150 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_591_singleton__inject])]) ).
fof(i_0_2674,plain,
! [X5147,X5148] :
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5147),bot_bot_fun_nat_bool) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5148),bot_bot_fun_nat_bool)
| X5147 = X5148 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_590_singleton__inject])]) ).
cnf(i_0_2675,plain,
( hBOOL(hAPP_int_bool(X1,X2))
| collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X2)),X1)) = bot_bot_fun_int_bool ),
inference(split_conjunct,[status(thm)],[i_0_1567]) ).
cnf(i_0_2676,plain,
( hBOOL(hAPP_nat_bool(X1,X2))
| collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X2)),X1)) = bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_1568]) ).
fof(i_0_2677,plain,
! [X6053] :
( ( X6053 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6053)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6053))
| X6053 != zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_938_neq0__conv])]) ).
cnf(i_0_2678,plain,
collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X1)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(X1,semiri1621563631at_int))),
inference(split_conjunct,[status(thm)],[i_0_1609]) ).
fof(i_0_2679,plain,
! [X6082,X6083] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6082),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6082),X6083)) = zero_zero_nat,
inference(variable_rename,[status(thm)],[fact_954_diff__add__0]) ).
fof(i_0_2680,plain,
! [X6807,X6808,X6809] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X6807,X6808),X6809) = hAPP_bool_bool(hAPP_f1748468828l_bool(X6807,X6809),hAPP_f54304608l_bool(X6808,X6809)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo]) ).
fof(i_0_2681,plain,
! [X6804,X6805,X6806] : hAPP_f448129468l_bool(cOMBS_1912792529l_bool(X6804,X6805),X6806) = hAPP_bool_bool(hAPP_f1721100032l_bool(X6804,X6806),hAPP_f448129468l_bool(X6805,X6806)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo]) ).
fof(i_0_2682,plain,
! [X6819,X6820,X6821] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X6819,X6820),X6821) = hAPP_bool_bool(hAPP_f1476298914l_bool(X6819,X6821),hAPP_f1664156314l_bool(X6820,X6821)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O]) ).
fof(i_0_2683,plain,
! [X6768,X6769,X6770] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X6768,X6769),X6770) = hAPP_bool_bool(hAPP_f198738859l_bool(X6768,X6770),hAPP_fun_a_bool_bool(X6769,X6770)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_]) ).
fof(i_0_2684,plain,
! [X6735,X6736,X6737] : hAPP_nat_bool(cOMBS_nat_bool_bool(X6735,X6736),X6737) = hAPP_bool_bool(hAPP_n1006566506l_bool(X6735,X6737),hAPP_nat_bool(X6736,X6737)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).
fof(i_0_2685,plain,
! [X6732,X6733,X6734] : hAPP_int_bool(cOMBS_int_bool_bool(X6732,X6733),X6734) = hAPP_bool_bool(hAPP_i68813070l_bool(X6732,X6734),hAPP_int_bool(X6733,X6734)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).
fof(i_0_2686,plain,
! [X6741,X6742,X6743] : hAPP_pname_bool(cOMBS_568398431l_bool(X6741,X6742),X6743) = hAPP_bool_bool(hAPP_p393069232l_bool(X6741,X6743),hAPP_pname_bool(X6742,X6743)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).
fof(i_0_2687,plain,
! [X6696,X6697,X6698] : hAPP_a_bool(cOMBS_a_bool_bool(X6696,X6697),X6698) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X6696,X6698),hAPP_a_bool(X6697,X6698)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).
fof(i_0_2688,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(fof_simplification,[status(thm)],[fact_1193_rel__simps_I2_J]) ).
fof(i_0_2689,plain,
! [X6074,X6075] :
( ( X6074 = zero_zero_nat
| X6074 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6074),X6075) != hAPP_nat_nat(suc,zero_zero_nat) )
& ( X6075 = hAPP_nat_nat(suc,zero_zero_nat)
| X6074 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6074),X6075) != hAPP_nat_nat(suc,zero_zero_nat) )
& ( X6074 = zero_zero_nat
| X6075 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6074),X6075) != hAPP_nat_nat(suc,zero_zero_nat) )
& ( X6075 = hAPP_nat_nat(suc,zero_zero_nat)
| X6075 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6074),X6075) != hAPP_nat_nat(suc,zero_zero_nat) )
& ( X6074 != hAPP_nat_nat(suc,zero_zero_nat)
| X6075 != zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6074),X6075) = hAPP_nat_nat(suc,zero_zero_nat) )
& ( X6074 != zero_zero_nat
| X6075 != hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6074),X6075) = hAPP_nat_nat(suc,zero_zero_nat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_950_add__is__1])])]) ).
fof(i_0_2690,plain,
! [X6072,X6073] :
( ( X6072 = zero_zero_nat
| X6072 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6072),X6073) )
& ( X6073 = hAPP_nat_nat(suc,zero_zero_nat)
| X6072 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6072),X6073) )
& ( X6072 = zero_zero_nat
| X6073 = zero_zero_nat
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6072),X6073) )
& ( X6073 = hAPP_nat_nat(suc,zero_zero_nat)
| X6073 = zero_zero_nat
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6072),X6073) )
& ( X6072 != hAPP_nat_nat(suc,zero_zero_nat)
| X6073 != zero_zero_nat
| hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6072),X6073) )
& ( X6072 != zero_zero_nat
| X6073 != hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6072),X6073) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_949_one__is__add])])]) ).
fof(i_0_2691,plain,
! [X6525] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X6525)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X6525)),
inference(variable_rename,[status(thm)],[fact_1124_int__Suc]) ).
fof(i_0_2692,plain,
! [X6834,X6835,X6836] : hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(X6834),X6835),X6836) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(X6834,X6836),X6835),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool__007]) ).
fof(i_0_2693,plain,
! [X6837,X6838,X6839] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(X6837),X6838),X6839) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(X6837,X6839),X6838),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__008]) ).
fof(i_0_2694,plain,
! [X6888,X6889,X6890] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X6888),X6889),X6890) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X6888,X6890),X6889),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H]) ).
fof(i_0_2695,plain,
! [X6885,X6886,X6887] : hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(X6885),X6886),X6887) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(X6885,X6887),X6886),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__H]) ).
fof(i_0_2696,plain,
! [X6891,X6892,X6893] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X6891),X6892),X6893) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X6891,X6893),X6892),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_]) ).
fof(i_0_2697,plain,
! [X6882,X6883,X6884] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X6882),X6883),X6884) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X6882,X6884),X6883),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool]) ).
fof(i_0_2698,plain,
! [X6843,X6844,X6845] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X6843),X6844),X6845) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X6843,X6845),X6844),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_]) ).
fof(i_0_2699,plain,
! [X6840,X6841,X6842] : hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(X6840),X6841),X6842) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(X6840,X6842),X6841),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_]) ).
fof(i_0_2700,plain,
! [X6855,X6856,X6857] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X6855),X6856),X6857) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X6855,X6857),X6856),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It]) ).
fof(i_0_2701,plain,
! [X6825,X6826,X6827] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X6825),X6826),X6827) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X6825,X6827),X6826),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO]) ).
fof(i_0_2702,plain,
! [X6720,X6721,X6722] : hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(X6720),X6721),X6722) = hAPP_int_bool(hAPP_n1082236369t_bool(X6720,X6722),X6721),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Int__Oint_000tc__HOL__Obool_U]) ).
fof(i_0_2703,plain,
! [X6762,X6763,X6764] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(X6762),X6763),X6764) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X6762,X6764),X6763),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__]) ).
fof(i_0_2704,plain,
! [X6813,X6814,X6815] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(X6813),X6814),X6815) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X6813,X6815),X6814),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo]) ).
fof(i_0_2705,plain,
! [X6792,X6793,X6794] : hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(X6792),X6793),X6794) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(X6792,X6794),X6793),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_]) ).
fof(i_0_2706,plain,
! [X6723,X6724,X6725] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X6723),X6724),X6725) = hAPP_nat_bool(hAPP_n1699378549t_bool(X6723,X6725),X6724),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U]) ).
fof(i_0_2707,plain,
! [X6795,X6796,X6797] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X6795),X6796),X6797) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X6795,X6797),X6796),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).
fof(i_0_2708,plain,
! [X6759,X6760,X6761] : hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(X6759),X6760),X6761) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(X6759,X6761),X6760),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__]) ).
fof(i_0_2709,plain,
! [X6810,X6811,X6812] : hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(X6810),X6811),X6812) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(X6810,X6812),X6811),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo]) ).
fof(i_0_2710,plain,
! [X6789,X6790,X6791] : hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(X6789),X6790),X6791) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(X6789,X6791),X6790),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).
fof(i_0_2711,plain,
! [X6690,X6691,X6692] : hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(X6690),X6691),X6692) = hAPP_a_bool(hAPP_int_fun_a_bool(X6690,X6692),X6691),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000t__a_000tc__HOL__Obool_U]) ).
fof(i_0_2712,plain,
! [X6717,X6718,X6719] : hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(X6717),X6718),X6719) = hAPP_int_bool(hAPP_i1948725293t_bool(X6717,X6719),X6718),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U]) ).
fof(i_0_2713,plain,
! [X6786,X6787,X6788] : hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(X6786),X6787),X6788) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(X6786,X6788),X6787),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_]) ).
fof(i_0_2714,plain,
! [X6822,X6823,X6824] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X6822),X6823),X6824) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X6822,X6824),X6823),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob]) ).
fof(i_0_2715,plain,
! [X6744,X6745,X6746] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X6744),X6745),X6746) = hAPP_pname_bool(hAPP_p61793385e_bool(X6744,X6746),X6745),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U]) ).
fof(i_0_2716,plain,
! [X6699,X6700,X6701] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X6699),X6700),X6701) = hAPP_a_bool(hAPP_p1534023578a_bool(X6699,X6701),X6700),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U]) ).
fof(i_0_2717,plain,
! [X6777,X6778,X6779] : hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(X6777),X6778),X6779) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(X6777,X6779),X6778),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a]) ).
fof(i_0_2718,plain,
! [X6753,X6754,X6755] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X6753),X6754),X6755) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X6753,X6755),X6754),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo]) ).
fof(i_0_2719,plain,
! [X6677,X6678,X6679] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X6677),X6678),X6679) = hAPP_a_bool(hAPP_a_fun_a_bool(X6677,X6679),X6678),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U]) ).
cnf(i_0_2720,plain,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X1)))),
inference(split_conjunct,[status(thm)],[i_0_1610]) ).
cnf(i_0_2721,plain,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X1)))),
inference(split_conjunct,[status(thm)],[i_0_1611]) ).
fof(i_0_2722,plain,
! [X6632,X6633] :
( ~ hBOOL(X6633)
| ~ hBOOL(X6632)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X6633),X6632)) ),
inference(variable_rename,[status(thm)],[i_0_1612]) ).
fof(i_0_2723,plain,
! [X5397] :
( ~ is_a(X5397)
| hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5397),bot_bot_fun_a_bool)) = X5397 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_696_the__elem__eq])]) ).
fof(i_0_2724,plain,
! [X6186,X6187] :
( ( X6186 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6186),X6187) != hAPP_nat_nat(suc,zero_zero_nat) )
& ( X6187 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6186),X6187) != hAPP_nat_nat(suc,zero_zero_nat) )
& ( X6186 != hAPP_nat_nat(suc,zero_zero_nat)
| X6187 != hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6186),X6187) = hAPP_nat_nat(suc,zero_zero_nat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_997_mult__eq__1__iff])])]) ).
cnf(i_0_2725,plain,
( number_number_of_int(X2) = zero_zero_int
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2)))
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
| number_number_of_nat(X2) != number_number_of_nat(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1566]) ).
fof(i_0_2726,plain,
! [X6647,X6648] :
( ~ hBOOL(X6648)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X6647),X6648)) ),
inference(variable_rename,[status(thm)],[i_0_1613]) ).
fof(i_0_2727,plain,
! [X6638,X6639] :
( ~ hBOOL(X6639)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X6639),X6638)) ),
inference(variable_rename,[status(thm)],[i_0_1614]) ).
fof(i_0_2728,plain,
! [X6640,X6641] :
( ~ hBOOL(X6641)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X6640),X6641)) ),
inference(variable_rename,[status(thm)],[i_0_1615]) ).
fof(i_0_2729,plain,
! [X5541] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X5541)),one_one_nat) = X5541,
inference(variable_rename,[status(thm)],[fact_746_diff__Suc__1]) ).
fof(i_0_2730,plain,
! [X5399] : hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5399),bot_bot_fun_int_bool)) = X5399,
inference(variable_rename,[status(thm)],[fact_698_the__elem__eq]) ).
fof(i_0_2731,plain,
! [X5398] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5398),bot_bot_fun_nat_bool)) = X5398,
inference(variable_rename,[status(thm)],[fact_697_the__elem__eq]) ).
cnf(i_0_2732,plain,
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2)))
| number_number_of_nat(X2) = number_number_of_nat(X1)
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
| number_number_of_int(X2) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[i_0_1566]) ).
fof(i_0_2733,plain,
! [X6645,X6646] :
( hBOOL(X6646)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X6646),X6645)) ),
inference(variable_rename,[status(thm)],[help_fimplies_1_1_U]) ).
fof(i_0_2734,plain,
! [X6852,X6853,X6854] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X6852,X6853),X6854) = hAPP_b589554111l_bool(X6852,hAPP_f1664156314l_bool(X6853,X6854)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011]) ).
fof(i_0_2735,plain,
! [X6849,X6850,X6851] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X6849,X6850),X6851) = hAPP_b589554111l_bool(X6849,hAPP_f54304608l_bool(X6850,X6851)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010]) ).
fof(i_0_2736,plain,
! [X6846,X6847,X6848] : hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(X6846,X6847),X6848) = hAPP_b589554111l_bool(X6846,hAPP_f448129468l_bool(X6847,X6848)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009]) ).
fof(i_0_2737,plain,
! [X6867,X6868,X6869] : hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(X6867,X6868),X6869) = hAPP_f284875647l_bool(X6867,hAPP_n1082236369t_bool(X6868,X6869)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__013]) ).
fof(i_0_2738,plain,
! [X6870,X6871,X6872] : hAPP_i1718399025l_bool(cOMBB_516767136ol_int(X6870,X6871),X6872) = hAPP_f103356543l_bool(X6870,hAPP_i418383825t_bool(X6871,X6872)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_]) ).
fof(i_0_2739,plain,
! [X6828,X6829,X6830] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X6828,X6829),X6830) = hAPP_b589554111l_bool(X6828,hAPP_fun_a_bool_bool(X6829,X6830)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006]) ).
fof(i_0_2740,plain,
! [X6816,X6817,X6818] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X6816,X6817),X6818) = hAPP_b589554111l_bool(X6816,hAPP_pname_bool(X6817,X6818)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_005]) ).
fof(i_0_2741,plain,
! [X6801,X6802,X6803] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X6801,X6802),X6803) = hAPP_b589554111l_bool(X6801,hAPP_nat_bool(X6802,X6803)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_004]) ).
fof(i_0_2742,plain,
! [X6798,X6799,X6800] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X6798,X6799),X6800) = hAPP_b589554111l_bool(X6798,hAPP_int_bool(X6799,X6800)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_003]) ).
fof(i_0_2743,plain,
! [X6765,X6766,X6767] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X6765,X6766),X6767) = hAPP_b589554111l_bool(X6765,hAPP_a_bool(X6766,X6767)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo]) ).
fof(i_0_2744,plain,
! [X6771,X6772,X6773] : hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(X6771,X6772),X6773) = hAPP_i1948725293t_bool(X6771,hAPP_nat_int(X6772,X6773)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_]) ).
fof(i_0_2745,plain,
! [X6864,X6865,X6866] : hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(X6864,X6865),X6866) = hAPP_f284875647l_bool(X6864,hAPP_i1948725293t_bool(X6865,X6866)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_]) ).
fof(i_0_2746,plain,
! [X6831,X6832,X6833] : hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(X6831,X6832),X6833) = hAPP_n215258509l_bool(X6831,hAPP_nat_nat(X6832,X6833)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO]) ).
fof(i_0_2747,plain,
! [X6873,X6874,X6875] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(X6873,X6874),X6875) = hAPP_f103356543l_bool(X6873,hAPP_n1699378549t_bool(X6874,X6875)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__014]) ).
fof(i_0_2748,plain,
! [X6774,X6775,X6776] : hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(X6774,X6775),X6776) = hAPP_n1699378549t_bool(X6774,hAPP_nat_nat(X6775,X6776)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).
fof(i_0_2749,plain,
! [X6879,X6880,X6881] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(X6879,X6880),X6881) = hAPP_f434788991l_bool(X6879,hAPP_n1025906991e_bool(X6880,X6881)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_015]) ).
fof(i_0_2750,plain,
! [X6861,X6862,X6863] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(X6861,X6862),X6863) = hAPP_f1631501043l_bool(X6861,hAPP_nat_fun_a_bool(X6862,X6863)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___012]) ).
fof(i_0_2751,plain,
! [X6714,X6715,X6716] : hAPP_nat_bool(cOMBB_int_bool_nat(X6714,X6715),X6716) = hAPP_int_bool(X6714,hAPP_nat_int(X6715,X6716)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Nat__Onat_U]) ).
fof(i_0_2752,plain,
! [X6783,X6784,X6785] : hAPP_nat_bool(cOMBB_955900739ol_nat(X6783,X6784),X6785) = hAPP_f54304608l_bool(X6783,hAPP_n1699378549t_bool(X6784,X6785)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo]) ).
fof(i_0_2753,plain,
! [X6729,X6730,X6731] : hAPP_nat_bool(cOMBB_bool_bool_nat(X6729,X6730),X6731) = hAPP_bool_bool(X6729,hAPP_nat_bool(X6730,X6731)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U]) ).
fof(i_0_2754,plain,
! [X6876,X6877,X6878] : hAPP_i1587699435l_bool(cOMBB_607112096ol_int(X6876,X6877),X6878) = hAPP_f434788991l_bool(X6876,hAPP_i7355787e_bool(X6877,X6878)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It]) ).
fof(i_0_2755,plain,
! [X6858,X6859,X6860] : hAPP_i888906320l_bool(cOMBB_313729068ol_int(X6858,X6859),X6860) = hAPP_f1631501043l_bool(X6858,hAPP_int_fun_a_bool(X6859,X6860)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__]) ).
fof(i_0_2756,plain,
! [X6747,X6748,X6749] : hAPP_int_fun_a_bool(cOMBB_375279840ol_int(X6747,X6748),X6749) = hAPP_a_fun_a_bool(X6747,hAPP_int_a(X6748,X6749)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Int__Oint]) ).
fof(i_0_2757,plain,
! [X6780,X6781,X6782] : hAPP_int_bool(cOMBB_1418110531ol_int(X6780,X6781),X6782) = hAPP_f448129468l_bool(X6780,hAPP_i1948725293t_bool(X6781,X6782)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo]) ).
fof(i_0_2758,plain,
! [X6726,X6727,X6728] : hAPP_int_bool(cOMBB_bool_bool_int(X6726,X6727),X6728) = hAPP_bool_bool(X6726,hAPP_int_bool(X6727,X6728)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Int__Oint_U]) ).
fof(i_0_2759,plain,
! [X6756,X6757,X6758] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X6756,X6757),X6758) = hAPP_a_fun_a_bool(X6756,hAPP_pname_a(X6757,X6758)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna]) ).
fof(i_0_2760,plain,
! [X6738,X6739,X6740] : hAPP_pname_bool(cOMBB_647938656_pname(X6738,X6739),X6740) = hAPP_bool_bool(X6738,hAPP_pname_bool(X6739,X6740)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U]) ).
fof(i_0_2761,plain,
! [X6750,X6751,X6752] : hAPP_a_bool(cOMBB_1273333599bool_a(X6750,X6751),X6752) = hAPP_fun_a_bool_bool(X6750,hAPP_a_fun_a_bool(X6751,X6752)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__]) ).
fof(i_0_2762,plain,
! [X6693,X6694,X6695] : hAPP_a_bool(cOMBB_bool_bool_a(X6693,X6694),X6695) = hAPP_bool_bool(X6693,hAPP_a_bool(X6694,X6695)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U]) ).
fof(i_0_2763,plain,
! [X6708,X6709] :
( X6708 != X6709
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X6708),X6709)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T]) ).
fof(i_0_2764,plain,
! [X4722,X4723] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4722),X4723))
| X4722 != X4723 )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4723),X4722))
| X4722 != X4723 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1616])])]) ).
fof(i_0_2765,plain,
! [X4665,X4666] :
( X4665 != X4666
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4665),X4666)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_408_equalityD1])]) ).
fof(i_0_2766,plain,
! [X4438,X4439] :
( X4438 != X4439
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4438),X4439)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_314_order__eq__refl])]) ).
fof(i_0_2767,plain,
! [X4671,X4672] :
( X4671 != X4672
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4672),X4671)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_411_equalityD2])]) ).
fof(i_0_2768,plain,
! [X6704,X6705] :
( X6704 != X6705
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X6704),X6705)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T]) ).
fof(i_0_2769,plain,
! [X4720,X4721] :
( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4720),X4721))
| X4720 != X4721 )
& ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4721),X4720))
| X4720 != X4721 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1617])])]) ).
fof(i_0_2770,plain,
! [X4663,X4664] :
( X4663 != X4664
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4663),X4664)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_407_equalityD1])]) ).
fof(i_0_2771,plain,
! [X4436,X4437] :
( X4436 != X4437
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4436),X4437)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_313_order__eq__refl])]) ).
fof(i_0_2772,plain,
! [X4669,X4670] :
( X4669 != X4670
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4670),X4669)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_410_equalityD2])]) ).
fof(i_0_2773,plain,
! [X6712,X6713] :
( X6712 != X6713
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X6712),X6713)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T]) ).
fof(i_0_2774,plain,
! [X6688,X6689] :
( X6688 != X6689
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X6688),X6689)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T]) ).
fof(i_0_2775,plain,
! [X4724,X4725] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4724),X4725))
| X4724 != X4725 )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4725),X4724))
| X4724 != X4725 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1618])])]) ).
fof(i_0_2776,plain,
! [X4667,X4668] :
( X4667 != X4668
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4667),X4668)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_409_equalityD1])]) ).
fof(i_0_2777,plain,
! [X4444,X4445] :
( X4444 != X4445
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4444),X4445)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_317_order__eq__refl])]) ).
fof(i_0_2778,plain,
! [X4673,X4674] :
( X4673 != X4674
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4674),X4673)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_412_equalityD2])]) ).
fof(i_0_2779,plain,
! [X6667,X6668] :
( X6667 != X6668
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X6667),X6668)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__Nat__Onat_T]) ).
fof(i_0_2780,plain,
! [X4442,X4443] :
( X4442 != X4443
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4442),X4443)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_316_order__eq__refl])]) ).
fof(i_0_2781,plain,
! [X3893,X3894] :
( X3893 != X3894
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3893),X3894)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_128_eq__imp__le])]) ).
fof(i_0_2782,plain,
! [X6663,X6664] :
( X6663 != X6664
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X6663),X6664)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__Int__Oint_T]) ).
fof(i_0_2783,plain,
! [X4440,X4441] :
( X4440 != X4441
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4440),X4441)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_315_order__eq__refl])]) ).
fof(i_0_2784,plain,
! [X6671,X6672] :
( X6671 != X6672
| hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X6671),X6672)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__Com__Opname_T]) ).
fof(i_0_2785,plain,
! [X6653,X6654] :
( X6653 != X6654
| hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X6653),X6654)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000t__a_T]) ).
fof(i_0_2786,plain,
! [X5282,X5283,X5284] : hAPP_nat_nat(nat_case_nat(X5282,X5283),hAPP_nat_nat(suc,X5284)) = hAPP_nat_nat(X5283,X5284),
inference(variable_rename,[status(thm)],[fact_663_nat__case__Suc]) ).
fof(i_0_2787,plain,
! [X4655] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4655),X4655)),
inference(variable_rename,[status(thm)],[fact_402_subset__refl]) ).
fof(i_0_2788,plain,
! [X4418] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4418),X4418)),
inference(variable_rename,[status(thm)],[fact_302_order__refl]) ).
fof(i_0_2789,plain,
! [X4654] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4654),X4654)),
inference(variable_rename,[status(thm)],[fact_401_subset__refl]) ).
fof(i_0_2790,plain,
! [X4417] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4417),X4417)),
inference(variable_rename,[status(thm)],[fact_301_order__refl]) ).
fof(i_0_2791,plain,
! [X4656] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4656),X4656)),
inference(variable_rename,[status(thm)],[fact_403_subset__refl]) ).
fof(i_0_2792,plain,
! [X4421] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X4421),X4421)),
inference(variable_rename,[status(thm)],[fact_305_order__refl]) ).
fof(i_0_2793,plain,
! [X4420] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4420),X4420)),
inference(variable_rename,[status(thm)],[fact_304_order__refl]) ).
fof(i_0_2794,plain,
! [X3897] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3897),X3897)),
inference(variable_rename,[status(thm)],[fact_130_le__refl]) ).
fof(i_0_2795,plain,
! [X6291] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X6291),X6291)),
inference(variable_rename,[status(thm)],[fact_1044_zle__refl]) ).
fof(i_0_2796,plain,
! [X4419] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4419),X4419)),
inference(variable_rename,[status(thm)],[fact_303_order__refl]) ).
fof(i_0_2797,plain,
! [X6244,X6245] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6244),X6245) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6245),X6244),
inference(variable_rename,[status(thm)],[fact_1021_zmult__commute]) ).
fof(i_0_2798,plain,
! [X6289,X6290] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6289),X6290) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6290),X6289),
inference(variable_rename,[status(thm)],[fact_1043_zadd__commute]) ).
fof(i_0_2799,plain,
! [X6235,X6236] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6235),X6236) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6236),X6235),
inference(variable_rename,[status(thm)],[fact_1016_nat__mult__commute]) ).
fof(i_0_2800,plain,
! [X5708,X5709] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5708),X5709) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5709),X5708),
inference(variable_rename,[status(thm)],[fact_798_nat__add__commute]) ).
fof(i_0_2801,plain,
! [X6049] :
( X6049 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X6049)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_935_gr0I])]) ).
fof(i_0_2802,plain,
! [X5228] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X5228)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5228),bot_bot_fun_a_bool),
inference(variable_rename,[status(thm)],[fact_636_singleton__conv]) ).
cnf(i_0_2803,plain,
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
| X2 = X1
| hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X2)))
| number_number_of_nat(X2) != number_number_of_nat(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1566]) ).
fof(i_0_2804,plain,
! [X5212] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X5212)),
inference(variable_rename,[status(thm)],[fact_626_bot__least]) ).
fof(i_0_2805,plain,
! [X4942] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X4942)),
inference(variable_rename,[status(thm)],[fact_501_empty__subsetI]) ).
fof(i_0_2806,plain,
! [X5213] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X5213)),
inference(variable_rename,[status(thm)],[fact_627_bot__least]) ).
fof(i_0_2807,plain,
! [X4943] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X4943)),
inference(variable_rename,[status(thm)],[fact_502_empty__subsetI]) ).
fof(i_0_2808,plain,
! [X5215] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X5215)),
inference(variable_rename,[status(thm)],[fact_629_bot__least]) ).
fof(i_0_2809,plain,
! [X4944] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X4944)),
inference(variable_rename,[status(thm)],[fact_503_empty__subsetI]) ).
fof(i_0_2810,plain,
! [X6037] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X6037)),
inference(variable_rename,[status(thm)],[fact_925_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_2811,plain,
! [X6034] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X6034)),
inference(variable_rename,[status(thm)],[fact_922_le0]) ).
fof(i_0_2812,plain,
! [X5214] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),X5214)),
inference(variable_rename,[status(thm)],[fact_628_bot__least]) ).
fof(i_0_2813,plain,
! [X5296,X5297] :
( ( X5297 != bot_bo844097828e_bool
| image_pname_a(cOMBK_a_pname(X5296),X5297) = bot_bot_fun_a_bool
| ~ is_fun_pname_bool(X5297) )
& ( X5297 = bot_bo844097828e_bool
| image_pname_a(cOMBK_a_pname(X5296),X5297) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5296),bot_bot_fun_a_bool)
| ~ is_fun_pname_bool(X5297) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_668_image__constant__conv])])]) ).
fof(i_0_2814,plain,
! [X6212,X6213] :
( X6212 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6212),X6213)
| X6213 = one_one_nat
| X6212 = zero_zero_nat ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1007_mult__eq__self__implies__10])]) ).
fof(i_0_2815,plain,
! [X5231] : collect_a(hAPP_a_fun_a_bool(fequal_a,X5231)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5231),bot_bot_fun_a_bool),
inference(variable_rename,[status(thm)],[fact_639_singleton__conv2]) ).
fof(i_0_2816,plain,
! [X4961,X4962,X4963] :
( ( collect_a(X4961) != bot_bot_fun_a_bool
| ~ is_a(X4962)
| ~ hBOOL(hAPP_a_bool(X4961,X4962)) )
& ( is_a(esk89_1(X4963))
| collect_a(X4963) = bot_bot_fun_a_bool )
& ( hBOOL(hAPP_a_bool(X4963,esk89_1(X4963)))
| collect_a(X4963) = bot_bot_fun_a_bool ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1619])])])])])]) ).
fof(i_0_2817,plain,
! [X4983,X4984,X4985] :
( ( bot_bot_fun_a_bool != collect_a(X4983)
| ~ is_a(X4984)
| ~ hBOOL(hAPP_a_bool(X4983,X4984)) )
& ( is_a(esk92_1(X4985))
| bot_bot_fun_a_bool = collect_a(X4985) )
& ( hBOOL(hAPP_a_bool(X4985,esk92_1(X4985)))
| bot_bot_fun_a_bool = collect_a(X4985) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1620])])])])])]) ).
cnf(i_0_2818,plain,
( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X1)) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1621]) ).
cnf(i_0_2819,plain,
( hAPP_nat_nat(suc,number_number_of_nat(X1)) = one_one_nat
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1596]) ).
fof(i_0_2820,plain,
! [X6145,X6146] :
( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6145),X6146) != zero_zero_nat
| X6145 = zero_zero_nat
| X6146 = zero_zero_nat )
& ( X6145 != zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6145),X6146) = zero_zero_nat )
& ( X6146 != zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6145),X6146) = zero_zero_nat ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_980_mult__is__0])])]) ).
fof(i_0_2821,plain,
! [X6043,X6044] :
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6043),X6044) != X6043
| X6044 = zero_zero_nat ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_931_add__eq__self__zero])]) ).
fof(i_0_2822,plain,
! [X6045,X6046] :
( ( X6045 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6045),X6046) != zero_zero_nat )
& ( X6046 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6045),X6046) != zero_zero_nat )
& ( X6045 != zero_zero_nat
| X6046 != zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6045),X6046) = zero_zero_nat ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_932_add__is__0])])]) ).
fof(i_0_2823,plain,
! [X6180,X6181] :
( ( X6180 = one_one_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6180),X6181) != one_one_nat )
& ( X6181 = one_one_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6180),X6181) != one_one_nat )
& ( X6180 != one_one_nat
| X6181 != one_one_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6180),X6181) = one_one_nat ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_993_nat__mult__eq__1__iff])])]) ).
fof(i_0_2824,plain,
! [X6183,X6184] :
( ( X6183 = one_one_nat
| one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6183),X6184) )
& ( X6184 = one_one_nat
| one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6183),X6184) )
& ( X6183 != one_one_nat
| X6184 != one_one_nat
| one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6183),X6184) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_995_nat__1__eq__mult__iff])])]) ).
fof(i_0_2825,plain,
! [X5183,X5184] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5183),X5184) != bot_bot_fun_int_bool,
inference(variable_rename,[status(thm)],[fact_605_insert__not__empty]) ).
fof(i_0_2826,plain,
! [X5181,X5182] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5181),X5182) != bot_bot_fun_nat_bool,
inference(variable_rename,[status(thm)],[fact_604_insert__not__empty]) ).
fof(i_0_2827,plain,
! [X5179,X5180] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5179),X5180) != bot_bot_fun_a_bool,
inference(variable_rename,[status(thm)],[fact_603_insert__not__empty]) ).
fof(i_0_2828,plain,
! [X5187,X5188] : bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X5187),X5188),
inference(variable_rename,[status(thm)],[fact_607_empty__not__insert]) ).
fof(i_0_2829,plain,
! [X5189,X5190] : bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5189),X5190),
inference(variable_rename,[status(thm)],[fact_608_empty__not__insert]) ).
fof(i_0_2830,plain,
! [X5185,X5186] : bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X5185),X5186),
inference(variable_rename,[status(thm)],[fact_606_empty__not__insert]) ).
fof(i_0_2831,plain,
! [X5294,X5295] :
( ( X5295 != bot_bot_fun_nat_bool
| image_nat_int(cOMBK_int_nat(X5294),X5295) = bot_bot_fun_int_bool )
& ( X5295 = bot_bot_fun_nat_bool
| image_nat_int(cOMBK_int_nat(X5294),X5295) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X5294),bot_bot_fun_int_bool) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_667_image__constant__conv])]) ).
cnf(i_0_2832,plain,
hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X1))) = hAPP_nat_nat(suc,X1),
inference(split_conjunct,[status(thm)],[i_0_1622]) ).
cnf(i_0_2833,plain,
collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X1)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool),
inference(split_conjunct,[status(thm)],[i_0_1623]) ).
cnf(i_0_2834,plain,
collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool),
inference(split_conjunct,[status(thm)],[i_0_1624]) ).
fof(i_0_2835,plain,
! [X6630] :
( ~ hBOOL(hAPP_bool_bool(fNot,X6630))
| ~ hBOOL(X6630) ),
inference(variable_rename,[status(thm)],[i_0_1625]) ).
cnf(i_0_2836,plain,
( bot_bot_fun_nat_bool != collect_nat(X1)
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1626]) ).
cnf(i_0_2837,plain,
( bot_bot_fun_int_bool != collect_int(X1)
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1627]) ).
cnf(i_0_2838,plain,
( collect_nat(X1) != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1628]) ).
cnf(i_0_2839,plain,
( collect_int(X1) != bot_bot_fun_int_bool
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1629]) ).
cnf(i_0_2840,plain,
collect_int(hAPP_i1948725293t_bool(fequal_int,X1)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool),
inference(split_conjunct,[status(thm)],[i_0_1630]) ).
fof(i_0_2841,plain,
! [X5856] : hAPP_nat_nat(suc,X5856) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X5856),one_one_nat),
inference(variable_rename,[status(thm)],[fact_850_Suc__eq__plus1]) ).
cnf(i_0_2842,plain,
collect_nat(hAPP_n1699378549t_bool(fequal_nat,X1)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool),
inference(split_conjunct,[status(thm)],[i_0_1631]) ).
fof(i_0_2843,plain,
! [X6502] : hAPP_f22106695ol_nat(finite_card_nat,X6502) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,X6502)),
inference(variable_rename,[status(thm)],[fact_1113_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J]) ).
fof(i_0_2844,plain,
! [X6006] : hAPP_n1699378549t_bool(ord_less_nat,X6006) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X6006)),
inference(variable_rename,[status(thm)],[fact_913_less__eq__Suc__le__raw]) ).
cnf(i_0_2845,plain,
( number_number_of_nat(X1) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1632]) ).
cnf(i_0_2846,plain,
( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(X1)))
| hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X1)) = number_number_of_int(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1621]) ).
fof(i_0_2847,plain,
! [X6655,X6656] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X6655),X6656) = X6655,
inference(variable_rename,[status(thm)],[help_If_1_1_If_000tc__Nat__Onat_T]) ).
fof(i_0_2848,plain,
! [X6657,X6658] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X6657),X6658) = X6658,
inference(variable_rename,[status(thm)],[help_If_2_1_If_000tc__Nat__Onat_T]) ).
fof(i_0_2849,plain,
! [X5855] : hAPP_nat_nat(suc,X5855) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X5855),
inference(variable_rename,[status(thm)],[fact_849_Suc__eq__plus1__left]) ).
fof(i_0_2850,plain,
! [X5021] :
( ( ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X5021))
| hBOOL(bot_bot_bool) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X5021)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_541_bot__fun__def])]) ).
fof(i_0_2851,plain,
! [X5018] :
( ( ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X5018))
| hBOOL(bot_bot_bool) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X5018)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_535_bot__apply])]) ).
fof(i_0_2852,plain,
! [X5022] :
( ( ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X5022))
| hBOOL(bot_bot_bool) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X5022)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_542_bot__fun__def])]) ).
fof(i_0_2853,plain,
! [X5019] :
( ( ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X5019))
| hBOOL(bot_bot_bool) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X5019)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_536_bot__apply])]) ).
fof(i_0_2854,plain,
! [X5023] :
( ( ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X5023))
| hBOOL(bot_bot_bool) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X5023)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_543_bot__fun__def])]) ).
fof(i_0_2855,plain,
! [X5020] :
( ( ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X5020))
| hBOOL(bot_bot_bool) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X5020)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_537_bot__apply])]) ).
cnf(i_0_2856,plain,
hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X1))) = X1,
inference(split_conjunct,[status(thm)],[i_0_1633]) ).
fof(i_0_2857,hypothesis,
! [X3615,X3616] :
( ~ is_fun1661590463l_bool(X3615)
| ~ is_fun_pname_bool(X3616)
| is_bool(hAPP_f1664156314l_bool(X3615,X3616)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool])]) ).
fof(i_0_2858,hypothesis,
! [X3607,X3608] :
( ~ is_fun949378684l_bool(X3607)
| ~ is_fun_a_bool(X3608)
| is_bool(hAPP_fun_a_bool_bool(X3607,X3608)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool])]) ).
fof(i_0_2859,plain,
! [X3573,X3574] :
( ~ is_fun_pname_bool(X3573)
| ~ is_pname(X3574)
| is_bool(hAPP_pname_bool(X3573,X3574)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool])]) ).
fof(i_0_2860,plain,
! [X3561,X3562] :
( ~ is_fun_a_bool(X3561)
| ~ is_a(X3562)
| is_bool(hAPP_a_bool(X3561,X3562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__HOL__Obool])]) ).
cnf(i_0_2861,plain,
( hBOOL(hAPP_nat_bool(X1,esk91_1(X1)))
| bot_bot_fun_nat_bool = collect_nat(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1626]) ).
cnf(i_0_2862,plain,
( hBOOL(hAPP_int_bool(X1,esk90_1(X1)))
| bot_bot_fun_int_bool = collect_int(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1627]) ).
cnf(i_0_2863,plain,
( hBOOL(hAPP_nat_bool(X1,esk88_1(X1)))
| collect_nat(X1) = bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_1628]) ).
cnf(i_0_2864,plain,
( hBOOL(hAPP_int_bool(X1,esk87_1(X1)))
| collect_int(X1) = bot_bot_fun_int_bool ),
inference(split_conjunct,[status(thm)],[i_0_1629]) ).
fof(i_0_2865,plain,
! [X4970] :
( ~ is_fun_a_bool(X4970)
| hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4970),bot_bot_fun_a_bool) = X4970 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_516_Diff__empty])]) ).
fof(i_0_2866,plain,
! [X6554,X6555] :
( ( hAPP_nat_int(semiri1621563631at_int,X6554) != hAPP_nat_int(semiri1621563631at_int,X6555)
| X6554 = X6555 )
& ( X6554 != X6555
| hAPP_nat_int(semiri1621563631at_int,X6554) = hAPP_nat_int(semiri1621563631at_int,X6555) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1139_transfer__int__nat__relations_I1_J])]) ).
fof(i_0_2867,plain,
! [X6541,X6542] :
( ( hAPP_nat_int(semiri1621563631at_int,X6541) != hAPP_nat_int(semiri1621563631at_int,X6542)
| X6541 = X6542 )
& ( X6541 != X6542
| hAPP_nat_int(semiri1621563631at_int,X6541) = hAPP_nat_int(semiri1621563631at_int,X6542) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1132_int__int__eq])]) ).
fof(i_0_2868,plain,
! [X3884,X3885] :
( ( hAPP_nat_nat(suc,X3884) != hAPP_nat_nat(suc,X3885)
| X3884 = X3885 )
& ( X3884 != X3885
| hAPP_nat_nat(suc,X3884) = hAPP_nat_nat(suc,X3885) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_123_nat_Oinject])]) ).
fof(i_0_2869,plain,
! [X3882,X3883] :
( hAPP_nat_nat(suc,X3882) != hAPP_nat_nat(suc,X3883)
| X3882 = X3883 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_122_Suc__inject])]) ).
fof(i_0_2870,plain,
! [X6547,X6548] :
( ( X6547 != X6548
| image_nat_int(semiri1621563631at_int,X6547) = image_nat_int(semiri1621563631at_int,X6548) )
& ( image_nat_int(semiri1621563631at_int,X6547) != image_nat_int(semiri1621563631at_int,X6548)
| X6547 = X6548 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1136_transfer__nat__int__set__relations_I3_J])]) ).
fof(i_0_2871,plain,
! [X6574] : abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X6574)) = hAPP_nat_int(semiri1621563631at_int,X6574),
inference(variable_rename,[status(thm)],[fact_1152_abs__int__eq]) ).
cnf(i_0_2872,plain,
~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(pls))),
inference(split_conjunct,[status(thm)],[i_0_1634]) ).
fof(i_0_2873,plain,
~ hBOOL(hAPP_int_bool(nat_neg,zero_zero_int)),
inference(fof_simplification,[status(thm)],[fact_1149_not__neg__0]) ).
fof(i_0_2874,plain,
~ hBOOL(hAPP_int_bool(nat_neg,one_one_int)),
inference(fof_simplification,[status(thm)],[fact_1148_not__neg__1]) ).
fof(i_0_2875,plain,
! [X3613,X3614] :
( ~ is_fun_pname_bool(X3614)
| is_pname(hAPP_f1297739591_pname(X3613,X3614)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname])]) ).
fof(i_0_2876,plain,
! [X3571,X3572] :
( ~ is_pname(X3572)
| is_pname(hAPP_pname_pname(X3571,X3572)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname])]) ).
fof(i_0_2877,plain,
! [X3605,X3606] :
( ~ is_fun_a_bool(X3606)
| is_a(hAPP_fun_a_bool_a(X3605,X3606)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a])]) ).
fof(i_0_2878,hypothesis,
! [X3569,X3570] :
( ~ is_pname(X3570)
| is_a(hAPP_pname_a(X3569,X3570)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000t__a])]) ).
fof(i_0_2879,plain,
! [X3559,X3560] :
( ~ is_a(X3560)
| is_a(hAPP_a_a(X3559,X3560)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000t__a])]) ).
fof(i_0_2880,plain,
! [X3631,X3632] :
( ~ is_fun1661590463l_bool(X3632)
| is_fun1661590463l_bool(hAPP_f559147733l_bool(X3631,X3632)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_002])]) ).
fof(i_0_2881,plain,
! [X3619,X3620] :
( ~ is_fun_pname_bool(X3620)
| is_fun1661590463l_bool(hAPP_f434788991l_bool(X3619,X3620)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc])]) ).
fof(i_0_2882,hypothesis,
! [X3579,X3580] :
( ~ is_pname(X3580)
| is_fun1661590463l_bool(hAPP_p338031245l_bool(X3579,X3580)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo])]) ).
fof(i_0_2883,plain,
! [X3525,X3526] :
( ~ is_fun_pname_bool(X3526)
| is_fun1661590463l_bool(image_47868345e_bool(X3525,X3526)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_])]) ).
fof(i_0_2884,plain,
! [X3517,X3518] :
( ~ is_fun_a_bool(X3518)
| is_fun1661590463l_bool(image_819518260e_bool(X3517,X3518)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J])]) ).
fof(i_0_2885,plain,
! [X3489,X3490] :
( ~ is_fun1661590463l_bool(X3490)
| is_fun1661590463l_bool(cOMBS_350070575l_bool(X3489,X3490)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t])]) ).
fof(i_0_2886,plain,
! [X3629,X3630] :
( ~ is_fun1661590463l_bool(X3630)
| is_bool(hAPP_f1935102916l_bool(X3629,X3630)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo])]) ).
fof(i_0_2887,plain,
! [X3625,X3626] :
( ~ is_fun949378684l_bool(X3626)
| is_bool(hAPP_f621171935l_bool(X3625,X3626)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__])]) ).
fof(i_0_2888,plain,
! [X3581,X3582] :
( ~ is_bool(X3582)
| is_bool(hAPP_bool_bool(X3581,X3582)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool])]) ).
fof(i_0_2889,plain,
! [X3627,X3628] :
( ~ is_fun949378684l_bool(X3628)
| is_fun949378684l_bool(hAPP_f2117159681l_bool(X3627,X3628)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___001])]) ).
fof(i_0_2890,hypothesis,
! [X3611,X3612] :
( ~ is_fun_a_bool(X3612)
| is_fun949378684l_bool(hAPP_f1631501043l_bool(X3611,X3612)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL])]) ).
fof(i_0_2891,hypothesis,
! [X3567,X3568] :
( ~ is_a(X3568)
| is_fun949378684l_bool(hAPP_a85458249l_bool(X3567,X3568)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J])]) ).
fof(i_0_2892,plain,
! [X3523,X3524] :
( ~ is_fun_pname_bool(X3524)
| is_fun949378684l_bool(image_112932426a_bool(X3523,X3524)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J])]) ).
fof(i_0_2893,plain,
! [X3515,X3516] :
( ~ is_fun_a_bool(X3516)
| is_fun949378684l_bool(image_a_fun_a_bool(X3515,X3516)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J])]) ).
fof(i_0_2894,plain,
! [X3487,X3488] :
( ~ is_fun949378684l_bool(X3488)
| is_fun949378684l_bool(cOMBS_1035972772l_bool(X3487,X3488)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo])]) ).
fof(i_0_2895,plain,
! [X3617,X3618] :
( ~ is_fun_pname_bool(X3618)
| is_fun_pname_bool(hAPP_f759274231e_bool(X3617,X3618)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op])]) ).
fof(i_0_2896,plain,
! [X3577,X3578] :
( ~ is_pname(X3578)
| is_fun_pname_bool(hAPP_p61793385e_bool(X3577,X3578)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J])]) ).
fof(i_0_2897,plain,
! [X3565,X3566] :
( ~ is_a(X3566)
| is_fun_pname_bool(hAPP_a93125764e_bool(X3565,X3566)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J])]) ).
fof(i_0_2898,plain,
! [X3549,X3550] :
( ~ is_fun1661590463l_bool(X3550)
| is_fun_pname_bool(image_1283814551_pname(X3549,X3550)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam])]) ).
fof(i_0_2899,plain,
! [X3545,X3546] :
( ~ is_fun949378684l_bool(X3546)
| is_fun_pname_bool(image_1854862208_pname(X3545,X3546)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname])]) ).
fof(i_0_2900,plain,
! [X3521,X3522] :
( ~ is_fun_pname_bool(X3522)
| is_fun_pname_bool(image_pname_pname(X3521,X3522)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname])]) ).
fof(i_0_2901,plain,
! [X3513,X3514] :
( ~ is_fun_a_bool(X3514)
| is_fun_pname_bool(image_a_pname(X3513,X3514)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000t__a_000tc__Com__Opname])]) ).
fof(i_0_2902,plain,
! [X3485,X3486] :
( ~ is_fun_pname_bool(X3486)
| is_fun_pname_bool(cOMBS_568398431l_bool(X3485,X3486)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool])]) ).
fof(i_0_2903,plain,
! [X3478,X3479] :
( ~ is_fun_pname_bool(X3479)
| is_fun_pname_bool(cOMBB_647938656_pname(X3478,X3479)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname])]) ).
fof(i_0_2904,hypothesis,
! [X3609,X3610] :
( ~ is_fun_a_bool(X3610)
| is_fun_a_bool(hAPP_f2050579477a_bool(X3609,X3610)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J])]) ).
fof(i_0_2905,plain,
! [X3575,X3576] :
( ~ is_pname(X3576)
| is_fun_a_bool(hAPP_p1534023578a_bool(X3575,X3576)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J])]) ).
fof(i_0_2906,plain,
! [X3563,X3564] :
( ~ is_a(X3564)
| is_fun_a_bool(hAPP_a_fun_a_bool(X3563,X3564)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J])]) ).
fof(i_0_2907,plain,
! [X3547,X3548] :
( ~ is_fun1661590463l_bool(X3548)
| is_fun_a_bool(image_876012084bool_a(X3547,X3548)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a])]) ).
fof(i_0_2908,plain,
! [X3543,X3544] :
( ~ is_fun949378684l_bool(X3544)
| is_fun_a_bool(image_fun_a_bool_a(X3543,X3544)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a])]) ).
fof(i_0_2909,hypothesis,
! [X3519,X3520] :
( ~ is_fun_pname_bool(X3520)
| is_fun_a_bool(image_pname_a(X3519,X3520)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000t__a])]) ).
fof(i_0_2910,plain,
! [X3511,X3512] :
( ~ is_fun_a_bool(X3512)
| is_fun_a_bool(image_a_a(X3511,X3512)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000t__a_000t__a])]) ).
fof(i_0_2911,plain,
! [X3483,X3484] :
( ~ is_fun_a_bool(X3484)
| is_fun_a_bool(cOMBS_a_bool_bool(X3483,X3484)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool])]) ).
fof(i_0_2912,plain,
! [X3480,X3481] :
( ~ is_fun949378684l_bool(X3480)
| is_fun_a_bool(cOMBB_1273333599bool_a(X3480,X3481)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__a])]) ).
fof(i_0_2913,plain,
! [X3476,X3477] :
( ~ is_fun_a_bool(X3477)
| is_fun_a_bool(cOMBB_bool_bool_a(X3476,X3477)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a])]) ).
fof(i_0_2914,plain,
! [X6040] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6040),X6040) = zero_zero_nat,
inference(variable_rename,[status(thm)],[fact_927_diff__self__eq__0]) ).
fof(i_0_2915,plain,
! [X4966] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4966),X4966) = bot_bot_fun_int_bool,
inference(variable_rename,[status(thm)],[fact_512_Diff__cancel]) ).
fof(i_0_2916,plain,
! [X4965] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4965),X4965) = bot_bot_fun_nat_bool,
inference(variable_rename,[status(thm)],[fact_511_Diff__cancel]) ).
fof(i_0_2917,plain,
! [X4967] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X4967),X4967) = bot_bot_fun_a_bool,
inference(variable_rename,[status(thm)],[fact_513_Diff__cancel]) ).
fof(i_0_2918,plain,
! [X6243] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X6243),one_one_int) = X6243,
inference(variable_rename,[status(thm)],[fact_1020_zmult__1__right]) ).
fof(i_0_2919,plain,
! [X6616] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6616),pls) = X6616,
inference(variable_rename,[status(thm)],[fact_1186_add__Pls__right]) ).
fof(i_0_2920,plain,
! [X6273] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X6273),zero_zero_int) = X6273,
inference(variable_rename,[status(thm)],[fact_1033_zadd__0__right]) ).
fof(i_0_2921,plain,
! [X6614] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X6614),pls) = X6614,
inference(variable_rename,[status(thm)],[fact_1184_diff__bin__simps_I1_J]) ).
fof(i_0_2922,plain,
! [X6182] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6182),one_one_nat) = X6182,
inference(variable_rename,[status(thm)],[fact_994_nat__mult__1__right]) ).
fof(i_0_2923,plain,
! [X6047] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X6047),zero_zero_nat) = X6047,
inference(variable_rename,[status(thm)],[fact_933_Nat_Oadd__0__right]) ).
fof(i_0_2924,plain,
! [X6041] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X6041),zero_zero_nat) = X6041,
inference(variable_rename,[status(thm)],[fact_928_minus__nat_Odiff__0]) ).
fof(i_0_2925,plain,
! [X4969] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X4969),bot_bot_fun_int_bool) = X4969,
inference(variable_rename,[status(thm)],[fact_515_Diff__empty]) ).
fof(i_0_2926,plain,
! [X4968] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X4968),bot_bot_fun_nat_bool) = X4968,
inference(variable_rename,[status(thm)],[fact_514_Diff__empty]) ).
fof(i_0_2927,plain,
! [X6144] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X6144),zero_zero_nat) = zero_zero_nat,
inference(variable_rename,[status(thm)],[fact_979_mult__0__right]) ).
fof(i_0_2928,plain,
! [X6242] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X6242) = X6242,
inference(variable_rename,[status(thm)],[fact_1019_zmult__1]) ).
fof(i_0_2929,plain,
! [X6615] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X6615) = X6615,
inference(variable_rename,[status(thm)],[fact_1185_add__Pls]) ).
fof(i_0_2930,plain,
! [X6274] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),X6274) = X6274,
inference(variable_rename,[status(thm)],[fact_1034_zadd__0]) ).
fof(i_0_2931,plain,
! [X6185] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),X6185) = X6185,
inference(variable_rename,[status(thm)],[fact_996_nat__mult__1]) ).
fof(i_0_2932,plain,
! [X6048] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X6048) = X6048,
inference(variable_rename,[status(thm)],[fact_934_plus__nat_Oadd__0]) ).
fof(i_0_2933,plain,
! [X6617] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),X6617) = pls,
inference(variable_rename,[status(thm)],[fact_1187_mult__Pls]) ).
fof(i_0_2934,plain,
! [X6143] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),X6143) = zero_zero_nat,
inference(variable_rename,[status(thm)],[fact_978_mult__0]) ).
fof(i_0_2935,plain,
! [X6042] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),X6042) = zero_zero_nat,
inference(variable_rename,[status(thm)],[fact_929_diff__0__eq__0]) ).
fof(i_0_2936,plain,
! [X4988] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),X4988) = bot_bot_fun_int_bool,
inference(variable_rename,[status(thm)],[fact_525_empty__Diff]) ).
fof(i_0_2937,plain,
! [X4987] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),X4987) = bot_bot_fun_nat_bool,
inference(variable_rename,[status(thm)],[fact_524_empty__Diff]) ).
fof(i_0_2938,plain,
! [X4989] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),X4989) = bot_bot_fun_a_bool,
inference(variable_rename,[status(thm)],[fact_526_empty__Diff]) ).
fof(i_0_2939,plain,
! [X6631] :
( hBOOL(X6631)
| hBOOL(hAPP_bool_bool(fNot,X6631)) ),
inference(variable_rename,[status(thm)],[help_fNot_2_1_U]) ).
fof(i_0_2940,plain,
! [X5196,X5197] :
( ( image_pname_a(X5196,X5197) != bot_bot_fun_a_bool
| X5197 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X5197) )
& ( X5197 != bot_bo844097828e_bool
| image_pname_a(X5196,X5197) = bot_bot_fun_a_bool
| ~ is_fun_pname_bool(X5197) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_613_image__is__empty])])]) ).
fof(i_0_2941,plain,
! [X5202,X5203] :
( ( bot_bot_fun_a_bool != image_pname_a(X5202,X5203)
| X5203 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X5203) )
& ( X5203 != bot_bo844097828e_bool
| bot_bot_fun_a_bool = image_pname_a(X5202,X5203)
| ~ is_fun_pname_bool(X5203) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_617_empty__is__image])])]) ).
fof(i_0_2942,plain,
! [X3583,X3584] : is_a(hAPP_int_a(X3583,X3584)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000t__a]) ).
fof(i_0_2943,plain,
! [X3603,X3604] : is_fun1661590463l_bool(hAPP_n850744903l_bool(X3603,X3604)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool]) ).
fof(i_0_2944,plain,
! [X3593,X3594] : is_fun1661590463l_bool(hAPP_i1587699435l_bool(X3593,X3594)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool]) ).
fof(i_0_2945,plain,
! [X3541,X3542] : is_fun1661590463l_bool(image_1655916159e_bool(X3541,X3542)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).
fof(i_0_2946,plain,
! [X3533,X3534] : is_fun1661590463l_bool(image_637364955e_bool(X3533,X3534)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).
fof(i_0_2947,plain,
! [X3643,X3644] : is_bool(hAPP_f937997336l_bool(X3643,X3644)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO]) ).
fof(i_0_2948,plain,
! [X3641,X3642] : is_bool(hAPP_f1593524852l_bool(X3641,X3642)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HO]) ).
fof(i_0_2949,plain,
! [X3639,X3640] : is_bool(hAPP_f389811538l_bool(X3639,X3640)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__]) ).
fof(i_0_2950,plain,
! [X3637,X3638] : is_bool(hAPP_f292226953l_bool(X3637,X3638)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_]) ).
fof(i_0_2951,plain,
! [X3635,X3636] : is_bool(hAPP_f1637334154l_bool(X3635,X3636)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_]) ).
fof(i_0_2952,plain,
! [X3633,X3634] : is_bool(hAPP_f215623910l_bool(X3633,X3634)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HOL__Obool_]) ).
fof(i_0_2953,plain,
! [X3623,X3624] : is_bool(hAPP_f54304608l_bool(X3623,X3624)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).
fof(i_0_2954,plain,
! [X3621,X3622] : is_bool(hAPP_f448129468l_bool(X3621,X3622)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).
fof(i_0_2955,hypothesis,
! [X3595,X3596] : is_bool(hAPP_nat_bool(X3595,X3596)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool]) ).
fof(i_0_2956,plain,
! [X3585,X3586] : is_bool(hAPP_int_bool(X3585,X3586)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool]) ).
fof(i_0_2957,plain,
! [X3505,X3506] : is_bool(finite795500164em_nat(X3505,X3506)),
inference(variable_rename,[status(thm)],[gsy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat]) ).
fof(i_0_2958,plain,
! [X3503,X3504] : is_bool(finite1432773856em_int(X3503,X3504)),
inference(variable_rename,[status(thm)],[gsy_c_Finite__Set_Ofolding__one__idem_000tc__Int__Oint]) ).
fof(i_0_2959,plain,
! [X3501,X3502] : is_bool(finite89670078_pname(X3501,X3502)),
inference(variable_rename,[status(thm)],[gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname]) ).
fof(i_0_2960,plain,
! [X3499,X3500] : is_bool(finite1819937229idem_a(X3499,X3500)),
inference(variable_rename,[status(thm)],[gsy_c_Finite__Set_Ofolding__one__idem_000t__a]) ).
fof(i_0_2961,plain,
! [X3497,X3498] : is_bool(finite988810631ne_nat(X3497,X3498)),
inference(variable_rename,[status(thm)],[gsy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat]) ).
fof(i_0_2962,plain,
! [X3495,X3496] : is_bool(finite1626084323ne_int(X3495,X3496)),
inference(variable_rename,[status(thm)],[gsy_c_Finite__Set_Ofolding__one_000tc__Int__Oint]) ).
fof(i_0_2963,plain,
! [X3493,X3494] : is_bool(finite1282449217_pname(X3493,X3494)),
inference(variable_rename,[status(thm)],[gsy_c_Finite__Set_Ofolding__one_000tc__Com__Opname]) ).
fof(i_0_2964,plain,
! [X3491,X3492] : is_bool(finite_folding_one_a(X3491,X3492)),
inference(variable_rename,[status(thm)],[gsy_c_Finite__Set_Ofolding__one_000t__a]) ).
fof(i_0_2965,plain,
! [X3601,X3602] : is_fun949378684l_bool(hAPP_n1414589940l_bool(X3601,X3602)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL]) ).
fof(i_0_2966,plain,
! [X3591,X3592] : is_fun949378684l_bool(hAPP_i888906320l_bool(X3591,X3592)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL]) ).
fof(i_0_2967,plain,
! [X3539,X3540] : is_fun949378684l_bool(image_nat_fun_a_bool(X3539,X3540)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).
fof(i_0_2968,plain,
! [X3531,X3532] : is_fun949378684l_bool(image_int_fun_a_bool(X3531,X3532)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).
fof(i_0_2969,plain,
! [X3599,X3600] : is_fun_pname_bool(hAPP_n1025906991e_bool(X3599,X3600)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).
fof(i_0_2970,plain,
! [X3589,X3590] : is_fun_pname_bool(hAPP_i7355787e_bool(X3589,X3590)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).
fof(i_0_2971,plain,
! [X3557,X3558] : is_fun_pname_bool(image_1921560913_pname(X3557,X3558)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname]) ).
fof(i_0_2972,plain,
! [X3553,X3554] : is_fun_pname_bool(image_62782965_pname(X3553,X3554)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__Com__Opname]) ).
fof(i_0_2973,plain,
! [X3537,X3538] : is_fun_pname_bool(image_nat_pname(X3537,X3538)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname]) ).
fof(i_0_2974,plain,
! [X3529,X3530] : is_fun_pname_bool(image_int_pname(X3529,X3530)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Int__Oint_000tc__Com__Opname]) ).
fof(i_0_2975,plain,
! [X3597,X3598] : is_fun_a_bool(hAPP_nat_fun_a_bool(X3597,X3598)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).
fof(i_0_2976,plain,
! [X3587,X3588] : is_fun_a_bool(hAPP_int_fun_a_bool(X3587,X3588)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).
fof(i_0_2977,plain,
! [X3555,X3556] : is_fun_a_bool(image_fun_nat_bool_a(X3555,X3556)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a]) ).
fof(i_0_2978,plain,
! [X3551,X3552] : is_fun_a_bool(image_fun_int_bool_a(X3551,X3552)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000t__a]) ).
fof(i_0_2979,plain,
! [X3535,X3536] : is_fun_a_bool(image_nat_a(X3535,X3536)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a]) ).
fof(i_0_2980,plain,
! [X3527,X3528] : is_fun_a_bool(image_int_a(X3527,X3528)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Int__Oint_000t__a]) ).
fof(i_0_2981,plain,
! [X6684,X6685] :
( ~ is_bool(X6684)
| hAPP_nat_bool(cOMBK_bool_nat(X6684),X6685) = X6684 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U])]) ).
fof(i_0_2982,plain,
! [X6682,X6683] :
( ~ is_bool(X6682)
| hAPP_int_bool(cOMBK_bool_int(X6682),X6683) = X6682 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Int__Oint_U])]) ).
fof(i_0_2983,plain,
! [X6675,X6676] :
( ~ is_a(X6675)
| hAPP_pname_a(cOMBK_a_pname(X6675),X6676) = X6675 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U])]) ).
fof(i_0_2984,plain,
! [X6673,X6674] :
( ~ is_bool(X6673)
| hAPP_a_bool(cOMBK_bool_a(X6673),X6674) = X6673 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U])]) ).
fof(i_0_2985,plain,
! [X5194,X5195] :
( ( image_nat_int(X5194,X5195) != bot_bot_fun_int_bool
| X5195 = bot_bot_fun_nat_bool )
& ( X5195 != bot_bot_fun_nat_bool
| image_nat_int(X5194,X5195) = bot_bot_fun_int_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_612_image__is__empty])]) ).
fof(i_0_2986,plain,
! [X5200,X5201] :
( ( bot_bot_fun_int_bool != image_nat_int(X5200,X5201)
| X5201 = bot_bot_fun_nat_bool )
& ( X5201 != bot_bot_fun_nat_bool
| bot_bot_fun_int_bool = image_nat_int(X5200,X5201) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_616_empty__is__image])]) ).
fof(i_0_2987,plain,
! [X6472] :
( ( hAPP_nat_int(semiri1621563631at_int,X6472) != zero_zero_int
| X6472 = zero_zero_nat )
& ( X6472 != zero_zero_nat
| hAPP_nat_int(semiri1621563631at_int,X6472) = zero_zero_int ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1100_int__eq__0__conv])]) ).
fof(i_0_2988,plain,
! [X3886] : hAPP_nat_nat(suc,X3886) != X3886,
inference(variable_rename,[status(thm)],[fact_124_Suc__n__not__n]) ).
fof(i_0_2989,plain,
! [X3887] : X3887 != hAPP_nat_nat(suc,X3887),
inference(variable_rename,[status(thm)],[fact_125_n__not__Suc__n]) ).
fof(i_0_2990,plain,
! [X6137] :
( X6137 = zero_zero_nat
| X6137 = hAPP_nat_nat(suc,esk185_1(X6137)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_975_not0__implies__Suc])])]) ).
fof(i_0_2991,plain,
! [X6132] :
( X6132 = zero_zero_nat
| X6132 = hAPP_nat_nat(suc,esk183_1(X6132)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_973_nat_Oexhaust])])]) ).
fof(i_0_2992,plain,
! [X6680,X6681] : hAPP_nat_int(cOMBK_int_nat(X6680),X6681) = X6680,
inference(variable_rename,[status(thm)],[help_COMBK_1_1_COMBK_000tc__Int__Oint_000tc__Nat__Onat_U]) ).
fof(i_0_2993,plain,
! [X6058] : hAPP_nat_nat(suc,X6058) != zero_zero_nat,
inference(variable_rename,[status(thm)],[fact_943_Suc__not__Zero]) ).
fof(i_0_2994,plain,
! [X6057] : hAPP_nat_nat(suc,X6057) != zero_zero_nat,
inference(variable_rename,[status(thm)],[fact_942_nat_Osimps_I3_J]) ).
fof(i_0_2995,plain,
! [X6055] : hAPP_nat_nat(suc,X6055) != zero_zero_nat,
inference(variable_rename,[status(thm)],[fact_940_Suc__neq__Zero]) ).
fof(i_0_2996,plain,
! [X6060] : zero_zero_nat != hAPP_nat_nat(suc,X6060),
inference(variable_rename,[status(thm)],[fact_945_Zero__not__Suc]) ).
fof(i_0_2997,plain,
! [X6059] : zero_zero_nat != hAPP_nat_nat(suc,X6059),
inference(variable_rename,[status(thm)],[fact_944_nat_Osimps_I2_J]) ).
fof(i_0_2998,plain,
! [X6056] : zero_zero_nat != hAPP_nat_nat(suc,X6056),
inference(variable_rename,[status(thm)],[fact_941_Zero__neq__Suc]) ).
fof(i_0_2999,plain,
! [X3510] :
( ~ is_fun1661590463l_bool(X3510)
| is_fun1661590463l_bool(collec1974731493e_bool(X3510)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J])]) ).
fof(i_0_3000,plain,
! [X3645] :
( ~ is_fun_a_bool(X3645)
| is_fun949378684l_bool(p(X3645)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_v_P])]) ).
fof(i_0_3001,plain,
! [X3509] :
( ~ is_fun949378684l_bool(X3509)
| is_fun949378684l_bool(collect_fun_a_bool(X3509)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J])]) ).
fof(i_0_3002,plain,
! [X3508] :
( ~ is_fun_pname_bool(X3508)
| is_fun_pname_bool(collect_pname(X3508)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000tc__Com__Opname])]) ).
fof(i_0_3003,plain,
! [X3507] :
( ~ is_fun_a_bool(X3507)
| is_fun_a_bool(collect_a(X3507)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000t__a])]) ).
fof(i_0_3004,plain,
! [X3482] :
( ~ is_bool(X3482)
| is_fun_a_bool(cOMBK_bool_a(X3482)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBK_000tc__HOL__Obool_000t__a])]) ).
fof(i_0_3005,plain,
! [X6660] : hAPP_nat_nat(cOMBI_nat,X6660) = X6660,
inference(variable_rename,[status(thm)],[help_COMBI_1_1_COMBI_000tc__Nat__Onat_U]) ).
fof(i_0_3006,plain,
! [X5198] : image_nat_int(X5198,bot_bot_fun_nat_bool) = bot_bot_fun_int_bool,
inference(variable_rename,[status(thm)],[fact_614_image__empty]) ).
fof(i_0_3007,plain,
! [X5199] : image_pname_a(X5199,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
inference(variable_rename,[status(thm)],[fact_615_image__empty]) ).
fof(i_0_3008,plain,
! [X3646] : is_a(mgt(X3646)),
inference(variable_rename,[status(thm)],[gsy_v_mgt]) ).
fof(i_0_3009,plain,
! [X3647] : is_bool(wt(X3647)),
inference(variable_rename,[status(thm)],[gsy_v_wt]) ).
fof(i_0_3010,plain,
! [X6659] :
( ~ is_bool(X6659)
| X6659 = fTrue
| X6659 = fFalse ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_If_3_1_If_000tc__Nat__Onat_T])]) ).
fof(i_0_3011,plain,
! [X6644] :
( ~ is_bool(X6644)
| X6644 = fTrue
| X6644 = fFalse ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T])]) ).
fof(i_0_3012,plain,
~ hBOOL(fFalse),
inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).
cnf(i_0_3013,plain,
bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
inference(split_conjunct,[status(thm)],[fact_539_empty__def]) ).
cnf(i_0_3014,plain,
bot_bot_fun_int_bool = collect_int(cOMBK_bool_int(fFalse)),
inference(split_conjunct,[status(thm)],[fact_538_empty__def]) ).
cnf(i_0_3015,plain,
zero_zero_int = number_number_of_int(pls),
inference(split_conjunct,[status(thm)],[fact_1176_zero__is__num__zero]) ).
cnf(i_0_3016,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk221_4(X1,X2,X3,X4)),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_nat_int(X2,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X2,X4)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X2,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk220_4(X1,X2,X3,X4)),one_one_nat))),hAPP_nat_int(X2,esk220_4(X1,X2,X3,X4))))),one_one_int)) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_3017,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),esk221_4(X2,X3,X4,X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),hAPP_nat_int(X3,X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X3,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X3,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk220_4(X2,X3,X4,X1)),one_one_nat))),hAPP_nat_int(X3,esk220_4(X2,X3,X4,X1))))),one_one_int)) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_3018,plain,
( hAPP_nat_int(X1,esk221_4(X2,X1,X3,X4)) = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),hAPP_nat_int(X1,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X1,X4)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk220_4(X2,X1,X3,X4)),one_one_nat))),hAPP_nat_int(X1,esk220_4(X2,X1,X3,X4))))),one_one_int)) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_3019,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk219_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_nat_int(X2,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X2,zero_zero_nat)),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X2,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk218_3(X1,X2,X3)),one_one_nat))),hAPP_nat_int(X2,esk218_3(X1,X2,X3))))),one_one_int)) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_3020,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk217_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_nat_int(X2,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X2,zero_zero_nat)),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X2,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk216_3(X1,X2,X3)),one_one_nat))),hAPP_nat_int(X2,esk216_3(X1,X2,X3))))),one_one_int)) ),
inference(split_conjunct,[status(thm)],[i_0_1637]),
[final] ).
cnf(i_0_3021,plain,
( hAPP_nat_int(X1,esk219_3(X2,X1,X3)) = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),hAPP_nat_int(X1,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X1,zero_zero_nat)),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk218_3(X2,X1,X3)),one_one_nat))),hAPP_nat_int(X1,esk218_3(X2,X1,X3))))),one_one_int)) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_3022,plain,
( hAPP_nat_int(X1,esk217_3(X2,X1,X3)) = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),hAPP_nat_int(X1,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X1,zero_zero_nat)),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk216_3(X2,X1,X3)),one_one_nat))),hAPP_nat_int(X1,esk216_3(X2,X1,X3))))),one_one_int)) ),
inference(split_conjunct,[status(thm)],[i_0_1637]),
[final] ).
cnf(i_0_3023,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),X3))),one_one_int)),X1))),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1638]),
[final] ).
cnf(i_0_3024,plain,
hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X1))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)))),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1639,c_0_1640]),c_0_1640]),
[final] ).
cnf(i_0_3025,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),X4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X3)),X5)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),X3)),X4)),X5))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1641]),
[final] ).
cnf(i_0_3026,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),X4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X3)),X5)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),X3)),X4)),X5))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1642]),
[final] ).
cnf(i_0_3027,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),X2))),one_one_int)),X1))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1643]),
[final] ).
cnf(i_0_3028,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X4)),X2)),X3)),X5))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X4),X2)),X5)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1641]),
[final] ).
cnf(i_0_3029,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X4)),X2)),X3)),X5))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X4),X2)),X5)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1642]),
[final] ).
cnf(i_0_3030,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(X3,X2)),X2))
| X2 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(X1,esk148_3(X2,X1,X3)),esk149_3(X2,X1,X3))),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk148_3(X2,X1,X3)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk149_3(X2,X1,X3)),bot_bo844097828e_bool))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(finite1282449217_pname(X1,X3))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1644]),
[final] ).
cnf(i_0_3031,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(X3,X2)),X2))
| X2 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_a_a(hAPP_a_fun_a_a(X1,esk142_3(X2,X1,X3)),esk143_3(X2,X1,X3))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk142_3(X2,X1,X3)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk143_3(X2,X1,X3)),bot_bot_fun_a_bool))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(finite_folding_one_a(X1,X3))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1645]),
[final] ).
cnf(i_0_3032,plain,
( X3 = bot_bot_fun_nat_bool
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(X2,X3)),X3))
| ~ hBOOL(finite988810631ne_nat(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(X1,esk146_3(X3,X1,X2)),esk147_3(X3,X1,X2))),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk146_3(X3,X1,X2)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk147_3(X3,X1,X2)),bot_bot_fun_nat_bool)))) ),
inference(split_conjunct,[status(thm)],[i_0_1646]),
[final] ).
cnf(i_0_3033,plain,
( X3 = bot_bot_fun_int_bool
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(X2,X3)),X3))
| ~ hBOOL(finite1626084323ne_int(X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(X1,esk144_3(X3,X1,X2)),esk145_3(X3,X1,X2))),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk144_3(X3,X1,X2)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk145_3(X3,X1,X2)),bot_bot_fun_int_bool)))) ),
inference(split_conjunct,[status(thm)],[i_0_1647]),
[final] ).
cnf(i_0_3034,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1648,c_0_1649]),c_0_1640]),c_0_1640]),c_0_1640]),c_0_1640]),
[final] ).
cnf(i_0_3035,plain,
( hBOOL(hAPP_int_bool(X1,esk203_3(X1,X2,X3)))
| ~ hBOOL(hAPP_int_bool(X1,esk202_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP_int_bool(X2,esk202_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP_int_bool(X2,X5))
| ~ hBOOL(hAPP_int_bool(X2,esk200_3(X1,X2,X3)))
| ~ hBOOL(hAPP_int_bool(X2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk200_3(X1,X2,X3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk201_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1650]),
[final] ).
cnf(i_0_3036,plain,
( hBOOL(hAPP_int_bool(X1,esk199_3(X1,X2,X3)))
| ~ hBOOL(hAPP_int_bool(X1,esk198_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP_int_bool(X2,esk198_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP_int_bool(X2,X5))
| ~ hBOOL(hAPP_int_bool(X2,esk196_3(X1,X2,X3)))
| ~ hBOOL(hAPP_int_bool(X2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk196_3(X1,X2,X3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk197_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1651]),
[final] ).
cnf(i_0_3037,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,esk198_4(X1,X2,X3,X4)),X4))
| hBOOL(hAPP_int_bool(X1,esk199_3(X1,X2,X3)))
| ~ hBOOL(hAPP_int_bool(X2,X5))
| ~ hBOOL(hAPP_int_bool(X2,esk196_3(X1,X2,X3)))
| ~ hBOOL(hAPP_int_bool(X2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk196_3(X1,X2,X3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk197_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1651]),
[final] ).
cnf(i_0_3038,plain,
( hBOOL(hAPP_int_bool(X1,esk202_4(X1,X2,X3,X4)))
| hBOOL(hAPP_int_bool(X2,esk202_4(X1,X2,X3,X4)))
| hBOOL(hAPP_int_bool(X1,esk203_3(X1,X2,X3)))
| ~ hBOOL(hAPP_int_bool(X2,X5))
| ~ hBOOL(hAPP_int_bool(X2,esk200_3(X1,X2,X3)))
| ~ hBOOL(hAPP_int_bool(X2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk200_3(X1,X2,X3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk201_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1650]),
[final] ).
cnf(i_0_3039,plain,
( hBOOL(hAPP_int_bool(X1,esk198_4(X1,X2,X3,X4)))
| hBOOL(hAPP_int_bool(X2,esk198_4(X1,X2,X3,X4)))
| hBOOL(hAPP_int_bool(X1,esk199_3(X1,X2,X3)))
| ~ hBOOL(hAPP_int_bool(X2,X5))
| ~ hBOOL(hAPP_int_bool(X2,esk196_3(X1,X2,X3)))
| ~ hBOOL(hAPP_int_bool(X2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk196_3(X1,X2,X3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk197_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1651]),
[final] ).
cnf(i_0_3040,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X4)),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X4)),X5)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3)),X4)),X5)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1652]),
[final] ).
cnf(i_0_3041,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X4)),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X4)),X5)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3)),X4)),X5)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1653]),
[final] ).
cnf(i_0_3042,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1654,c_0_1649]),c_0_1640]),c_0_1640]),
[final] ).
cnf(i_0_3043,plain,
( hBOOL(hAPP_int_bool(X1,esk203_3(X1,X2,X3)))
| hBOOL(hAPP_int_bool(X2,esk200_3(X1,X2,X3)))
| hBOOL(hAPP_int_bool(X2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk200_3(X1,X2,X3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk201_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP_int_bool(X1,esk202_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP_int_bool(X2,esk202_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP_int_bool(X2,X5))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1650]),
[final] ).
cnf(i_0_3044,plain,
( hBOOL(hAPP_int_bool(X1,esk199_3(X1,X2,X3)))
| hBOOL(hAPP_int_bool(X2,esk196_3(X1,X2,X3)))
| hBOOL(hAPP_int_bool(X2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk196_3(X1,X2,X3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk197_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP_int_bool(X1,esk198_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP_int_bool(X2,esk198_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP_int_bool(X2,X5))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1651]),
[final] ).
cnf(i_0_3045,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X4),X1)),X2)),X5)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X4),X2)),X5)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1652]),
[final] ).
cnf(i_0_3046,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X4),X1)),X2)),X5)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X4),X2)),X5)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1653]),
[final] ).
cnf(i_0_3047,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),esk202_4(X2,X3,X4,X1)))
| hBOOL(hAPP_int_bool(X2,esk203_3(X2,X3,X4)))
| ~ hBOOL(hAPP_int_bool(X3,X5))
| ~ hBOOL(hAPP_int_bool(X3,esk200_3(X2,X3,X4)))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk200_3(X2,X3,X4)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk201_3(X2,X3,X4)),X4))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1650]),
[final] ).
cnf(i_0_3048,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,esk198_4(X1,X2,X3,X4)),X4))
| hBOOL(hAPP_int_bool(X1,esk199_3(X1,X2,X3)))
| hBOOL(hAPP_int_bool(X2,esk196_3(X1,X2,X3)))
| hBOOL(hAPP_int_bool(X2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk196_3(X1,X2,X3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk197_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP_int_bool(X2,X5))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1651]),
[final] ).
cnf(i_0_3049,plain,
( hBOOL(hAPP_int_bool(X1,esk202_4(X1,X2,X3,X4)))
| hBOOL(hAPP_int_bool(X2,esk202_4(X1,X2,X3,X4)))
| hBOOL(hAPP_int_bool(X1,esk203_3(X1,X2,X3)))
| hBOOL(hAPP_int_bool(X2,esk200_3(X1,X2,X3)))
| hBOOL(hAPP_int_bool(X2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk200_3(X1,X2,X3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk201_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP_int_bool(X2,X5))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1650]),
[final] ).
cnf(i_0_3050,plain,
( hBOOL(hAPP_int_bool(X1,esk198_4(X1,X2,X3,X4)))
| hBOOL(hAPP_int_bool(X2,esk198_4(X1,X2,X3,X4)))
| hBOOL(hAPP_int_bool(X1,esk199_3(X1,X2,X3)))
| hBOOL(hAPP_int_bool(X2,esk196_3(X1,X2,X3)))
| hBOOL(hAPP_int_bool(X2,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk196_3(X1,X2,X3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk197_3(X1,X2,X3)),X3))))
| ~ hBOOL(hAPP_int_bool(X2,X5))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1651]),
[final] ).
cnf(i_0_3051,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X2)),hAPP_pname_a(X2,esk62_2(X2,X1)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1655]),
[final] ).
cnf(i_0_3052,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),esk202_4(X2,X3,X4,X1)))
| hBOOL(hAPP_int_bool(X2,esk203_3(X2,X3,X4)))
| hBOOL(hAPP_int_bool(X3,esk200_3(X2,X3,X4)))
| hBOOL(hAPP_int_bool(X3,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk200_3(X2,X3,X4)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,esk201_3(X2,X3,X4)),X4))))
| ~ hBOOL(hAPP_int_bool(X3,X5))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1650]),
[final] ).
cnf(i_0_3053,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk221_4(X1,X2,X3,X4)),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk220_4(X1,X2,X3,X4)),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_nat_int(X2,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X2,X4)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_3054,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X3)),X4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),X5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)),X3)),X4)),X5)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1656]),
[final] ).
cnf(i_0_3055,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)),X3)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X4)),X5)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X5))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1657]),
[final] ).
cnf(i_0_3056,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)),X3)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X4)),X5)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X5),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1658]),
[final] ).
cnf(i_0_3057,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),esk221_4(X2,X3,X4,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk220_4(X2,X3,X4,X1)),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),hAPP_nat_int(X3,X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X3,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_3058,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk221_4(X1,X2,X3,X4)),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),esk220_4(X1,X2,X3,X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_nat_int(X2,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X2,X4)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_3059,plain,
number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls))),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1659,c_0_1640]),c_0_1640]),
[final] ).
cnf(i_0_3060,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,X2)),hAPP_n1699378549t_bool(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1,esk51_3(X2,X3,X1))),hAPP_n1699378549t_bool(X1,hAPP_nat_nat(suc,esk51_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1660]),
[final] ).
cnf(i_0_3061,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(X1,X2)),hAPP_n1082236369t_bool(X1,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(X1,esk52_3(X2,X3,X1))),hAPP_n1082236369t_bool(X1,hAPP_nat_nat(suc,esk52_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1661]),
[final] ).
cnf(i_0_3062,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X1,X2)),hAPP_n1025906991e_bool(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X1,esk46_3(X2,X3,X1))),hAPP_n1025906991e_bool(X1,hAPP_nat_nat(suc,esk46_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1662]),
[final] ).
cnf(i_0_3063,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X1,X2)),hAPP_nat_fun_a_bool(X1,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X1,esk48_3(X2,X3,X1))),hAPP_nat_fun_a_bool(X1,hAPP_nat_nat(suc,esk48_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1663]),
[final] ).
cnf(i_0_3064,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,esk49_3(X2,X3,X1))),hAPP_nat_nat(X1,hAPP_nat_nat(suc,esk49_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1664]),
[final] ).
cnf(i_0_3065,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X1,X2)),hAPP_nat_int(X1,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X1,esk50_3(X2,X3,X1))),hAPP_nat_int(X1,hAPP_nat_nat(suc,esk50_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1665]),
[final] ).
cnf(i_0_3066,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,X2)),hAPP_nat_bool(X1,X3)))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,esk47_3(X2,X3,X1))),hAPP_nat_bool(X1,hAPP_nat_nat(suc,esk47_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1666]),
[final] ).
cnf(i_0_3067,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(X1,X2)),X3)),hAPP_nat_nat(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X1,esk166_3(X2,X3,X1))),hAPP_nat_nat(X1,esk167_3(X2,X3,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1667]),
[final] ).
cnf(i_0_3068,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X5),X2))
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)),X3) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X4),X5)),X6)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X4),X5)),X6)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X6))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1668]),
[final] ).
cnf(i_0_3069,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X2)),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1669,c_0_1640]),c_0_1640]),
[final] ).
cnf(i_0_3070,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X2)),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1670,c_0_1640]),c_0_1640]),
[final] ).
cnf(i_0_3071,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X2)),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1671,c_0_1640]),c_0_1640]),
[final] ).
cnf(i_0_3072,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X2)),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1672,c_0_1640]),c_0_1640]),
[final] ).
cnf(i_0_3073,plain,
( hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk195_3(X2,X1,X3)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,esk194_3(X2,X1,X3)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_3074,plain,
( hAPP_nat_int(X1,esk221_4(X2,X1,X3,X4)) = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk220_4(X2,X1,X3,X4)),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),hAPP_nat_int(X1,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X1,X4)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_3075,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),X4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X3)),X5)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X4),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)),X3)),X5))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1674]),
[final] ).
cnf(i_0_3076,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1,X2)),hAPP_nat_nat(X1,X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X1,esk171_3(X2,X3,X1))),hAPP_nat_nat(X1,esk172_3(X2,X3,X1))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1675]),
[final] ).
cnf(i_0_3077,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),esk221_4(X2,X3,X4,X1)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),esk220_4(X2,X3,X4,X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),hAPP_nat_int(X3,X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X3,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_3078,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)),X3)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1676]),
[final] ).
cnf(i_0_3079,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X2)),hAPP_n1699378549t_bool(X2,esk54_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1677,c_0_1678]),
[final] ).
cnf(i_0_3080,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,X2)),hAPP_n1082236369t_bool(X2,esk53_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1679,c_0_1678]),
[final] ).
cnf(i_0_3081,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X2)),hAPP_n1025906991e_bool(X2,esk55_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1680,c_0_1678]),
[final] ).
cnf(i_0_3082,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X2)),hAPP_nat_fun_a_bool(X2,esk56_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1681,c_0_1678]),
[final] ).
cnf(i_0_3083,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,X2)),hAPP_nat_int(X2,esk63_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1682,c_0_1678]),
[final] ).
cnf(i_0_3084,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X2,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,X2)),hAPP_i418383825t_bool(X2,esk59_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1683,c_0_1684]),
[final] ).
cnf(i_0_3085,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X2,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,X2)),hAPP_i1948725293t_bool(X2,esk58_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1685,c_0_1684]),
[final] ).
cnf(i_0_3086,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X2,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,X2)),hAPP_i7355787e_bool(X2,esk60_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1686,c_0_1684]),
[final] ).
cnf(i_0_3087,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X2,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,X2)),hAPP_int_fun_a_bool(X2,esk61_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1687,c_0_1684]),
[final] ).
cnf(i_0_3088,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X2,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,X2)),hAPP_int_a(X2,esk57_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1688,c_0_1684]),
[final] ).
cnf(i_0_3089,plain,
( hBOOL(hAPP_f54304608l_bool(X1,X3))
| ~ hBOOL(hAPP_f54304608l_bool(X1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk105_3(X1,X2,X3)),esk106_3(X1,X2,X3))))
| ~ hBOOL(hAPP_f54304608l_bool(X1,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1689]),
[final] ).
cnf(i_0_3090,plain,
( hBOOL(hAPP_f448129468l_bool(X1,X3))
| ~ hBOOL(hAPP_f448129468l_bool(X1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk103_3(X1,X2,X3)),esk104_3(X1,X2,X3))))
| ~ hBOOL(hAPP_f448129468l_bool(X1,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1690]),
[final] ).
cnf(i_0_3091,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk107_3(X1,X2,X3)),esk108_3(X1,X2,X3))))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1691]),
[final] ).
cnf(i_0_3092,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk101_3(X1,X2,X3)),esk102_3(X1,X2,X3))))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_3093,plain,
( hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X4),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2),X3))))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,esk193_3(X2,X1,X3)),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(X1,X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1693]),
[final] ).
cnf(i_0_3094,plain,
( hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X4),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2),X3))))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk192_3(X2,X1,X3)),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(X1,X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1694]),
[final] ).
cnf(i_0_3095,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X5))
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)),X3) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X4),X5)),X6)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X4),X5)),X6)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X6),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1695]),
[final] ).
cnf(i_0_3096,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)),pls)) ),
inference(rw,[status(thm)],[i_0_1696,c_0_1640]),
[final] ).
cnf(i_0_3097,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)),pls)) ),
inference(rw,[status(thm)],[i_0_1697,c_0_1640]),
[final] ).
cnf(i_0_3098,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[i_0_1698]),
[final] ).
cnf(i_0_3099,plain,
( hBOOL(hAPP_fun_a_bool_bool(p(X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X1)),bot_bot_fun_a_bool)))
| ~ hBOOL(hAPP_fun_a_bool_bool(p(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X1)),X2)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(the_com(body(X1)))),bot_bot_fun_a_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_1699]),
[final] ).
cnf(i_0_3100,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X2)),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1700,c_0_1640]),c_0_1640]),
[final] ).
cnf(i_0_3101,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X2)),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1701,c_0_1640]),c_0_1640]),
[final] ).
cnf(i_0_3102,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X2)),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1702,c_0_1640]),c_0_1640]),
[final] ).
cnf(i_0_3103,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X2)),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1703,c_0_1640]),c_0_1640]),
[final] ).
cnf(i_0_3104,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,esk195_3(X1,X2,X3)),X3))
| hBOOL(hAPP_int_bool(X2,X1))
| ~ hBOOL(hAPP_int_bool(X2,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,esk194_3(X1,X2,X3)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_3105,plain,
( hAPP_nat_int(X1,esk221_4(X2,X1,X3,X4)) = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),esk220_4(X2,X1,X3,X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),hAPP_nat_int(X1,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X1,X4)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_3106,plain,
( hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk187_3(X1,X2,X3)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_3107,plain,
( hBOOL(hAPP_int_bool(X1,X3))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,esk189_3(X1,X2,X3)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1705]),
[final] ).
cnf(i_0_3108,plain,
( hBOOL(hAPP_int_bool(X1,X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),esk194_3(X2,X1,X3)))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk195_3(X2,X1,X3)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_3109,plain,
( hBOOL(hAPP_int_bool(X1,esk195_3(X2,X1,X3)))
| hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,esk194_3(X2,X1,X3)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_3110,plain,
( hBOOL(hAPP_int_bool(X1,X2))
| hBOOL(hAPP_int_bool(X1,esk194_3(X2,X1,X3)))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk195_3(X2,X1,X3)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_3111,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1706]),
[final] ).
cnf(i_0_3112,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1707]),
[final] ).
cnf(i_0_3113,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1708]),
[final] ).
cnf(i_0_3114,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1709]),
[final] ).
cnf(i_0_3115,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk166_3(X1,X2,X3)),esk167_3(X1,X2,X3)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(X3,X1)),X2)),hAPP_nat_nat(X3,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1667]),
[final] ).
cnf(i_0_3116,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X1,X3)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X1,esk79_3(X1,X2,X3))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1710]),
[final] ).
cnf(i_0_3117,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X3)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,esk80_3(X1,X2,X3))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1711]),
[final] ).
cnf(i_0_3118,plain,
( hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,esk188_3(X1,X2,X3)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X1,X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1712]),
[final] ).
cnf(i_0_3119,plain,
( hBOOL(hAPP_int_bool(X1,X3))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,esk190_3(X1,X2,X3)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1713]),
[final] ).
cnf(i_0_3120,plain,
( hBOOL(hAPP_f54304608l_bool(X1,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(X1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,esk114_2(X1,X2)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk113_2(X1,X2)),bot_bot_fun_nat_bool))))
| ~ hBOOL(hAPP_f54304608l_bool(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1714]),
[final] ).
cnf(i_0_3121,plain,
( hBOOL(hAPP_f448129468l_bool(X1,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(X1,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,esk112_2(X1,X2)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk111_2(X1,X2)),bot_bot_fun_int_bool))))
| ~ hBOOL(hAPP_f448129468l_bool(X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1715]),
[final] ).
cnf(i_0_3122,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,esk116_2(X1,X2)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk115_2(X1,X2)),bot_bo844097828e_bool))))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_3123,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,esk110_2(X1,X2)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk109_2(X1,X2)),bot_bot_fun_a_bool))))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1717]),
[final] ).
cnf(i_0_3124,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1718]),
[final] ).
cnf(i_0_3125,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1719]),
[final] ).
cnf(i_0_3126,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1719]),
[final] ).
cnf(i_0_3127,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))),X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1720]),
[final] ).
cnf(i_0_3128,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1721]),
[final] ).
cnf(i_0_3129,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1721]),
[final] ).
cnf(i_0_3130,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1722]),
[final] ).
cnf(i_0_3131,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),bot_bo844097828e_bool))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_3132,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_3133,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1724]),
[final] ).
cnf(i_0_3134,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1725]),
[final] ).
cnf(i_0_3135,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1725]),
[final] ).
cnf(i_0_3136,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X1)),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X1)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1726]),
[final] ).
cnf(i_0_3137,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X1)),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X1)),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1727]),
[final] ).
cnf(i_0_3138,plain,
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),X1)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X2)))) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1728,c_0_1678]),c_0_1678]),
[final] ).
cnf(i_0_3139,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),X4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X3)),X5)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),X3)),X4) != X5
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1729]),
[final] ).
cnf(i_0_3140,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X4)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X4)),X5)
| X1 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3)),X4)),X5)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1730]),
[final] ).
cnf(i_0_3141,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X3),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1731]),
[final] ).
cnf(i_0_3142,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(rw,[status(thm)],[i_0_1732,c_0_1640]),
[final] ).
cnf(i_0_3143,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[i_0_1698]),
[final] ).
cnf(i_0_3144,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)),pls))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(rw,[status(thm)],[i_0_1733,c_0_1640]),
[final] ).
cnf(i_0_3145,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk219_3(X1,X2,X3)),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk218_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_nat_int(X2,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X2,zero_zero_nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_3146,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk217_3(X1,X2,X3)),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk216_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_nat_int(X2,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X2,zero_zero_nat)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1637]),
[final] ).
cnf(i_0_3147,plain,
( hBOOL(hAPP_fun_a_bool_bool(p(X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X2)),bot_bot_fun_a_bool)))
| ~ hBOOL(hAPP_fun_a_bool_bool(p(X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,esk86_2(X1,X2))),bot_bot_fun_a_bool)))
| ~ hBOOL(wt(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1734]),
[final] ).
cnf(i_0_3148,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X4)),X2)),X3) = X5
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),X3) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X4),X2)),X5)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1729]),
[final] ).
cnf(i_0_3149,plain,
( X3 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X4),X1)),X2)),X5)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),X3) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X4),X2)),X5)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1730]),
[final] ).
cnf(i_0_3150,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X2))
| X2 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(X1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk160_2(X1,X2)),esk161_2(X1,X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk159_2(X1,X2)),bot_bo844097828e_bool)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_3151,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| X2 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk151_2(X1,X2)),esk152_2(X1,X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk150_2(X1,X2)),bot_bot_fun_a_bool)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_3152,plain,
( hBOOL(hAPP_f54304608l_bool(X1,X2))
| X2 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(X1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk157_2(X1,X2)),esk158_2(X1,X2))))
| ~ hBOOL(hAPP_f54304608l_bool(X1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk156_2(X1,X2)),bot_bot_fun_nat_bool)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1737]),
[final] ).
cnf(i_0_3153,plain,
( hBOOL(hAPP_f448129468l_bool(X1,X2))
| X2 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(X1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk154_2(X1,X2)),esk155_2(X1,X2))))
| ~ hBOOL(hAPP_f448129468l_bool(X1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk153_2(X1,X2)),bot_bot_fun_int_bool)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_3154,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1719]),
[final] ).
cnf(i_0_3155,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))),X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1721]),
[final] ).
cnf(i_0_3156,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_3157,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1725]),
[final] ).
cnf(i_0_3158,plain,
( hBOOL(hAPP_f54304608l_bool(X1,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk105_3(X1,X2,X3)),esk106_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(X1,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1689]),
[final] ).
cnf(i_0_3159,plain,
( hBOOL(hAPP_f448129468l_bool(X1,X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk103_3(X1,X2,X3)),esk104_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(X1,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1690]),
[final] ).
cnf(i_0_3160,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk107_3(X1,X2,X3)),esk108_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1691]),
[final] ).
cnf(i_0_3161,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk101_3(X1,X2,X3)),esk102_3(X1,X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_3162,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(X1,X2)),image_nat_int(X1,X3))),image_nat_int(X1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X3)))),
inference(split_conjunct,[status(thm)],[i_0_1739]),
[final] ).
cnf(i_0_3163,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(X1,X2)),image_pname_a(X1,X3))),image_pname_a(X1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X3)))),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_3164,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X2)),X4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),X2)),X4),
inference(split_conjunct,[status(thm)],[i_0_1741]),
[final] ).
cnf(i_0_3165,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,X2)),hAPP_f957591787ol_nat(finite_card_int,X1))),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X1))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_3166,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,X2)),hAPP_f22106695ol_nat(finite_card_nat,X1))),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1743]),
[final] ).
cnf(i_0_3167,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,X1))),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1744]),
[final] ).
cnf(i_0_3168,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,X1))),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1745]),
[final] ).
cnf(i_0_3169,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X3)),X1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X3)),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1746]),
[final] ).
cnf(i_0_3170,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1))) ),
inference(rw,[status(thm)],[i_0_1747,c_0_1640]),
[final] ).
cnf(i_0_3171,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1))) ),
inference(rw,[status(thm)],[i_0_1748,c_0_1640]),
[final] ).
cnf(i_0_3172,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X3)),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X3)),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1726]),
[final] ).
cnf(i_0_3173,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X3)),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X3)),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1727]),
[final] ).
cnf(i_0_3174,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_int_bool(X3,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_3175,plain,
( hBOOL(hAPP_int_bool(X3,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_3176,plain,
( hBOOL(hAPP_int_bool(nat_neg,X1))
| ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1750,c_0_1649]),c_0_1649]),c_0_1640]),
[final] ).
cnf(i_0_3177,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
inference(split_conjunct,[status(thm)],[i_0_1751]),
[final] ).
cnf(i_0_3178,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_3179,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1753]),
[final] ).
cnf(i_0_3180,plain,
( hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3))))
| ~ hBOOL(hAPP_int_bool(X1,zero_zero_int))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_3181,plain,
( hAPP_nat_int(X1,esk219_3(X2,X1,X3)) = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk218_3(X2,X1,X3)),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),hAPP_nat_int(X1,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X1,zero_zero_nat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_3182,plain,
( hAPP_nat_int(X1,esk217_3(X2,X1,X3)) = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk216_3(X2,X1,X3)),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),hAPP_nat_int(X1,X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(X1,zero_zero_nat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1637]),
[final] ).
cnf(i_0_3183,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk171_3(X1,X2,X3)),esk172_3(X1,X2,X3)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X3,X1)),hAPP_nat_nat(X3,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1675]),
[final] ).
cnf(i_0_3184,plain,
( hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),X1)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X2))) = hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,X2))))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1754,c_0_1678]),c_0_1678]),
[final] ).
cnf(i_0_3185,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X2))
| X2 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk160_2(X1,X2)),esk161_2(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk159_2(X1,X2)),bot_bo844097828e_bool)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_3186,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| X2 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk151_2(X1,X2)),esk152_2(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk150_2(X1,X2)),bot_bot_fun_a_bool)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_3187,plain,
( hBOOL(hAPP_f54304608l_bool(X1,X2))
| X2 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk157_2(X1,X2)),esk158_2(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(X1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk156_2(X1,X2)),bot_bot_fun_nat_bool)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1737]),
[final] ).
cnf(i_0_3188,plain,
( hBOOL(hAPP_f448129468l_bool(X1,X2))
| X2 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk154_2(X1,X2)),esk155_2(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(X1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk153_2(X1,X2)),bot_bot_fun_int_bool)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_3189,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1755]),
[final] ).
cnf(i_0_3190,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1756]),
[final] ).
cnf(i_0_3191,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1757]),
[final] ).
cnf(i_0_3192,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1758]),
[final] ).
cnf(i_0_3193,plain,
( hBOOL(hAPP_int_bool(X1,esk193_3(X2,X1,X3)))
| hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X4),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2),X3))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(X1,X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1693]),
[final] ).
cnf(i_0_3194,plain,
( hBOOL(hAPP_int_bool(X1,esk192_3(X2,X1,X3)))
| hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X4),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2),X3))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(X1,X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1694]),
[final] ).
cnf(i_0_3195,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,esk82_2(X1,X2))),hAPP_nat_bool(X2,esk82_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1759]),
[final] ).
cnf(i_0_3196,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,esk69_2(X1,X2))),hAPP_nat_bool(X2,esk69_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1760]),
[final] ).
cnf(i_0_3197,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X1,esk81_2(X1,X2))),hAPP_int_bool(X2,esk81_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1761]),
[final] ).
cnf(i_0_3198,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X1,esk68_2(X1,X2))),hAPP_int_bool(X2,esk68_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1762]),
[final] ).
cnf(i_0_3199,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X1,esk83_2(X1,X2))),hAPP_a_bool(X2,esk83_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1763]),
[final] ).
cnf(i_0_3200,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X1,esk70_2(X1,X2))),hAPP_a_bool(X2,esk70_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1764]),
[final] ).
cnf(i_0_3201,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,esk187_3(X1,X2,X3)),X3))
| hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_3202,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1765]),
[final] ).
cnf(i_0_3203,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1766]),
[final] ).
cnf(i_0_3204,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X3)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_1767]),
[final] ).
cnf(i_0_3205,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X3)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_1768]),
[final] ).
cnf(i_0_3206,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_1769]),
[final] ).
cnf(i_0_3207,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_1770]),
[final] ).
cnf(i_0_3208,plain,
( hBOOL(hAPP_f54304608l_bool(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(X1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk121_2(X1,X2)),esk122_2(X1,X2))))
| ~ hBOOL(hAPP_f54304608l_bool(X1,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1771]),
[final] ).
cnf(i_0_3209,plain,
( hBOOL(hAPP_f448129468l_bool(X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(X1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk119_2(X1,X2)),esk120_2(X1,X2))))
| ~ hBOOL(hAPP_f448129468l_bool(X1,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1772]),
[final] ).
cnf(i_0_3210,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk123_2(X1,X2)),esk124_2(X1,X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_3211,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk117_2(X1,X2)),esk118_2(X1,X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_3212,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X2))
| is_pname(esk159_2(X1,X2))
| X2 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(X1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk160_2(X1,X2)),esk161_2(X1,X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_3213,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| is_a(esk150_2(X1,X2))
| X2 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk151_2(X1,X2)),esk152_2(X1,X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_3214,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1775]),
[final] ).
cnf(i_0_3215,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_3216,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_3217,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1778]),
[final] ).
cnf(i_0_3218,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1779]),
[final] ).
cnf(i_0_3219,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1780]),
[final] ).
cnf(i_0_3220,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1781]),
[final] ).
cnf(i_0_3221,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1782]),
[final] ).
cnf(i_0_3222,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1783]),
[final] ).
cnf(i_0_3223,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1784]),
[final] ).
cnf(i_0_3224,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1785]),
[final] ).
cnf(i_0_3225,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1786]),
[final] ).
cnf(i_0_3226,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,esk195_3(X1,X2,X3)),X3))
| hBOOL(hAPP_int_bool(X2,X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),esk194_3(X1,X2,X3)))
| ~ hBOOL(hAPP_int_bool(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_3227,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_3228,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1753]),
[final] ).
cnf(i_0_3229,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_3230,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1775]),
[final] ).
cnf(i_0_3231,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(rw,[status(thm)],[i_0_1787,c_0_1640]),
[final] ).
cnf(i_0_3232,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),X1)) ),
inference(rw,[status(thm)],[i_0_1788,c_0_1640]),
[final] ).
cnf(i_0_3233,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
| hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X3))),one_one_nat)
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1789]),
[final] ).
cnf(i_0_3234,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
| hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X3))),one_one_nat)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1790]),
[final] ).
cnf(i_0_3235,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3))
| hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X3))),one_one_nat)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1791]),
[final] ).
cnf(i_0_3236,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3))
| hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X3))),one_one_nat)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1792]),
[final] ).
cnf(i_0_3237,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1766]),
[final] ).
cnf(i_0_3238,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,esk195_3(X1,X2,X3)),X3))
| hBOOL(hAPP_int_bool(X2,X1))
| hBOOL(hAPP_int_bool(X2,esk194_3(X1,X2,X3)))
| ~ hBOOL(hAPP_int_bool(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_3239,plain,
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)) = bot_bo844097828e_bool
| hAPP_f1297739591_pname(X3,X1) = hAPP_pname_pname(hAPP_p1170154830_pname(X4,X2),hAPP_f1297739591_pname(X3,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(finite1282449217_pname(X4,X3))
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1793]),
[final] ).
cnf(i_0_3240,plain,
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool
| hAPP_fun_a_bool_a(X3,X1) = hAPP_a_a(hAPP_a_fun_a_a(X4,X2),hAPP_fun_a_bool_a(X3,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(finite_folding_one_a(X4,X3))
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1794]),
[final] ).
cnf(i_0_3241,plain,
( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool
| hAPP_f1594865479ol_int(X3,X1) = hAPP_int_int(hAPP_int_fun_int_int(X4,X2),hAPP_f1594865479ol_int(X3,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(finite1626084323ne_int(X4,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1795]),
[final] ).
cnf(i_0_3242,plain,
( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
| hAPP_f22106695ol_nat(X3,X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X4,X2),hAPP_f22106695ol_nat(X3,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(finite988810631ne_nat(X4,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1796]),
[final] ).
cnf(i_0_3243,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X2)),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk133_2(X1,X2)),hAPP_nat_nat(X2,esk133_2(X1,X2)))) ),
inference(rw,[status(thm)],[i_0_1797,c_0_1678]),
[final] ).
cnf(i_0_3244,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1798]),
[final] ).
cnf(i_0_3245,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1799]),
[final] ).
cnf(i_0_3246,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1800]),
[final] ).
cnf(i_0_3247,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1801]),
[final] ).
cnf(i_0_3248,plain,
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)) = bot_bo844097828e_bool
| hAPP_f1297739591_pname(X3,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1)) = hAPP_pname_pname(hAPP_p1170154830_pname(X4,X2),hAPP_f1297739591_pname(X3,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(finite1282449217_pname(X4,X3))
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1802]),
[final] ).
cnf(i_0_3249,plain,
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool
| hAPP_fun_a_bool_a(X3,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1)) = hAPP_a_a(hAPP_a_fun_a_a(X4,X2),hAPP_fun_a_bool_a(X3,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(finite_folding_one_a(X4,X3))
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1803]),
[final] ).
cnf(i_0_3250,plain,
( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool
| hAPP_f1594865479ol_int(X3,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1)) = hAPP_int_int(hAPP_int_fun_int_int(X4,X2),hAPP_f1594865479ol_int(X3,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(finite1626084323ne_int(X4,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1804]),
[final] ).
cnf(i_0_3251,plain,
( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
| hAPP_f22106695ol_nat(X3,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X4,X2),hAPP_f22106695ol_nat(X3,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(finite988810631ne_nat(X4,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1805]),
[final] ).
cnf(i_0_3252,plain,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,esk12_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_1921560913_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1806]),
[final] ).
cnf(i_0_3253,plain,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,esk2_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_fun_nat_bool_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1807]),
[final] ).
cnf(i_0_3254,plain,
( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,esk11_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_62782965_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1808]),
[final] ).
cnf(i_0_3255,plain,
( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,esk1_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_fun_int_bool_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1809]),
[final] ).
cnf(i_0_3256,plain,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,esk13_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_1283814551_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1810]),
[final] ).
cnf(i_0_3257,plain,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,esk3_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_876012084bool_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1811]),
[final] ).
cnf(i_0_3258,plain,
( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,esk14_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_1854862208_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1812]),
[final] ).
cnf(i_0_3259,plain,
( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,esk4_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_fun_a_bool_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1813]),
[final] ).
cnf(i_0_3260,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk37_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_nat_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1814]),
[final] ).
cnf(i_0_3261,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk36_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),image_nat_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
| ~ is_fun949378684l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_3262,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk35_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),image_1655916159e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
| ~ is_fun1661590463l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1816]),
[final] ).
cnf(i_0_3263,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk32_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_nat_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1817]),
[final] ).
cnf(i_0_3264,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,esk43_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_int_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_3265,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,esk42_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),image_int_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
| ~ is_fun949378684l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1819]),
[final] ).
cnf(i_0_3266,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,esk41_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),image_637364955e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
| ~ is_fun1661590463l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1820]),
[final] ).
cnf(i_0_3267,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,esk38_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_int_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1821]),
[final] ).
cnf(i_0_3268,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk44_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1822]),
[final] ).
cnf(i_0_3269,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk31_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_pname_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1823]),
[final] ).
cnf(i_0_3270,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk30_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),image_112932426a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
| ~ is_fun949378684l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1824]),
[final] ).
cnf(i_0_3271,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk29_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),image_47868345e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
| ~ is_fun1661590463l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1825]),
[final] ).
cnf(i_0_3272,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk10_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_a_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1826]),
[final] ).
cnf(i_0_3273,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk9_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),image_a_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
| ~ is_fun949378684l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1827]),
[final] ).
cnf(i_0_3274,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk8_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),image_819518260e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
| ~ is_fun1661590463l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1828]),
[final] ).
cnf(i_0_3275,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk5_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_a_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1829]),
[final] ).
cnf(i_0_3276,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,esk161_2(X1,X2)))
| hBOOL(hAPP_f1664156314l_bool(X1,X2))
| X2 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(X1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk159_2(X1,X2)),bot_bo844097828e_bool)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_3277,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,esk152_2(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| X2 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk150_2(X1,X2)),bot_bot_fun_a_bool)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_3278,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk161_2(X1,X2)))
| hBOOL(hAPP_f1664156314l_bool(X1,X2))
| X2 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(X1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk159_2(X1,X2)),bot_bo844097828e_bool)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_3279,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk152_2(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| X2 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk150_2(X1,X2)),bot_bot_fun_a_bool)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_3280,plain,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,esk23_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_1133522419ol_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1830]),
[final] ).
cnf(i_0_3281,plain,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,esk17_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_496248727ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1831]),
[final] ).
cnf(i_0_3282,plain,
( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,esk22_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_2069007511ol_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1832]),
[final] ).
cnf(i_0_3283,plain,
( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,esk16_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_1431733819ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1833]),
[final] ).
cnf(i_0_3284,plain,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,esk24_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_41399353ol_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1834]),
[final] ).
cnf(i_0_3285,plain,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,esk18_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_1551609309ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1835]),
[final] ).
cnf(i_0_3286,plain,
( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,esk25_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_fun_a_bool_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1836]),
[final] ).
cnf(i_0_3287,plain,
( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,esk19_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_fun_a_bool_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1837]),
[final] ).
cnf(i_0_3288,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk45_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_nat_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1838]),
[final] ).
cnf(i_0_3289,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk34_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),image_26036933t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1839]),
[final] ).
cnf(i_0_3290,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk33_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),image_1556378401t_bool(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1840]),
[final] ).
cnf(i_0_3291,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,esk40_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),image_892525857t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1841]),
[final] ).
cnf(i_0_3292,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,esk39_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),image_275383677t_bool(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1842]),
[final] ).
cnf(i_0_3293,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk28_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),image_2129980159t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1843]),
[final] ).
cnf(i_0_3294,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk27_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),image_1512837979t_bool(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1844]),
[final] ).
cnf(i_0_3295,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk26_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_pname_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1845]),
[final] ).
cnf(i_0_3296,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk20_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_pname_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1846]),
[final] ).
cnf(i_0_3297,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk21_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_a_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1847]),
[final] ).
cnf(i_0_3298,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk15_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_a_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1848]),
[final] ).
cnf(i_0_3299,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk7_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),image_a_fun_nat_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1849]),
[final] ).
cnf(i_0_3300,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk6_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),image_a_fun_int_bool(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1850]),
[final] ).
cnf(i_0_3301,plain,
( hBOOL(hAPP_f54304608l_bool(X1,esk158_2(X1,X2)))
| hBOOL(hAPP_f54304608l_bool(X1,X2))
| X2 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(X1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk156_2(X1,X2)),bot_bot_fun_nat_bool)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1737]),
[final] ).
cnf(i_0_3302,plain,
( hBOOL(hAPP_f448129468l_bool(X1,esk155_2(X1,X2)))
| hBOOL(hAPP_f448129468l_bool(X1,X2))
| X2 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(X1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk153_2(X1,X2)),bot_bot_fun_int_bool)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_3303,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X4)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1851]),
[final] ).
cnf(i_0_3304,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X4)),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1852]),
[final] ).
cnf(i_0_3305,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X4)),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1853]),
[final] ).
cnf(i_0_3306,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1854]),
[final] ).
cnf(i_0_3307,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1855]),
[final] ).
cnf(i_0_3308,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1856]),
[final] ).
cnf(i_0_3309,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1857]),
[final] ).
cnf(i_0_3310,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1858]),
[final] ).
cnf(i_0_3311,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X4)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1859]),
[final] ).
cnf(i_0_3312,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X3)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1860]),
[final] ).
cnf(i_0_3313,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X3)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X4)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1861]),
[final] ).
cnf(i_0_3314,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk158_2(X1,X2)))
| hBOOL(hAPP_f54304608l_bool(X1,X2))
| X2 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(X1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk156_2(X1,X2)),bot_bot_fun_nat_bool)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1737]),
[final] ).
cnf(i_0_3315,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk155_2(X1,X2)))
| hBOOL(hAPP_f448129468l_bool(X1,X2))
| X2 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(X1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk153_2(X1,X2)),bot_bot_fun_int_bool)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_3316,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk105_3(X1,X2,X3)),X2))
| hBOOL(hAPP_f54304608l_bool(X1,X3))
| ~ hBOOL(hAPP_f54304608l_bool(X1,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1689]),
[final] ).
cnf(i_0_3317,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk103_3(X1,X2,X3)),X2))
| hBOOL(hAPP_f448129468l_bool(X1,X3))
| ~ hBOOL(hAPP_f448129468l_bool(X1,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1690]),
[final] ).
cnf(i_0_3318,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk107_3(X1,X2,X3)),X2))
| hBOOL(hAPP_f1664156314l_bool(X1,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1691]),
[final] ).
cnf(i_0_3319,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk101_3(X1,X2,X3)),X2))
| hBOOL(hAPP_fun_a_bool_bool(X1,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_3320,plain,
( hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)))
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1862,c_0_1649]),c_0_1649]),c_0_1640]),
[final] ).
cnf(i_0_3321,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_3322,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1863]),
[final] ).
cnf(i_0_3323,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1775]),
[final] ).
cnf(i_0_3324,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1755]),
[final] ).
cnf(i_0_3325,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1864]),
[final] ).
cnf(i_0_3326,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1757]),
[final] ).
cnf(i_0_3327,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X3),X1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1865]),
[final] ).
cnf(i_0_3328,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1767]),
[final] ).
cnf(i_0_3329,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X2))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1768]),
[final] ).
cnf(i_0_3330,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1769]),
[final] ).
cnf(i_0_3331,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1770]),
[final] ).
cnf(i_0_3332,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,esk64_3(X2,X1,X3))))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1866]),
[final] ).
cnf(i_0_3333,plain,
( hBOOL(hAPP_int_bool(X3,zero_zero_int))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(X3,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_3334,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk72_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1867]),
[final] ).
cnf(i_0_3335,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk74_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1868]),
[final] ).
cnf(i_0_3336,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk67_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1869]),
[final] ).
cnf(i_0_3337,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1870]),
[final] ).
cnf(i_0_3338,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1871]),
[final] ).
cnf(i_0_3339,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1798]),
[final] ).
cnf(i_0_3340,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X3)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1799]),
[final] ).
cnf(i_0_3341,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk73_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),image_nat_int(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1872]),
[final] ).
cnf(i_0_3342,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk66_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),image_nat_int(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1873]),
[final] ).
cnf(i_0_3343,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk71_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),image_nat_int(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1874]),
[final] ).
cnf(i_0_3344,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),esk189_3(X2,X1,X3)))
| hBOOL(hAPP_int_bool(X2,X3))
| ~ hBOOL(hAPP_int_bool(X2,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1705]),
[final] ).
cnf(i_0_3345,plain,
( is_pname(esk160_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(X1,X2))
| X2 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(X1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk159_2(X1,X2)),bot_bo844097828e_bool)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_3346,plain,
( is_fun_pname_bool(esk161_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(X1,X2))
| X2 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(X1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk159_2(X1,X2)),bot_bo844097828e_bool)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_3347,plain,
( is_a(esk151_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| X2 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk150_2(X1,X2)),bot_bot_fun_a_bool)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_3348,plain,
( is_fun_a_bool(esk152_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| X2 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk150_2(X1,X2)),bot_bot_fun_a_bool)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_3349,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk168_3(X1,X2,X3)),X3))
| hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1875]),
[final] ).
cnf(i_0_3350,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,esk188_3(X1,X2,X3)),X3))
| hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(X1,X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1712]),
[final] ).
cnf(i_0_3351,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,esk168_3(X1,X2,X3))))
| hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1875]),
[final] ).
cnf(i_0_3352,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X2))
| X2 = bot_bo844097828e_bool
| esk161_2(X1,X2) != bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(X1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk159_2(X1,X2)),bot_bo844097828e_bool)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_3353,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| X2 = bot_bot_fun_a_bool
| esk152_2(X1,X2) != bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk150_2(X1,X2)),bot_bot_fun_a_bool)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_3354,plain,
( hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,X2)))) != zero_zero_nat
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),X1)) ),
inference(rw,[status(thm)],[i_0_1876,c_0_1678]),
[final] ).
cnf(i_0_3355,plain,
( hBOOL(hAPP_f54304608l_bool(X1,X2))
| X2 = bot_bot_fun_nat_bool
| esk158_2(X1,X2) != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(X1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk156_2(X1,X2)),bot_bot_fun_nat_bool)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1737]),
[final] ).
cnf(i_0_3356,plain,
( hBOOL(hAPP_f448129468l_bool(X1,X2))
| X2 = bot_bot_fun_int_bool
| esk155_2(X1,X2) != bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(X1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk153_2(X1,X2)),bot_bot_fun_int_bool)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_3357,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk79_3(X1,X2,X3)),X3))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1710]),
[final] ).
cnf(i_0_3358,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk80_3(X1,X2,X3)),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1711]),
[final] ).
cnf(i_0_3359,plain,
( hBOOL(hAPP_int_bool(X1,esk187_3(X1,X2,X3)))
| hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1704]),
[final] ).
cnf(i_0_3360,plain,
( hBOOL(hAPP_int_bool(X1,esk189_3(X1,X2,X3)))
| hBOOL(hAPP_int_bool(X1,X3))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1705]),
[final] ).
cnf(i_0_3361,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(suc,X2))),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1877]),
[final] ).
cnf(i_0_3362,plain,
( hAPP_f957591787ol_nat(finite_card_int,X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1878]),
[final] ).
cnf(i_0_3363,plain,
( hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1879]),
[final] ).
cnf(i_0_3364,plain,
( hAPP_fun_a_bool_nat(finite_card_a,X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1880]),
[final] ).
cnf(i_0_3365,plain,
( hAPP_f921600141ol_nat(finite_card_pname,X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1881]),
[final] ).
cnf(i_0_3366,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1882]),
[final] ).
cnf(i_0_3367,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1882]),
[final] ).
cnf(i_0_3368,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1883]),
[final] ).
cnf(i_0_3369,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1883]),
[final] ).
cnf(i_0_3370,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1884]),
[final] ).
cnf(i_0_3371,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1884]),
[final] ).
cnf(i_0_3372,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1885]),
[final] ).
cnf(i_0_3373,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1885]),
[final] ).
cnf(i_0_3374,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1886]),
[final] ).
cnf(i_0_3375,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1887]),
[final] ).
cnf(i_0_3376,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1887]),
[final] ).
cnf(i_0_3377,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1888]),
[final] ).
cnf(i_0_3378,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1889]),
[final] ).
cnf(i_0_3379,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1))),X3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1890]),
[final] ).
cnf(i_0_3380,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X2)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_3381,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(X1,esk178_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1892]),
[final] ).
cnf(i_0_3382,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(X1,esk177_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1893]),
[final] ).
cnf(i_0_3383,plain,
( hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))) = hAPP_f957591787ol_nat(finite_card_int,X1)
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1894]),
[final] ).
cnf(i_0_3384,plain,
( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))) = hAPP_f22106695ol_nat(finite_card_nat,X1)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1895]),
[final] ).
cnf(i_0_3385,plain,
( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))) = hAPP_fun_a_bool_nat(finite_card_a,X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_3386,plain,
( hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))) = hAPP_f921600141ol_nat(finite_card_pname,X1)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1897]),
[final] ).
cnf(i_0_3387,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1898]),
[final] ).
cnf(i_0_3388,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X1)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1899]),
[final] ).
cnf(i_0_3389,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X1)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1900]),
[final] ).
cnf(i_0_3390,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1901]),
[final] ).
cnf(i_0_3391,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1902]),
[final] ).
cnf(i_0_3392,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_3393,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1756]),
[final] ).
cnf(i_0_3394,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1903]),
[final] ).
cnf(i_0_3395,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1758]),
[final] ).
cnf(i_0_3396,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1904]),
[final] ).
cnf(i_0_3397,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1905]),
[final] ).
cnf(i_0_3398,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1906]),
[final] ).
cnf(i_0_3399,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1779]),
[final] ).
cnf(i_0_3400,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1780]),
[final] ).
cnf(i_0_3401,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1907]),
[final] ).
cnf(i_0_3402,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1782]),
[final] ).
cnf(i_0_3403,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1908]),
[final] ).
cnf(i_0_3404,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1909]),
[final] ).
cnf(i_0_3405,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X3)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1910]),
[final] ).
cnf(i_0_3406,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X3)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1911]),
[final] ).
cnf(i_0_3407,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X3)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X3)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1784]),
[final] ).
cnf(i_0_3408,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1912]),
[final] ).
cnf(i_0_3409,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1913]),
[final] ).
cnf(i_0_3410,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1786]),
[final] ).
cnf(i_0_3411,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1801]),
[final] ).
cnf(i_0_3412,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1801]),
[final] ).
cnf(i_0_3413,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X2)),X3)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2))),X3),
inference(split_conjunct,[status(thm)],[i_0_1914]),
[final] ).
cnf(i_0_3414,plain,
( hBOOL(hAPP_int_bool(X1,esk195_3(X2,X1,X3)))
| hBOOL(hAPP_int_bool(X1,X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),esk194_3(X2,X1,X3)))
| ~ hBOOL(hAPP_int_bool(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_3415,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(X1,esk64_3(X2,X1,X3)))
| ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1866]),
[final] ).
cnf(i_0_3416,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X3)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1882]),
[final] ).
cnf(i_0_3417,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X3)),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1883]),
[final] ).
cnf(i_0_3418,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X3)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1884]),
[final] ).
cnf(i_0_3419,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X3)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1885]),
[final] ).
cnf(i_0_3420,plain,
( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1915]),
[final] ).
cnf(i_0_3421,plain,
( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1916]),
[final] ).
cnf(i_0_3422,plain,
( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1917]),
[final] ).
cnf(i_0_3423,plain,
( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1918]),
[final] ).
cnf(i_0_3424,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(X1,esk178_3(X1,X2,X3)))
| ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(split_conjunct,[status(thm)],[i_0_1892]),
[final] ).
cnf(i_0_3425,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(X1,esk177_3(X1,X2,X3)))
| ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(split_conjunct,[status(thm)],[i_0_1893]),
[final] ).
cnf(i_0_3426,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1919]),
[final] ).
cnf(i_0_3427,plain,
( hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,esk168_3(X1,X2,X3)))
| ~ hBOOL(hAPP_nat_bool(X1,X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1875]),
[final] ).
cnf(i_0_3428,plain,
( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1920]),
[final] ).
cnf(i_0_3429,plain,
( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1921]),
[final] ).
cnf(i_0_3430,plain,
( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1922]),
[final] ).
cnf(i_0_3431,plain,
( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1923]),
[final] ).
cnf(i_0_3432,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1758]),
[final] ).
cnf(i_0_3433,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1756]),
[final] ).
cnf(i_0_3434,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[i_0_1924]),
[final] ).
cnf(i_0_3435,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X2)),
inference(split_conjunct,[status(thm)],[i_0_1925]),
[final] ).
cnf(i_0_3436,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),X2)),hAPP_nat_nat(suc,X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),X3),
inference(split_conjunct,[status(thm)],[i_0_1926]),
[final] ).
cnf(i_0_3437,plain,
( hBOOL(hAPP_int_bool(X1,esk195_3(X2,X1,X3)))
| hBOOL(hAPP_int_bool(X1,X2))
| hBOOL(hAPP_int_bool(X1,esk194_3(X2,X1,X3)))
| ~ hBOOL(hAPP_int_bool(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_3438,plain,
hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))),X3),
inference(split_conjunct,[status(thm)],[i_0_1927]),
[final] ).
cnf(i_0_3439,plain,
hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))),X3),
inference(split_conjunct,[status(thm)],[i_0_1928]),
[final] ).
cnf(i_0_3440,plain,
hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))),X3),
inference(split_conjunct,[status(thm)],[i_0_1929]),
[final] ).
cnf(i_0_3441,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1930]),
[final] ).
cnf(i_0_3442,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X2),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1930]),
[final] ).
cnf(i_0_3443,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1931]),
[final] ).
cnf(i_0_3444,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X2),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1931]),
[final] ).
cnf(i_0_3445,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1932]),
[final] ).
cnf(i_0_3446,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X2),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1932]),
[final] ).
cnf(i_0_3447,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1933]),
[final] ).
cnf(i_0_3448,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X2),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1933]),
[final] ).
cnf(i_0_3449,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1934]),
[final] ).
cnf(i_0_3450,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X2),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1934]),
[final] ).
cnf(i_0_3451,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1935]),
[final] ).
cnf(i_0_3452,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X2),X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1935]),
[final] ).
cnf(i_0_3453,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X1)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1936]),
[final] ).
cnf(i_0_3454,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1937]),
[final] ).
cnf(i_0_3455,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X2),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3456,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X2),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1939]),
[final] ).
cnf(i_0_3457,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X2),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1940]),
[final] ).
cnf(i_0_3458,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X2),X1))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1941]),
[final] ).
cnf(i_0_3459,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1942]),
[final] ).
cnf(i_0_3460,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1943]),
[final] ).
cnf(i_0_3461,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1))),X3)
| hBOOL(hAPP_int_bool(nat_neg,X2))
| hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1944,c_0_1649]),c_0_1649]),
[final] ).
cnf(i_0_3462,plain,
( X1 = X2
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X2)),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1945,c_0_1640]),c_0_1640]),
[final] ).
cnf(i_0_3463,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1946]),
[final] ).
cnf(i_0_3464,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),hAPP_nat_nat(suc,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1947]),
[final] ).
cnf(i_0_3465,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| hBOOL(hAPP_int_bool(X3,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_3466,plain,
( X1 = X2
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun1661590463l_bool(X2)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1948]),
[final] ).
cnf(i_0_3467,plain,
( X1 = X2
| ~ is_fun949378684l_bool(X1)
| ~ is_fun949378684l_bool(X2)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1949]),
[final] ).
cnf(i_0_3468,plain,
( X1 = X2
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1950]),
[final] ).
cnf(i_0_3469,plain,
( X1 = X2
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1951]),
[final] ).
cnf(i_0_3470,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X1)))),
inference(split_conjunct,[status(thm)],[i_0_1952]),
[final] ).
cnf(i_0_3471,plain,
( X2 = X1
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1953]),
[final] ).
cnf(i_0_3472,plain,
( X2 = X1
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X1)),hAPP_f521865025ol_nat(finite1876863882t_bool,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1954]),
[final] ).
cnf(i_0_3473,plain,
( X2 = X1
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),hAPP_f22106695ol_nat(finite_card_nat,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1955]),
[final] ).
cnf(i_0_3474,plain,
( X2 = X1
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X1)),hAPP_f957591787ol_nat(finite_card_int,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1956]),
[final] ).
cnf(i_0_3475,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1957]),
[final] ).
cnf(i_0_3476,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1719]),
[final] ).
cnf(i_0_3477,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X3))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1958]),
[final] ).
cnf(i_0_3478,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1721]),
[final] ).
cnf(i_0_3479,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_3480,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1959]),
[final] ).
cnf(i_0_3481,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1725]),
[final] ).
cnf(i_0_3482,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1960]),
[final] ).
cnf(i_0_3483,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk12_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_1921560913_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1806]),
[final] ).
cnf(i_0_3484,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk2_3(X1,X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_fun_nat_bool_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1807]),
[final] ).
cnf(i_0_3485,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,esk11_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_62782965_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1808]),
[final] ).
cnf(i_0_3486,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,esk1_3(X1,X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_fun_int_bool_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1809]),
[final] ).
cnf(i_0_3487,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk13_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_1283814551_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1810]),
[final] ).
cnf(i_0_3488,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk3_3(X1,X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_876012084bool_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1811]),
[final] ).
cnf(i_0_3489,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk14_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_1854862208_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1812]),
[final] ).
cnf(i_0_3490,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk4_3(X1,X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_fun_a_bool_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1813]),
[final] ).
cnf(i_0_3491,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk37_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_nat_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1814]),
[final] ).
cnf(i_0_3492,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk36_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),image_nat_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
| ~ is_fun949378684l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_3493,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk35_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),image_1655916159e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
| ~ is_fun1661590463l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1816]),
[final] ).
cnf(i_0_3494,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk32_3(X1,X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_nat_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1817]),
[final] ).
cnf(i_0_3495,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk43_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_int_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_3496,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk42_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),image_int_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
| ~ is_fun949378684l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1819]),
[final] ).
cnf(i_0_3497,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk41_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),image_637364955e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
| ~ is_fun1661590463l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1820]),
[final] ).
cnf(i_0_3498,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk38_3(X1,X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_int_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1821]),
[final] ).
cnf(i_0_3499,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk44_3(X1,X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1822]),
[final] ).
cnf(i_0_3500,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk31_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_pname_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1823]),
[final] ).
cnf(i_0_3501,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk30_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),image_112932426a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
| ~ is_fun949378684l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1824]),
[final] ).
cnf(i_0_3502,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk29_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),image_47868345e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
| ~ is_fun1661590463l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1825]),
[final] ).
cnf(i_0_3503,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk10_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_a_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1826]),
[final] ).
cnf(i_0_3504,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk9_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),image_a_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
| ~ is_fun949378684l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1827]),
[final] ).
cnf(i_0_3505,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk8_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),image_819518260e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
| ~ is_fun1661590463l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1828]),
[final] ).
cnf(i_0_3506,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk5_3(X1,X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_a_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1829]),
[final] ).
cnf(i_0_3507,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),esk190_3(X2,X1,X3)))
| hBOOL(hAPP_int_bool(X2,X3))
| ~ hBOOL(hAPP_int_bool(X2,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1713]),
[final] ).
cnf(i_0_3508,plain,
( number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),number_number_of_nat(X1)))
| hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1961,c_0_1649]),c_0_1640]),
[final] ).
cnf(i_0_3509,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk23_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_1133522419ol_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1830]),
[final] ).
cnf(i_0_3510,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk17_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_496248727ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1831]),
[final] ).
cnf(i_0_3511,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,esk22_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_2069007511ol_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1832]),
[final] ).
cnf(i_0_3512,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,esk16_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_1431733819ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1833]),
[final] ).
cnf(i_0_3513,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk24_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_41399353ol_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1834]),
[final] ).
cnf(i_0_3514,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk18_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_1551609309ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1835]),
[final] ).
cnf(i_0_3515,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk25_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_fun_a_bool_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1836]),
[final] ).
cnf(i_0_3516,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk19_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_fun_a_bool_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1837]),
[final] ).
cnf(i_0_3517,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk45_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_nat_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1838]),
[final] ).
cnf(i_0_3518,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk34_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),image_26036933t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1839]),
[final] ).
cnf(i_0_3519,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk33_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),image_1556378401t_bool(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1840]),
[final] ).
cnf(i_0_3520,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk40_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),image_892525857t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1841]),
[final] ).
cnf(i_0_3521,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk39_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),image_275383677t_bool(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1842]),
[final] ).
cnf(i_0_3522,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk28_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),image_2129980159t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1843]),
[final] ).
cnf(i_0_3523,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk27_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),image_1512837979t_bool(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1844]),
[final] ).
cnf(i_0_3524,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk26_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_pname_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1845]),
[final] ).
cnf(i_0_3525,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk20_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_pname_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1846]),
[final] ).
cnf(i_0_3526,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk21_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_a_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1847]),
[final] ).
cnf(i_0_3527,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk15_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_a_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1848]),
[final] ).
cnf(i_0_3528,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk7_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),image_a_fun_nat_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1849]),
[final] ).
cnf(i_0_3529,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk6_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),image_a_fun_int_bool(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1850]),
[final] ).
cnf(i_0_3530,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X3)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1962]),
[final] ).
cnf(i_0_3531,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X2))))
| ~ hBOOL(hAPP_int_bool(X1,zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_3532,plain,
( hBOOL(hAPP_f54304608l_bool(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk121_2(X1,X2)),esk122_2(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(X1,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1771]),
[final] ).
cnf(i_0_3533,plain,
( hBOOL(hAPP_f448129468l_bool(X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk119_2(X1,X2)),esk120_2(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(X1,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1772]),
[final] ).
cnf(i_0_3534,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk123_2(X1,X2)),esk124_2(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_3535,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk117_2(X1,X2)),esk118_2(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_3536,plain,
( hBOOL(hAPP_f54304608l_bool(X1,esk106_3(X1,X2,X3)))
| hBOOL(hAPP_f54304608l_bool(X1,X3))
| ~ hBOOL(hAPP_f54304608l_bool(X1,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1689]),
[final] ).
cnf(i_0_3537,plain,
( hBOOL(hAPP_f448129468l_bool(X1,esk104_3(X1,X2,X3)))
| hBOOL(hAPP_f448129468l_bool(X1,X3))
| ~ hBOOL(hAPP_f448129468l_bool(X1,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1690]),
[final] ).
cnf(i_0_3538,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,esk108_3(X1,X2,X3)))
| hBOOL(hAPP_f1664156314l_bool(X1,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1691]),
[final] ).
cnf(i_0_3539,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,esk102_3(X1,X2,X3)))
| hBOOL(hAPP_fun_a_bool_bool(X1,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_3540,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)),X3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1963]),
[final] ).
cnf(i_0_3541,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)),X3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1964]),
[final] ).
cnf(i_0_3542,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X2)),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_3543,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk106_3(X1,X2,X3)))
| hBOOL(hAPP_f54304608l_bool(X1,X3))
| ~ hBOOL(hAPP_f54304608l_bool(X1,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1689]),
[final] ).
cnf(i_0_3544,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk104_3(X1,X2,X3)))
| hBOOL(hAPP_f448129468l_bool(X1,X3))
| ~ hBOOL(hAPP_f448129468l_bool(X1,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1690]),
[final] ).
cnf(i_0_3545,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk108_3(X1,X2,X3)))
| hBOOL(hAPP_f1664156314l_bool(X1,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1691]),
[final] ).
cnf(i_0_3546,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk102_3(X1,X2,X3)))
| hBOOL(hAPP_fun_a_bool_bool(X1,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_3547,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X2))
| is_pname(esk159_2(X1,X2))
| X2 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk160_2(X1,X2)),esk161_2(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_3548,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| is_a(esk150_2(X1,X2))
| X2 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk151_2(X1,X2)),esk152_2(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_3549,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3550,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| X1 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1966]),
[final] ).
cnf(i_0_3551,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1967]),
[final] ).
cnf(i_0_3552,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1898]),
[final] ).
cnf(i_0_3553,plain,
hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),collect_a(X2)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1))),X2)),
inference(split_conjunct,[status(thm)],[i_0_1968]),
[final] ).
cnf(i_0_3554,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| X1 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1969]),
[final] ).
cnf(i_0_3555,plain,
( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,X1)),one_one_nat)
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1970]),
[final] ).
cnf(i_0_3556,plain,
( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,X2)),one_one_nat)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1971]),
[final] ).
cnf(i_0_3557,plain,
( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,X1)),one_one_nat)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_3558,plain,
( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,X2)),one_one_nat)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1973]),
[final] ).
cnf(i_0_3559,plain,
( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,X1)),one_one_nat)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1974]),
[final] ).
cnf(i_0_3560,plain,
( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),one_one_nat)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1975]),
[final] ).
cnf(i_0_3561,plain,
( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,X1)),one_one_nat)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1976]),
[final] ).
cnf(i_0_3562,plain,
( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),one_one_nat)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1977]),
[final] ).
cnf(i_0_3563,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1978]),
[final] ).
cnf(i_0_3564,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1979]),
[final] ).
cnf(i_0_3565,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1980]),
[final] ).
cnf(i_0_3566,plain,
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1981]),
[final] ).
cnf(i_0_3567,plain,
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1982]),
[final] ).
cnf(i_0_3568,plain,
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1983]),
[final] ).
cnf(i_0_3569,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1984]),
[final] ).
cnf(i_0_3570,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1985]),
[final] ).
cnf(i_0_3571,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1986]),
[final] ).
cnf(i_0_3572,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1987]),
[final] ).
cnf(i_0_3573,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1988]),
[final] ).
cnf(i_0_3574,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1989]),
[final] ).
cnf(i_0_3575,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(X2,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1990]),
[final] ).
cnf(i_0_3576,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(X2,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_3577,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(X2,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1992]),
[final] ).
cnf(i_0_3578,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(X2,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1993]),
[final] ).
cnf(i_0_3579,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(X2,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1994]),
[final] ).
cnf(i_0_3580,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(X2,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1995]),
[final] ).
cnf(i_0_3581,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(X2,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1996]),
[final] ).
cnf(i_0_3582,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X2,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1997]),
[final] ).
cnf(i_0_3583,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X2,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1998]),
[final] ).
cnf(i_0_3584,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X2,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3585,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X2,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2000]),
[final] ).
cnf(i_0_3586,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(X2,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_3587,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X2,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2002]),
[final] ).
cnf(i_0_3588,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X2,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2003]),
[final] ).
cnf(i_0_3589,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(X2,X1))),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2004]),
[final] ).
cnf(i_0_3590,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X2,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2005]),
[final] ).
cnf(i_0_3591,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X2,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2006]),
[final] ).
cnf(i_0_3592,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X2,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2007]),
[final] ).
cnf(i_0_3593,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X2,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_3594,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X2,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2009]),
[final] ).
cnf(i_0_3595,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(X2,X1))),hAPP_f957591787ol_nat(finite_card_int,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2010]),
[final] ).
cnf(i_0_3596,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X2,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2011]),
[final] ).
cnf(i_0_3597,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X2,X1))),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2012]),
[final] ).
cnf(i_0_3598,plain,
( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))),X2)
| hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2013,c_0_1649]),c_0_2014]),
[final] ).
cnf(i_0_3599,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1930]),
[final] ).
cnf(i_0_3600,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1931]),
[final] ).
cnf(i_0_3601,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1932]),
[final] ).
cnf(i_0_3602,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1933]),
[final] ).
cnf(i_0_3603,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1934]),
[final] ).
cnf(i_0_3604,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1935]),
[final] ).
cnf(i_0_3605,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,esk179_2(X2,X1)),one_one_nat)))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2015]),
[final] ).
cnf(i_0_3606,plain,
( hBOOL(hAPP_int_bool(X1,esk188_3(X1,X2,X3)))
| hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(X1,X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1712]),
[final] ).
cnf(i_0_3607,plain,
( hBOOL(hAPP_int_bool(X1,esk190_3(X1,X2,X3)))
| hBOOL(hAPP_int_bool(X1,X3))
| ~ hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1713]),
[final] ).
cnf(i_0_3608,plain,
( X1 = X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
| ~ is_pname(X1)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2016]),
[final] ).
cnf(i_0_3609,plain,
( X1 = X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2017]),
[final] ).
cnf(i_0_3610,plain,
( X1 = X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
| ~ is_a(X1)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2018]),
[final] ).
cnf(i_0_3611,plain,
( X1 = X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2019]),
[final] ).
cnf(i_0_3612,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2020]),
[final] ).
cnf(i_0_3613,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2021]),
[final] ).
cnf(i_0_3614,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2022]),
[final] ).
cnf(i_0_3615,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2023]),
[final] ).
cnf(i_0_3616,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)),X3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2024]),
[final] ).
cnf(i_0_3617,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X2)),X3) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X3)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2025]),
[final] ).
cnf(i_0_3618,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2026]),
[final] ).
cnf(i_0_3619,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),X3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2027]),
[final] ).
cnf(i_0_3620,plain,
( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2028]),
[final] ).
cnf(i_0_3621,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2028]),
[final] ).
cnf(i_0_3622,plain,
( X1 = X2
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2029]),
[final] ).
cnf(i_0_3623,plain,
( X1 = X2
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2030]),
[final] ).
cnf(i_0_3624,plain,
( X1 = X2
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2031]),
[final] ).
cnf(i_0_3625,plain,
( X1 = X2
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2032]),
[final] ).
cnf(i_0_3626,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk86_2(X1,X2)),u))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X2)),bot_bot_fun_a_bool)))
| ~ hBOOL(wt(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1734]),
[final] ).
cnf(i_0_3627,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2033]),
[final] ).
cnf(i_0_3628,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1978]),
[final] ).
cnf(i_0_3629,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2034]),
[final] ).
cnf(i_0_3630,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1979]),
[final] ).
cnf(i_0_3631,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1981]),
[final] ).
cnf(i_0_3632,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2035]),
[final] ).
cnf(i_0_3633,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1982]),
[final] ).
cnf(i_0_3634,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1984]),
[final] ).
cnf(i_0_3635,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2036]),
[final] ).
cnf(i_0_3636,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1985]),
[final] ).
cnf(i_0_3637,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1987]),
[final] ).
cnf(i_0_3638,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2037]),
[final] ).
cnf(i_0_3639,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1988]),
[final] ).
cnf(i_0_3640,plain,
( hBOOL(hAPP_nat_bool(X3,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1892]),
[final] ).
cnf(i_0_3641,plain,
( hBOOL(hAPP_nat_bool(X3,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1893]),
[final] ).
cnf(i_0_3642,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1978]),
[final] ).
cnf(i_0_3643,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2038]),
[final] ).
cnf(i_0_3644,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1719]),
[final] ).
cnf(i_0_3645,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X2)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1957]),
[final] ).
cnf(i_0_3646,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X3))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1981]),
[final] ).
cnf(i_0_3647,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X3))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2039]),
[final] ).
cnf(i_0_3648,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1721]),
[final] ).
cnf(i_0_3649,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X2)))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1958]),
[final] ).
cnf(i_0_3650,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1984]),
[final] ).
cnf(i_0_3651,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2040]),
[final] ).
cnf(i_0_3652,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_3653,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X2)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1959]),
[final] ).
cnf(i_0_3654,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1987]),
[final] ).
cnf(i_0_3655,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2041]),
[final] ).
cnf(i_0_3656,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1725]),
[final] ).
cnf(i_0_3657,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X2)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1960]),
[final] ).
cnf(i_0_3658,plain,
hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))),
inference(split_conjunct,[status(thm)],[i_0_2042]),
[final] ).
cnf(i_0_3659,plain,
hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),
inference(split_conjunct,[status(thm)],[i_0_2043]),
[final] ).
cnf(i_0_3660,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int))) ),
inference(split_conjunct,[status(thm)],[i_0_2044]),
[final] ).
cnf(i_0_3661,plain,
( cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X1) = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X2)
| ~ hBOOL(hAPP_int_bool(X2,esk191_2(X2,X1)))
| ~ hBOOL(hAPP_int_bool(X1,esk191_2(X2,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2045,c_0_1684]),c_0_1684]),
[final] ).
cnf(i_0_3662,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X1)),image_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2046]),
[final] ).
cnf(i_0_3663,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X1)),image_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2047]),
[final] ).
cnf(i_0_3664,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X1)),image_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2048]),
[final] ).
cnf(i_0_3665,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2049]),
[final] ).
cnf(i_0_3666,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2050]),
[final] ).
cnf(i_0_3667,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2051]),
[final] ).
cnf(i_0_3668,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2052]),
[final] ).
cnf(i_0_3669,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2053]),
[final] ).
cnf(i_0_3670,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_3671,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2055]),
[final] ).
cnf(i_0_3672,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2056]),
[final] ).
cnf(i_0_3673,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),one_one_int))) ),
inference(split_conjunct,[status(thm)],[i_0_2057]),
[final] ).
cnf(i_0_3674,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int))) ),
inference(split_conjunct,[status(thm)],[i_0_2058]),
[final] ).
cnf(i_0_3675,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2059]),
[final] ).
cnf(i_0_3676,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)),X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2060]),
[final] ).
cnf(i_0_3677,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X1)),X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2061]),
[final] ).
cnf(i_0_3678,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),hAPP_nat_nat(suc,X1))),
inference(split_conjunct,[status(thm)],[i_0_2062]),
[final] ).
cnf(i_0_3679,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)))),
inference(split_conjunct,[status(thm)],[i_0_2063]),
[final] ).
cnf(i_0_3680,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)))),
inference(split_conjunct,[status(thm)],[i_0_2064]),
[final] ).
cnf(i_0_3681,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2065]),
[final] ).
cnf(i_0_3682,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2020]),
[final] ).
cnf(i_0_3683,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2020]),
[final] ).
cnf(i_0_3684,plain,
( hAPP_f1297739591_pname(X3,X1) = X2
| hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)) != bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(finite1282449217_pname(X4,X3))
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1793]),
[final] ).
cnf(i_0_3685,plain,
( hAPP_fun_a_bool_a(X3,X1) = X2
| hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(finite_folding_one_a(X4,X3))
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1794]),
[final] ).
cnf(i_0_3686,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2066]),
[final] ).
cnf(i_0_3687,plain,
( X1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),esk178_3(X3,X1,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1892]),
[final] ).
cnf(i_0_3688,plain,
( X1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),esk177_3(X3,X1,X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1893]),
[final] ).
cnf(i_0_3689,plain,
( hAPP_f1594865479ol_int(X3,X1) = X2
| hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(finite1626084323ne_int(X4,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1795]),
[final] ).
cnf(i_0_3690,plain,
( hAPP_f22106695ol_nat(X3,X1) = X2
| hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(finite988810631ne_nat(X4,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1796]),
[final] ).
cnf(i_0_3691,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),esk174_2(X1,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2067]),
[final] ).
cnf(i_0_3692,plain,
( is_pname(esk149_3(X1,X2,X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(X3,X1)),X1))
| X1 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(finite1282449217_pname(X2,X3))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1644]),
[final] ).
cnf(i_0_3693,plain,
( is_pname(esk148_3(X1,X2,X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(X3,X1)),X1))
| X1 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(finite1282449217_pname(X2,X3))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1644]),
[final] ).
cnf(i_0_3694,plain,
( is_a(esk143_3(X1,X2,X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(X3,X1)),X1))
| X1 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(finite_folding_one_a(X2,X3))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1645]),
[final] ).
cnf(i_0_3695,plain,
( is_a(esk142_3(X1,X2,X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(X3,X1)),X1))
| X1 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(finite_folding_one_a(X2,X3))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1645]),
[final] ).
cnf(i_0_3696,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2068]),
[final] ).
cnf(i_0_3697,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X2),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2068]),
[final] ).
cnf(i_0_3698,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2069]),
[final] ).
cnf(i_0_3699,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,X2),X1))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2069]),
[final] ).
cnf(i_0_3700,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2070]),
[final] ).
cnf(i_0_3701,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X2),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2070]),
[final] ).
cnf(i_0_3702,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1),X2))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2071]),
[final] ).
cnf(i_0_3703,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X2),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2071]),
[final] ).
cnf(i_0_3704,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1),X2))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2072]),
[final] ).
cnf(i_0_3705,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X2),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2072]),
[final] ).
cnf(i_0_3706,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1),X2))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2073]),
[final] ).
cnf(i_0_3707,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X2),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2073]),
[final] ).
cnf(i_0_3708,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2074]),
[final] ).
cnf(i_0_3709,plain,
( number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1)) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2075,c_0_1649]),c_0_1640]),
[final] ).
cnf(i_0_3710,plain,
( X1 = bot_bot_fun_a_bool
| X1 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_2076]),
[final] ).
cnf(i_0_3711,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,X2)),hAPP_f957591787ol_nat(finite_card_int,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2077]),
[final] ).
cnf(i_0_3712,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X2)),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2078]),
[final] ).
cnf(i_0_3713,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2079]),
[final] ).
cnf(i_0_3714,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2080]),
[final] ).
cnf(i_0_3715,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X2)),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2081]),
[final] ).
cnf(i_0_3716,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,X2)),hAPP_f521865025ol_nat(finite1876863882t_bool,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2082]),
[final] ).
cnf(i_0_3717,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2083]),
[final] ).
cnf(i_0_3718,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2084]),
[final] ).
cnf(i_0_3719,plain,
( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))) = X1
| ~ is_fun_pname_bool(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2085]),
[final] ).
cnf(i_0_3720,plain,
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))) = X1
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2086]),
[final] ).
cnf(i_0_3721,plain,
( X1 = image_1921560913_pname(X2,esk12_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),image_1921560913_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1806]),
[final] ).
cnf(i_0_3722,plain,
( X1 = image_fun_nat_bool_a(X2,esk2_3(X2,X3,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_fun_nat_bool_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1807]),
[final] ).
cnf(i_0_3723,plain,
( X1 = image_62782965_pname(X2,esk11_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),image_62782965_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1808]),
[final] ).
cnf(i_0_3724,plain,
( X1 = image_fun_int_bool_a(X2,esk1_3(X2,X3,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_fun_int_bool_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1809]),
[final] ).
cnf(i_0_3725,plain,
( X1 = image_1283814551_pname(X2,esk13_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),image_1283814551_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1810]),
[final] ).
cnf(i_0_3726,plain,
( X1 = image_876012084bool_a(X2,esk3_3(X2,X3,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_876012084bool_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1811]),
[final] ).
cnf(i_0_3727,plain,
( X1 = image_1854862208_pname(X2,esk14_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),image_1854862208_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1812]),
[final] ).
cnf(i_0_3728,plain,
( X1 = image_fun_a_bool_a(X2,esk4_3(X2,X3,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_fun_a_bool_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1813]),
[final] ).
cnf(i_0_3729,plain,
( X1 = image_1655916159e_bool(X2,esk35_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),image_1655916159e_bool(X2,X3)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1816]),
[final] ).
cnf(i_0_3730,plain,
( X1 = image_nat_fun_a_bool(X2,esk36_3(X2,X3,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),image_nat_fun_a_bool(X2,X3)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_3731,plain,
( X1 = image_nat_pname(X2,esk37_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),image_nat_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1814]),
[final] ).
cnf(i_0_3732,plain,
( X1 = image_nat_a(X2,esk32_3(X2,X3,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_nat_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1817]),
[final] ).
cnf(i_0_3733,plain,
( X1 = image_637364955e_bool(X2,esk41_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),image_637364955e_bool(X2,X3)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1820]),
[final] ).
cnf(i_0_3734,plain,
( X1 = image_int_fun_a_bool(X2,esk42_3(X2,X3,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),image_int_fun_a_bool(X2,X3)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1819]),
[final] ).
cnf(i_0_3735,plain,
( X1 = image_int_pname(X2,esk43_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),image_int_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_3736,plain,
( X1 = image_int_a(X2,esk38_3(X2,X3,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_int_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1821]),
[final] ).
cnf(i_0_3737,plain,
( X1 = image_47868345e_bool(X2,esk29_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),image_47868345e_bool(X2,X3)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1825]),
[final] ).
cnf(i_0_3738,plain,
( X1 = image_112932426a_bool(X2,esk30_3(X2,X3,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),image_112932426a_bool(X2,X3)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1824]),
[final] ).
cnf(i_0_3739,plain,
( X1 = image_pname_pname(X2,esk31_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),image_pname_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1823]),
[final] ).
cnf(i_0_3740,plain,
( X1 = image_pname_a(X2,esk44_3(X2,X3,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1822]),
[final] ).
cnf(i_0_3741,plain,
( X1 = image_819518260e_bool(X2,esk8_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),image_819518260e_bool(X2,X3)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1828]),
[final] ).
cnf(i_0_3742,plain,
( X1 = image_a_fun_a_bool(X2,esk9_3(X2,X3,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),image_a_fun_a_bool(X2,X3)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1827]),
[final] ).
cnf(i_0_3743,plain,
( X1 = image_a_pname(X2,esk10_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),image_a_pname(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1826]),
[final] ).
cnf(i_0_3744,plain,
( X1 = image_a_a(X2,esk5_3(X2,X3,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_a_a(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1829]),
[final] ).
cnf(i_0_3745,plain,
( X1 = bot_bot_fun_nat_bool
| X1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_2087]),
[final] ).
cnf(i_0_3746,plain,
( X1 = bot_bot_fun_int_bool
| X1 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_2088]),
[final] ).
cnf(i_0_3747,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk176_2(X1,X2)),X2))
| X1 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_3748,plain,
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2090]),
[final] ).
cnf(i_0_3749,plain,
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2091]),
[final] ).
cnf(i_0_3750,plain,
( X1 = image_a_fun_nat_bool(X2,esk7_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),image_a_fun_nat_bool(X2,X3)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1849]),
[final] ).
cnf(i_0_3751,plain,
( X1 = image_a_fun_int_bool(X2,esk6_3(X2,X3,X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X1),image_a_fun_int_bool(X2,X3)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1850]),
[final] ).
cnf(i_0_3752,plain,
( X1 = image_pname_int(X2,esk26_3(X2,X3,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),image_pname_int(X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1845]),
[final] ).
cnf(i_0_3753,plain,
( X1 = image_pname_nat(X2,esk20_3(X2,X3,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),image_pname_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1846]),
[final] ).
cnf(i_0_3754,plain,
( X1 = image_nat_int(X2,esk45_3(X2,X3,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),image_nat_int(X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1838]),
[final] ).
cnf(i_0_3755,plain,
( X1 = image_fun_a_bool_int(X2,esk25_3(X2,X3,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),image_fun_a_bool_int(X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1836]),
[final] ).
cnf(i_0_3756,plain,
( X1 = image_41399353ol_int(X2,esk24_3(X2,X3,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),image_41399353ol_int(X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1834]),
[final] ).
cnf(i_0_3757,plain,
( X1 = image_1133522419ol_int(X2,esk23_3(X2,X3,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),image_1133522419ol_int(X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1830]),
[final] ).
cnf(i_0_3758,plain,
( X1 = image_2069007511ol_int(X2,esk22_3(X2,X3,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),image_2069007511ol_int(X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1832]),
[final] ).
cnf(i_0_3759,plain,
( X1 = image_a_int(X2,esk21_3(X2,X3,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),image_a_int(X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1847]),
[final] ).
cnf(i_0_3760,plain,
( X1 = image_fun_a_bool_nat(X2,esk19_3(X2,X3,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),image_fun_a_bool_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1837]),
[final] ).
cnf(i_0_3761,plain,
( X1 = image_1551609309ol_nat(X2,esk18_3(X2,X3,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),image_1551609309ol_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1835]),
[final] ).
cnf(i_0_3762,plain,
( X1 = image_496248727ol_nat(X2,esk17_3(X2,X3,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),image_496248727ol_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1831]),
[final] ).
cnf(i_0_3763,plain,
( X1 = image_1431733819ol_nat(X2,esk16_3(X2,X3,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),image_1431733819ol_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1833]),
[final] ).
cnf(i_0_3764,plain,
( X1 = image_a_nat(X2,esk15_3(X2,X3,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),image_a_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1848]),
[final] ).
cnf(i_0_3765,plain,
( X1 = image_892525857t_bool(X2,esk40_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),image_892525857t_bool(X2,X3)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1841]),
[final] ).
cnf(i_0_3766,plain,
( X1 = image_275383677t_bool(X2,esk39_3(X2,X3,X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X1),image_275383677t_bool(X2,X3)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1842]),
[final] ).
cnf(i_0_3767,plain,
( X1 = image_26036933t_bool(X2,esk34_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),image_26036933t_bool(X2,X3)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1839]),
[final] ).
cnf(i_0_3768,plain,
( X1 = image_1556378401t_bool(X2,esk33_3(X2,X3,X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X1),image_1556378401t_bool(X2,X3)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1840]),
[final] ).
cnf(i_0_3769,plain,
( X1 = image_2129980159t_bool(X2,esk28_3(X2,X3,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),image_2129980159t_bool(X2,X3)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1843]),
[final] ).
cnf(i_0_3770,plain,
( X1 = image_1512837979t_bool(X2,esk27_3(X2,X3,X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X1),image_1512837979t_bool(X2,X3)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1844]),
[final] ).
cnf(i_0_3771,plain,
( X1 = X2
| X1 = X3
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))
| ~ is_a(X1)
| ~ is_a(X4)
| ~ is_a(X3)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2092]),
[final] ).
cnf(i_0_3772,plain,
( X1 = X2
| X1 = X3
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool))
| ~ is_a(X4)
| ~ is_a(X1)
| ~ is_a(X2)
| ~ is_a(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2092]),
[final] ).
cnf(i_0_3773,plain,
( X1 = X2
| X3 = X2
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))
| ~ is_a(X1)
| ~ is_a(X3)
| ~ is_a(X4)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2092]),
[final] ).
cnf(i_0_3774,plain,
( X1 = X2
| X3 = X2
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4),bot_bot_fun_a_bool))
| ~ is_a(X3)
| ~ is_a(X1)
| ~ is_a(X2)
| ~ is_a(X4) ),
inference(split_conjunct,[status(thm)],[i_0_2092]),
[final] ).
cnf(i_0_3775,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X3)),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2093]),
[final] ).
cnf(i_0_3776,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X3)),X2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2094]),
[final] ).
cnf(i_0_3777,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X3)),X2) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2095]),
[final] ).
cnf(i_0_3778,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X3)),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2096]),
[final] ).
cnf(i_0_3779,plain,
( hBOOL(hAPP_nat_bool(X4,X3))
| X1 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)
| ~ hBOOL(hAPP_nat_bool(X4,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1892]),
[final] ).
cnf(i_0_3780,plain,
( hBOOL(hAPP_nat_bool(X4,X3))
| X1 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)
| ~ hBOOL(hAPP_nat_bool(X4,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1893]),
[final] ).
cnf(i_0_3781,plain,
( is_fun1661590463l_bool(esk13_3(X1,X2,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_1283814551_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1810]),
[final] ).
cnf(i_0_3782,plain,
( is_fun1661590463l_bool(esk3_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_876012084bool_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1811]),
[final] ).
cnf(i_0_3783,plain,
( is_fun949378684l_bool(esk14_3(X1,X2,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_1854862208_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1812]),
[final] ).
cnf(i_0_3784,plain,
( is_fun949378684l_bool(esk4_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_fun_a_bool_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1813]),
[final] ).
cnf(i_0_3785,plain,
( is_fun_pname_bool(esk44_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_pname_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1822]),
[final] ).
cnf(i_0_3786,plain,
( is_fun_pname_bool(esk31_3(X1,X2,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_pname_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1823]),
[final] ).
cnf(i_0_3787,plain,
( is_fun_pname_bool(esk30_3(X1,X2,X3))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),image_112932426a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
| ~ is_fun949378684l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1824]),
[final] ).
cnf(i_0_3788,plain,
( is_fun_pname_bool(esk29_3(X1,X2,X3))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),image_47868345e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
| ~ is_fun1661590463l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1825]),
[final] ).
cnf(i_0_3789,plain,
( is_fun_a_bool(esk10_3(X1,X2,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_a_pname(X1,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1826]),
[final] ).
cnf(i_0_3790,plain,
( is_fun_a_bool(esk9_3(X1,X2,X3))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),image_a_fun_a_bool(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
| ~ is_fun949378684l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1827]),
[final] ).
cnf(i_0_3791,plain,
( is_fun_a_bool(esk8_3(X1,X2,X3))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),image_819518260e_bool(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
| ~ is_fun1661590463l_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1828]),
[final] ).
cnf(i_0_3792,plain,
( is_fun_a_bool(esk5_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_a_a(X1,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1829]),
[final] ).
cnf(i_0_3793,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[i_0_2097]),
[final] ).
cnf(i_0_3794,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_3795,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[i_0_2099]),
[final] ).
cnf(i_0_3796,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[i_0_2100]),
[final] ).
cnf(i_0_3797,plain,
( X1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),esk178_3(X3,X1,X2))
| hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
| ~ hBOOL(hAPP_nat_bool(X3,zero_zero_nat)) ),
inference(split_conjunct,[status(thm)],[i_0_1892]),
[final] ).
cnf(i_0_3798,plain,
( X1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),esk177_3(X3,X1,X2))
| hBOOL(hAPP_nat_bool(X3,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
| ~ hBOOL(hAPP_nat_bool(X3,zero_zero_nat)) ),
inference(split_conjunct,[status(thm)],[i_0_1893]),
[final] ).
cnf(i_0_3799,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X3)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_2101]),
[final] ).
cnf(i_0_3800,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),X3)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_2102]),
[final] ).
cnf(i_0_3801,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_2103]),
[final] ).
cnf(i_0_3802,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_3803,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),X3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X3)),X2),
inference(split_conjunct,[status(thm)],[i_0_2105]),
[final] ).
cnf(i_0_3804,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk76_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_3805,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk75_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2107]),
[final] ).
cnf(i_0_3806,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk78_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2108]),
[final] ).
cnf(i_0_3807,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk77_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2109]),
[final] ).
cnf(i_0_3808,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X1,X3)),hAPP_a_bool(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ is_a(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1764]),
[final] ).
cnf(i_0_3809,plain,
( X1 = X3
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2110]),
[final] ).
cnf(i_0_3810,plain,
hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X3)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)),
inference(split_conjunct,[status(thm)],[i_0_2111]),
[final] ).
cnf(i_0_3811,plain,
hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X3)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)),
inference(split_conjunct,[status(thm)],[i_0_2112]),
[final] ).
cnf(i_0_3812,plain,
hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X3)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)),
inference(split_conjunct,[status(thm)],[i_0_2113]),
[final] ).
cnf(i_0_3813,plain,
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),X1)) = X1
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2114]),
[final] ).
cnf(i_0_3814,plain,
( hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,esk186_2(X2,X1))))
| ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(split_conjunct,[status(thm)],[i_0_2115]),
[final] ).
cnf(i_0_3815,plain,
( is_fun1661590463l_bool(esk24_3(X1,X2,X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_41399353ol_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1834]),
[final] ).
cnf(i_0_3816,plain,
( is_fun1661590463l_bool(esk18_3(X1,X2,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_1551609309ol_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1835]),
[final] ).
cnf(i_0_3817,plain,
( is_fun949378684l_bool(esk25_3(X1,X2,X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_fun_a_bool_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1836]),
[final] ).
cnf(i_0_3818,plain,
( is_fun949378684l_bool(esk19_3(X1,X2,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_fun_a_bool_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1837]),
[final] ).
cnf(i_0_3819,plain,
( is_fun_pname_bool(esk28_3(X1,X2,X3))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),image_2129980159t_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1843]),
[final] ).
cnf(i_0_3820,plain,
( is_fun_pname_bool(esk27_3(X1,X2,X3))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),image_1512837979t_bool(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1844]),
[final] ).
cnf(i_0_3821,plain,
( is_fun_pname_bool(esk26_3(X1,X2,X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_pname_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1845]),
[final] ).
cnf(i_0_3822,plain,
( is_fun_pname_bool(esk20_3(X1,X2,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_pname_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1846]),
[final] ).
cnf(i_0_3823,plain,
( is_fun_a_bool(esk21_3(X1,X2,X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_a_int(X1,X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1847]),
[final] ).
cnf(i_0_3824,plain,
( is_fun_a_bool(esk15_3(X1,X2,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_a_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1848]),
[final] ).
cnf(i_0_3825,plain,
( is_fun_a_bool(esk7_3(X1,X2,X3))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),image_a_fun_nat_bool(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1849]),
[final] ).
cnf(i_0_3826,plain,
( is_fun_a_bool(esk6_3(X1,X2,X3))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X3),image_a_fun_int_bool(X1,X2)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1850]),
[final] ).
cnf(i_0_3827,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_pname(X1)
| ~ is_pname(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2016]),
[final] ).
cnf(i_0_3828,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ is_a(X1)
| ~ is_a(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2018]),
[final] ).
cnf(i_0_3829,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) = hAPP_f957591787ol_nat(finite_card_int,X2)
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1971]),
[final] ).
cnf(i_0_3830,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) = hAPP_f22106695ol_nat(finite_card_nat,X2)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1973]),
[final] ).
cnf(i_0_3831,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))) = hAPP_fun_a_bool_nat(finite_card_a,X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1975]),
[final] ).
cnf(i_0_3832,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),bot_bo844097828e_bool))) = hAPP_f921600141ol_nat(finite_card_pname,X2)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1977]),
[final] ).
cnf(i_0_3833,plain,
( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,X2)),hAPP_f957591787ol_nat(finite_card_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2116]),
[final] ).
cnf(i_0_3834,plain,
( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,X2)),hAPP_f22106695ol_nat(finite_card_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2117]),
[final] ).
cnf(i_0_3835,plain,
( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,X2)),hAPP_fun_a_bool_nat(finite_card_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2118]),
[final] ).
cnf(i_0_3836,plain,
( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),X1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,X2)),hAPP_f921600141ol_nat(finite_card_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2119]),
[final] ).
cnf(i_0_3837,plain,
( X1 = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))
| ~ is_pname(X1)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2120]),
[final] ).
cnf(i_0_3838,plain,
( X1 = X2
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_2121]),
[final] ).
cnf(i_0_3839,plain,
( X1 = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))
| ~ is_a(X1)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2122]),
[final] ).
cnf(i_0_3840,plain,
( X1 = X2
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_2123]),
[final] ).
cnf(i_0_3841,plain,
( hAPP_f1297739591_pname(X3,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1)) = X2
| hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)) != bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(finite1282449217_pname(X4,X3))
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1802]),
[final] ).
cnf(i_0_3842,plain,
( hAPP_fun_a_bool_a(X3,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1)) = X2
| hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(finite_folding_one_a(X4,X3))
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1803]),
[final] ).
cnf(i_0_3843,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X3,X1)),image_nat_int(X3,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2124]),
[final] ).
cnf(i_0_3844,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X3,X1)),image_nat_int(X3,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2125]),
[final] ).
cnf(i_0_3845,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X3,X1)),image_pname_a(X3,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2126]),
[final] ).
cnf(i_0_3846,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X3,X1)),image_pname_a(X3,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2127]),
[final] ).
cnf(i_0_3847,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,X3)),hAPP_nat_bool(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2128]),
[final] ).
cnf(i_0_3848,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,X3)),hAPP_nat_bool(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2129]),
[final] ).
cnf(i_0_3849,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,X3)),hAPP_nat_bool(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1760]),
[final] ).
cnf(i_0_3850,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X1,X3)),hAPP_int_bool(X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_3851,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X1,X3)),hAPP_int_bool(X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2131]),
[final] ).
cnf(i_0_3852,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X1,X3)),hAPP_int_bool(X2,X3)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1762]),
[final] ).
cnf(i_0_3853,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X1,X3)),hAPP_a_bool(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2132]),
[final] ).
cnf(i_0_3854,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X1,X3)),hAPP_a_bool(X2,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2133]),
[final] ).
cnf(i_0_3855,plain,
( X1 = bot_bo844097828e_bool
| hAPP_pname_pname(hAPP_p1170154830_pname(X2,hAPP_f1297739591_pname(X3,X1)),hAPP_f1297739591_pname(X3,X4)) = hAPP_f1297739591_pname(X3,X4)
| ~ is_fun_pname_bool(X1)
| ~ hBOOL(finite89670078_pname(X2,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X4))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_2134]),
[final] ).
cnf(i_0_3856,plain,
( X1 = bot_bot_fun_a_bool
| hAPP_a_a(hAPP_a_fun_a_a(X2,hAPP_fun_a_bool_a(X3,X1)),hAPP_fun_a_bool_a(X3,X4)) = hAPP_fun_a_bool_a(X3,X4)
| ~ is_fun_a_bool(X1)
| ~ hBOOL(finite1819937229idem_a(X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X4))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_2135]),
[final] ).
cnf(i_0_3857,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk113_2(X1,X2)),esk114_2(X1,X2)))
| hBOOL(hAPP_f54304608l_bool(X1,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1714]),
[final] ).
cnf(i_0_3858,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk111_2(X1,X2)),esk112_2(X1,X2)))
| hBOOL(hAPP_f448129468l_bool(X1,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1715]),
[final] ).
cnf(i_0_3859,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk115_2(X1,X2)),esk116_2(X1,X2)))
| hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_3860,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk109_2(X1,X2)),esk110_2(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1717]),
[final] ).
cnf(i_0_3861,plain,
( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),X1)) = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2136]),
[final] ).
cnf(i_0_3862,plain,
( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),X1)) = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2137]),
[final] ).
cnf(i_0_3863,plain,
( is_pname(esk107_3(X1,X2,X3))
| hBOOL(hAPP_f1664156314l_bool(X1,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1691]),
[final] ).
cnf(i_0_3864,plain,
( is_fun_pname_bool(esk108_3(X1,X2,X3))
| hBOOL(hAPP_f1664156314l_bool(X1,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1691]),
[final] ).
cnf(i_0_3865,plain,
( is_a(esk101_3(X1,X2,X3))
| hBOOL(hAPP_fun_a_bool_bool(X1,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_3866,plain,
( is_fun_a_bool(esk102_3(X1,X2,X3))
| hBOOL(hAPP_fun_a_bool_bool(X1,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_3867,plain,
( hAPP_f1594865479ol_int(X3,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1)) = X2
| hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(finite1626084323ne_int(X4,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1804]),
[final] ).
cnf(i_0_3868,plain,
( hAPP_f22106695ol_nat(X3,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1)) = X2
| hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(finite988810631ne_nat(X4,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1805]),
[final] ).
cnf(i_0_3869,plain,
( X4 = bot_bot_fun_nat_bool
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(X1,hAPP_f22106695ol_nat(X2,X4)),hAPP_f22106695ol_nat(X2,X3)) = hAPP_f22106695ol_nat(X2,X3)
| ~ hBOOL(finite795500164em_nat(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2138]),
[final] ).
cnf(i_0_3870,plain,
( X4 = bot_bot_fun_int_bool
| hAPP_int_int(hAPP_int_fun_int_int(X1,hAPP_f1594865479ol_int(X2,X4)),hAPP_f1594865479ol_int(X2,X3)) = hAPP_f1594865479ol_int(X2,X3)
| ~ hBOOL(finite1432773856em_int(X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X4),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2139]),
[final] ).
cnf(i_0_3871,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2140]),
[final] ).
cnf(i_0_3872,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2141]),
[final] ).
cnf(i_0_3873,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2142]),
[final] ).
cnf(i_0_3874,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2143]),
[final] ).
cnf(i_0_3875,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2144]),
[final] ).
cnf(i_0_3876,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2145]),
[final] ).
cnf(i_0_3877,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2029]),
[final] ).
cnf(i_0_3878,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2146]),
[final] ).
cnf(i_0_3879,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2147]),
[final] ).
cnf(i_0_3880,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2148]),
[final] ).
cnf(i_0_3881,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2031]),
[final] ).
cnf(i_0_3882,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3883,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[final] ).
cnf(i_0_3884,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2151]),
[final] ).
cnf(i_0_3885,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X3),X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2152]),
[final] ).
cnf(i_0_3886,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2153]),
[final] ).
cnf(i_0_3887,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2154]),
[final] ).
cnf(i_0_3888,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2155]),
[final] ).
cnf(i_0_3889,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2156]),
[final] ).
cnf(i_0_3890,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2157]),
[final] ).
cnf(i_0_3891,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2158]),
[final] ).
cnf(i_0_3892,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2159]),
[final] ).
cnf(i_0_3893,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2160]),
[final] ).
cnf(i_0_3894,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2161]),
[final] ).
cnf(i_0_3895,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2162]),
[final] ).
cnf(i_0_3896,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2163]),
[final] ).
cnf(i_0_3897,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_3898,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2165]),
[final] ).
cnf(i_0_3899,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2166]),
[final] ).
cnf(i_0_3900,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_2167]),
[final] ).
cnf(i_0_3901,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_2168]),
[final] ).
cnf(i_0_3902,plain,
( X1 = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_2169]),
[final] ).
cnf(i_0_3903,plain,
( X1 = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_2170]),
[final] ).
cnf(i_0_3904,plain,
( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X3)),X2) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),X2)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2093]),
[final] ).
cnf(i_0_3905,plain,
( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X3)),X2) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),X2)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2171]),
[final] ).
cnf(i_0_3906,plain,
( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X3)),X2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2094]),
[final] ).
cnf(i_0_3907,plain,
( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X3)),X2) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2172]),
[final] ).
cnf(i_0_3908,plain,
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X3)),X2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2095]),
[final] ).
cnf(i_0_3909,plain,
( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X3)),X2) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2173]),
[final] ).
cnf(i_0_3910,plain,
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X3)),X2) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2096]),
[final] ).
cnf(i_0_3911,plain,
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X3)),X2) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2174]),
[final] ).
cnf(i_0_3912,plain,
( X1 = X2
| X1 = X3
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2175]),
[final] ).
cnf(i_0_3913,plain,
( X1 = X2
| X1 = X3
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2175]),
[final] ).
cnf(i_0_3914,plain,
( X1 = X2
| X1 = X3
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2176]),
[final] ).
cnf(i_0_3915,plain,
( X1 = X2
| X1 = X3
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2176]),
[final] ).
cnf(i_0_3916,plain,
( X1 = X2
| X3 = X2
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2175]),
[final] ).
cnf(i_0_3917,plain,
( X1 = X2
| X3 = X2
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4),bot_bot_fun_int_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2175]),
[final] ).
cnf(i_0_3918,plain,
( X1 = X2
| X3 = X2
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2176]),
[final] ).
cnf(i_0_3919,plain,
( X1 = X2
| X3 = X2
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4),bot_bot_fun_nat_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2176]),
[final] ).
cnf(i_0_3920,plain,
number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)) = hAPP_nat_nat(suc,zero_zero_nat),
inference(rw,[status(thm)],[i_0_2177,c_0_1640]),
[final] ).
cnf(i_0_3921,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)) = X1
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2178]),
[final] ).
cnf(i_0_3922,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)) = X1
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2179]),
[final] ).
cnf(i_0_3923,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X1)),image_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2046]),
[final] ).
cnf(i_0_3924,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,X1)),image_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2047]),
[final] ).
cnf(i_0_3925,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,X1)),image_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2048]),
[final] ).
cnf(i_0_3926,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2050]),
[final] ).
cnf(i_0_3927,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2180]),
[final] ).
cnf(i_0_3928,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2053]),
[final] ).
cnf(i_0_3929,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2051]),
[final] ).
cnf(i_0_3930,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2052]),
[final] ).
cnf(i_0_3931,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_3932,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2055]),
[final] ).
cnf(i_0_3933,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2056]),
[final] ).
cnf(i_0_3934,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2044]),
[final] ).
cnf(i_0_3935,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2058]),
[final] ).
cnf(i_0_3936,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2057]),
[final] ).
cnf(i_0_3937,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk63_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1426]),
[final] ).
cnf(i_0_3938,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk56_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1425]),
[final] ).
cnf(i_0_3939,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk55_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1424]),
[final] ).
cnf(i_0_3940,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk54_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1421]),
[final] ).
cnf(i_0_3941,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk53_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1423]),
[final] ).
cnf(i_0_3942,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk61_2(X1,X2)),X2))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1431]),
[final] ).
cnf(i_0_3943,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk60_2(X1,X2)),X2))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1430]),
[final] ).
cnf(i_0_3944,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk59_2(X1,X2)),X2))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1427]),
[final] ).
cnf(i_0_3945,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk58_2(X1,X2)),X2))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1429]),
[final] ).
cnf(i_0_3946,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk57_2(X1,X2)),X2))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1432]),
[final] ).
cnf(i_0_3947,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk62_2(X1,X2)),X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1655]),
[final] ).
cnf(i_0_3948,plain,
( X1 = hAPP_pname_a(X2,esk74_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1868]),
[final] ).
cnf(i_0_3949,plain,
( X1 = hAPP_pname_a(X2,esk67_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1869]),
[final] ).
cnf(i_0_3950,plain,
( X1 = image_pname_a(X2,esk72_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1867]),
[final] ).
cnf(i_0_3951,plain,
( X2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,esk209_2(X1,X2))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2181]),
[final] ).
cnf(i_0_3952,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X4),X1))
| X1 = bot_bo844097828e_bool
| hAPP_f1297739591_pname(X3,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4),X1)) = hAPP_pname_pname(hAPP_p1170154830_pname(X2,X4),hAPP_f1297739591_pname(X3,X1))
| ~ is_fun_pname_bool(X1)
| ~ hBOOL(finite1282449217_pname(X2,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2182]),
[final] ).
cnf(i_0_3953,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X4),X1))
| X1 = bot_bot_fun_a_bool
| hAPP_fun_a_bool_a(X3,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4),X1)) = hAPP_a_a(hAPP_a_fun_a_a(X2,X4),hAPP_fun_a_bool_a(X3,X1))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(finite_folding_one_a(X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2183]),
[final] ).
cnf(i_0_3954,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) = X2 ),
inference(split_conjunct,[status(thm)],[i_0_2184]),
[final] ).
cnf(i_0_3955,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) = X2 ),
inference(split_conjunct,[status(thm)],[i_0_2185]),
[final] ).
cnf(i_0_3956,plain,
( hBOOL(hAPP_nat_bool(X3,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),esk180_2(X2,X3)))
| ~ hBOOL(hAPP_nat_bool(X3,X1))
| ~ hBOOL(hAPP_nat_bool(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_3957,plain,
( hBOOL(hAPP_nat_bool(X3,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),esk179_2(X2,X3)))
| ~ hBOOL(hAPP_nat_bool(X3,X1))
| ~ hBOOL(hAPP_nat_bool(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2015]),
[final] ).
cnf(i_0_3958,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3959,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3960,plain,
( X1 = hAPP_nat_int(X2,esk73_3(X1,X2,X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),image_nat_int(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1872]),
[final] ).
cnf(i_0_3961,plain,
( X1 = hAPP_nat_int(X2,esk66_3(X1,X2,X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),image_nat_int(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1873]),
[final] ).
cnf(i_0_3962,plain,
( X1 = image_nat_int(X2,esk71_3(X1,X2,X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),image_nat_int(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1874]),
[final] ).
cnf(i_0_3963,plain,
number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)) = one_one_nat,
inference(rw,[status(thm)],[i_0_2187,c_0_1640]),
[final] ).
cnf(i_0_3964,plain,
one_one_nat = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls)),
inference(rw,[status(thm)],[i_0_2188,c_0_1640]),
[final] ).
cnf(i_0_3965,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X4),X3))
| X3 = bot_bot_fun_nat_bool
| hAPP_f22106695ol_nat(X2,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4),X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X1,X4),hAPP_f22106695ol_nat(X2,X3))
| ~ hBOOL(finite988810631ne_nat(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2189]),
[final] ).
cnf(i_0_3966,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X4),X3))
| X3 = bot_bot_fun_int_bool
| hAPP_f1594865479ol_int(X2,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4),X3)) = hAPP_int_int(hAPP_int_fun_int_int(X1,X4),hAPP_f1594865479ol_int(X2,X3))
| ~ hBOOL(finite1626084323ne_int(X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2190]),
[final] ).
cnf(i_0_3967,plain,
( X1 = X3
| hBOOL(hAPP_a_bool(X2,X3))
| ~ hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2),X3))
| ~ is_a(X1)
| ~ is_a(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2191]),
[final] ).
cnf(i_0_3968,plain,
( is_pname(esk74_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1868]),
[final] ).
cnf(i_0_3969,plain,
( is_pname(esk67_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X3)))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1869]),
[final] ).
cnf(i_0_3970,plain,
( is_fun_pname_bool(esk72_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_pname_a(X2,X3)))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1867]),
[final] ).
cnf(i_0_3971,plain,
( cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X1) = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X2)
| hBOOL(hAPP_int_bool(X2,esk191_2(X2,X1)))
| hBOOL(hAPP_int_bool(X1,esk191_2(X2,X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2192,c_0_1684]),c_0_1684]),
[final] ).
cnf(i_0_3972,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2193]),
[final] ).
cnf(i_0_3973,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2194]),
[final] ).
cnf(i_0_3974,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2195]),
[final] ).
cnf(i_0_3975,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2196]),
[final] ).
cnf(i_0_3976,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2197]),
[final] ).
cnf(i_0_3977,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2198]),
[final] ).
cnf(i_0_3978,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2199]),
[final] ).
cnf(i_0_3979,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2200]),
[final] ).
cnf(i_0_3980,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2201]),
[final] ).
cnf(i_0_3981,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2202]),
[final] ).
cnf(i_0_3982,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2203]),
[final] ).
cnf(i_0_3983,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2204]),
[final] ).
cnf(i_0_3984,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2205]),
[final] ).
cnf(i_0_3985,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2206]),
[final] ).
cnf(i_0_3986,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2207]),
[final] ).
cnf(i_0_3987,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2208]),
[final] ).
cnf(i_0_3988,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2209]),
[final] ).
cnf(i_0_3989,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2210]),
[final] ).
cnf(i_0_3990,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2211]),
[final] ).
cnf(i_0_3991,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2212]),
[final] ).
cnf(i_0_3992,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2213]),
[final] ).
cnf(i_0_3993,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2214]),
[final] ).
cnf(i_0_3994,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2215]),
[final] ).
cnf(i_0_3995,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2216]),
[final] ).
cnf(i_0_3996,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2217]),
[final] ).
cnf(i_0_3997,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2218]),
[final] ).
cnf(i_0_3998,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2219]),
[final] ).
cnf(i_0_3999,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2220]),
[final] ).
cnf(i_0_4000,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2221]),
[final] ).
cnf(i_0_4001,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_4002,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2223]),
[final] ).
cnf(i_0_4003,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2224]),
[final] ).
cnf(i_0_4004,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3),X4))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_2225]),
[final] ).
cnf(i_0_4005,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X2) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_2226]),
[final] ).
cnf(i_0_4006,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X4))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),X4) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2226]),
[final] ).
cnf(i_0_4007,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2227]),
[final] ).
cnf(i_0_4008,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2228]),
[final] ).
cnf(i_0_4009,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk164_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2229]),
[final] ).
cnf(i_0_4010,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk85_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2230]),
[final] ).
cnf(i_0_4011,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk170_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2231]),
[final] ).
cnf(i_0_4012,plain,
( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2232]),
[final] ).
cnf(i_0_4013,plain,
hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))),
inference(split_conjunct,[status(thm)],[i_0_2233]),
[final] ).
cnf(i_0_4014,plain,
hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2))),
inference(split_conjunct,[status(thm)],[i_0_2234]),
[final] ).
cnf(i_0_4015,plain,
hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))),
inference(split_conjunct,[status(thm)],[i_0_2235]),
[final] ).
cnf(i_0_4016,plain,
hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2))),
inference(split_conjunct,[status(thm)],[i_0_2236]),
[final] ).
cnf(i_0_4017,plain,
( X1 = hAPP_nat_nat(suc,esk174_2(X2,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2067]),
[final] ).
cnf(i_0_4018,plain,
( X2 = hAPP_nat_nat(suc,esk65_2(X1,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2237]),
[final] ).
cnf(i_0_4019,plain,
( hAPP_nat_nat(suc,X1) = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2238]),
[final] ).
cnf(i_0_4020,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)),X1) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2239]),
[final] ).
cnf(i_0_4021,plain,
( hBOOL(hAPP_int_bool(X1,X2))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,esk208_1(X1))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2240]),
[final] ).
cnf(i_0_4022,plain,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X2)))),
inference(rw,[status(thm)],[i_0_2241,c_0_1678]),
[final] ).
cnf(i_0_4023,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_4024,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2243]),
[final] ).
cnf(i_0_4025,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2244]),
[final] ).
cnf(i_0_4026,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2245]),
[final] ).
cnf(i_0_4027,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2246,c_0_1678]),c_0_1678]),
[final] ).
cnf(i_0_4028,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X2),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2247,c_0_1678]),c_0_1678]),
[final] ).
cnf(i_0_4029,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2248]),
[final] ).
cnf(i_0_4030,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X1),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2249,c_0_1684]),c_0_1684]),
[final] ).
cnf(i_0_4031,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X2),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2250,c_0_1684]),c_0_1684]),
[final] ).
cnf(i_0_4032,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2251]),
[final] ).
cnf(i_0_4033,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2252]),
[final] ).
cnf(i_0_4034,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2253]),
[final] ).
cnf(i_0_4035,plain,
( is_pname(esk80_3(X1,X2,X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1711]),
[final] ).
cnf(i_0_4036,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_2254]),
[final] ).
cnf(i_0_4037,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X3),
inference(split_conjunct,[status(thm)],[i_0_2255]),
[final] ).
cnf(i_0_4038,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)),X3) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2256]),
[final] ).
cnf(i_0_4039,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)),X3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2257]),
[final] ).
cnf(i_0_4040,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)),X3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2258]),
[final] ).
cnf(i_0_4041,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),X3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2259]),
[final] ).
cnf(i_0_4042,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2260]),
[final] ).
cnf(i_0_4043,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2261]),
[final] ).
cnf(i_0_4044,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),X3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_2262]),
[final] ).
cnf(i_0_4045,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2263]),
[final] ).
cnf(i_0_4046,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2142]),
[final] ).
cnf(i_0_4047,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2143]),
[final] ).
cnf(i_0_4048,plain,
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),X1)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)
| ~ hBOOL(hAPP_a_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2264]),
[final] ).
cnf(i_0_4049,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X2)),X1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2265]),
[final] ).
cnf(i_0_4050,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_pname_a(X4,X2)))
| ~ is_fun_pname_bool(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X3 != image_pname_a(X4,X1)
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1867]),
[final] ).
cnf(i_0_4051,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),image_pname_a(X4,X2)))
| ~ is_pname(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| X3 != hAPP_pname_a(X4,X1)
| ~ is_a(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1869]),
[final] ).
cnf(i_0_4052,plain,
( X2 = X3
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2) != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X3)
| ~ is_fun_pname_bool(X3)
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2266]),
[final] ).
cnf(i_0_4053,plain,
( X2 = X3
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X3)
| ~ is_fun_a_bool(X3)
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2267]),
[final] ).
cnf(i_0_4054,plain,
hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_2268]),
[final] ).
cnf(i_0_4055,plain,
hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_2269]),
[final] ).
cnf(i_0_4056,plain,
hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool))) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_2270]),
[final] ).
cnf(i_0_4057,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 = hAPP_nat_nat(suc,X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2271]),
[final] ).
cnf(i_0_4058,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 = hAPP_nat_nat(suc,X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2272]),
[final] ).
cnf(i_0_4059,hypothesis,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
inference(split_conjunct,[status(thm)],[conj_2]),
[final] ).
cnf(i_0_4060,plain,
( is_pname(esk86_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(X2)),bot_bot_fun_a_bool)))
| ~ hBOOL(wt(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1734]),
[final] ).
cnf(i_0_4061,plain,
( cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X1) = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X2)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk191_2(X1,X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2273,c_0_1684]),c_0_1684]),
[final] ).
cnf(i_0_4062,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_26036933t_bool(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2274]),
[final] ).
cnf(i_0_4063,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_892525857t_bool(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2275]),
[final] ).
cnf(i_0_4064,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),image_2129980159t_bool(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2276]),
[final] ).
cnf(i_0_4065,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1556378401t_bool(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2277]),
[final] ).
cnf(i_0_4066,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_275383677t_bool(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2278]),
[final] ).
cnf(i_0_4067,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),image_1512837979t_bool(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2279]),
[final] ).
cnf(i_0_4068,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_1655916159e_bool(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2280]),
[final] ).
cnf(i_0_4069,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_637364955e_bool(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2281]),
[final] ).
cnf(i_0_4070,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),image_47868345e_bool(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2282]),
[final] ).
cnf(i_0_4071,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_nat_fun_a_bool(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2283]),
[final] ).
cnf(i_0_4072,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_int_fun_a_bool(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2284]),
[final] ).
cnf(i_0_4073,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),image_112932426a_bool(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2285]),
[final] ).
cnf(i_0_4074,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_496248727ol_nat(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2286]),
[final] ).
cnf(i_0_4075,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1431733819ol_nat(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2287]),
[final] ).
cnf(i_0_4076,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_1551609309ol_nat(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2288]),
[final] ).
cnf(i_0_4077,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_fun_a_bool_nat(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2289]),
[final] ).
cnf(i_0_4078,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_a_nat(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2290]),
[final] ).
cnf(i_0_4079,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_1133522419ol_int(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2291]),
[final] ).
cnf(i_0_4080,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_2069007511ol_int(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2292]),
[final] ).
cnf(i_0_4081,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_41399353ol_int(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_4082,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_fun_a_bool_int(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2294]),
[final] ).
cnf(i_0_4083,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_nat_int(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2295]),
[final] ).
cnf(i_0_4084,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),image_a_int(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_4085,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1921560913_pname(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_4086,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_62782965_pname(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2298]),
[final] ).
cnf(i_0_4087,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1283814551_pname(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2299]),
[final] ).
cnf(i_0_4088,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_1854862208_pname(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_4089,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_nat_pname(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_4090,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_int_pname(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2302]),
[final] ).
cnf(i_0_4091,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_pname_pname(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_4092,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),image_a_pname(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2304]),
[final] ).
cnf(i_0_4093,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_nat_bool_a(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2305]),
[final] ).
cnf(i_0_4094,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_int_bool_a(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2306]),
[final] ).
cnf(i_0_4095,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_876012084bool_a(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2307]),
[final] ).
cnf(i_0_4096,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_fun_a_bool_a(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2308]),
[final] ).
cnf(i_0_4097,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_nat_a(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2309]),
[final] ).
cnf(i_0_4098,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_int_a(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2310]),
[final] ).
cnf(i_0_4099,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_pname_a(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2311]),
[final] ).
cnf(i_0_4100,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),image_a_a(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_4101,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),image_nat_int(X2,X4)))
| X1 != hAPP_nat_int(X2,X3)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_2313]),
[final] ).
cnf(i_0_4102,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),image_nat_int(X4,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| X3 != hAPP_nat_int(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2314]),
[final] ).
cnf(i_0_4103,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X3),image_nat_int(X4,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| X3 != hAPP_nat_int(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1873]),
[final] ).
cnf(i_0_4104,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X3),image_nat_int(X4,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X3 != image_nat_int(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1874]),
[final] ).
cnf(i_0_4105,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_pname_a(X2,X4)))
| X1 != hAPP_pname_a(X2,X3)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_2315]),
[final] ).
cnf(i_0_4106,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),image_pname_a(X4,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| X3 != hAPP_pname_a(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2316]),
[final] ).
cnf(i_0_4107,plain,
( X2 = X3
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_4108,plain,
( X2 = X3
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X3))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2318]),
[final] ).
cnf(i_0_4109,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2319]),
[final] ).
cnf(i_0_4110,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2320]),
[final] ).
cnf(i_0_4111,plain,
( X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2321]),
[final] ).
cnf(i_0_4112,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2322]),
[final] ).
cnf(i_0_4113,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2323]),
[final] ).
cnf(i_0_4114,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),X3)
| hBOOL(hAPP_int_bool(nat_neg,X2))
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2324,c_0_1649]),c_0_1649]),
[final] ).
cnf(i_0_4115,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1) != pls,
inference(rw,[status(thm)],[i_0_2325,c_0_1640]),
[final] ).
cnf(i_0_4116,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1) != zero_zero_int,
inference(split_conjunct,[status(thm)],[i_0_2326]),
[final] ).
cnf(i_0_4117,plain,
pls != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X1)),X1),
inference(rw,[status(thm)],[i_0_2327,c_0_1640]),
[final] ).
cnf(i_0_4118,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X1)),
inference(split_conjunct,[status(thm)],[i_0_2328]),
[final] ).
cnf(i_0_4119,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X3)))
| X1 != hAPP_nat_nat(suc,X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_4120,plain,
( X2 = X3
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X1)),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X1)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2329]),
[final] ).
cnf(i_0_4121,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),esk173_2(X1,X2)))
| X2 = hAPP_nat_nat(suc,X1)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2330]),
[final] ).
cnf(i_0_4122,plain,
( X1 = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[i_0_2331]),
[final] ).
cnf(i_0_4123,plain,
( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f957591787ol_nat(finite_card_int,X2)
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2332]),
[final] ).
cnf(i_0_4124,plain,
( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f22106695ol_nat(finite_card_nat,X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2333]),
[final] ).
cnf(i_0_4125,plain,
( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X1),X2)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2334]),
[final] ).
cnf(i_0_4126,plain,
( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X1),X2)) = hAPP_f55526627ol_nat(finite1340463720e_bool,X2)
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2335]),
[final] ).
cnf(i_0_4127,plain,
( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X1),X2)) = hAPP_f696928925ol_nat(finite346522414t_bool,X2)
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2336]),
[final] ).
cnf(i_0_4128,plain,
( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X1),X2)) = hAPP_f521865025ol_nat(finite1876863882t_bool,X2)
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X1),X2))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2337]),
[final] ).
cnf(i_0_4129,plain,
( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_fun_a_bool_nat(finite_card_a,X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2338]),
[final] ).
cnf(i_0_4130,plain,
( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)) = hAPP_f921600141ol_nat(finite_card_pname,X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2339]),
[final] ).
cnf(i_0_4131,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)),
inference(split_conjunct,[status(thm)],[i_0_2340]),
[final] ).
cnf(i_0_4132,plain,
( hBOOL(hAPP_int_bool(X2,hAPP_nat_int(semiri1621563631at_int,esk205_1(X2))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2341]),
[final] ).
cnf(i_0_4133,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2342,c_0_1678]),c_0_1678]),c_0_1678]),
[final] ).
cnf(i_0_4134,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_4135,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,X1),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2343,c_0_1684]),c_0_1684]),c_0_1684]),
[final] ).
cnf(i_0_4136,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2165]),
[final] ).
cnf(i_0_4137,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2166]),
[final] ).
cnf(i_0_4138,plain,
( X2 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),esk169_2(X1,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2344]),
[final] ).
cnf(i_0_4139,plain,
( X2 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),esk165_2(X1,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2345]),
[final] ).
cnf(i_0_4140,plain,
( X1 = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2346]),
[final] ).
cnf(i_0_4141,plain,
( X2 = X1
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2347]),
[final] ).
cnf(i_0_4142,plain,
( X1 = X2
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2348]),
[final] ).
cnf(i_0_4143,plain,
( X1 = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2349]),
[final] ).
cnf(i_0_4144,plain,
( X1 = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2350]),
[final] ).
cnf(i_0_4145,plain,
( X1 = X2
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2351]),
[final] ).
cnf(i_0_4146,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk76_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_4147,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk75_2(X1,X2)),X2))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2107]),
[final] ).
cnf(i_0_4148,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk78_2(X1,X2)),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2108]),
[final] ).
cnf(i_0_4149,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk77_2(X1,X2)),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2109]),
[final] ).
cnf(i_0_4150,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk179_2(X1,X2)),X1))
| hBOOL(hAPP_nat_bool(X2,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2015]),
[final] ).
cnf(i_0_4151,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk180_2(X1,X2)),X1))
| hBOOL(hAPP_nat_bool(X2,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_4152,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2352]),
[final] ).
cnf(i_0_4153,plain,
( X1 = bot_bo844097828e_bool
| hAPP_f1297739591_pname(X3,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X4),X1)) = hAPP_pname_pname(hAPP_p1170154830_pname(X2,X4),hAPP_f1297739591_pname(X3,X1))
| ~ is_fun_pname_bool(X1)
| ~ hBOOL(finite89670078_pname(X2,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2353]),
[final] ).
cnf(i_0_4154,plain,
( X1 = bot_bot_fun_a_bool
| hAPP_fun_a_bool_a(X3,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4),X1)) = hAPP_a_a(hAPP_a_fun_a_a(X2,X4),hAPP_fun_a_bool_a(X3,X1))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(finite1819937229idem_a(X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2354]),
[final] ).
cnf(i_0_4155,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),esk163_1(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2229]),
[final] ).
cnf(i_0_4156,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),esk84_1(X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2230]),
[final] ).
cnf(i_0_4157,plain,
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X2)),X1)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)
| ~ hBOOL(hAPP_a_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2355]),
[final] ).
cnf(i_0_4158,plain,
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X3,X1)),image_nat_int(X3,X2)) = image_nat_int(X3,X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2356]),
[final] ).
cnf(i_0_4159,plain,
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X3,X1)),image_pname_a(X3,X2)) = image_pname_a(X3,X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2357]),
[final] ).
cnf(i_0_4160,plain,
hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X1))),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2358,c_0_1684]),c_0_1684]),
[final] ).
cnf(i_0_4161,plain,
hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1))),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2359,c_0_1678]),c_0_1678]),
[final] ).
cnf(i_0_4162,plain,
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X4),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool))
| X1 != X2
| X3 != X4
| ~ is_a(X1)
| ~ is_a(X3)
| ~ is_a(X4)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2092]),
[final] ).
cnf(i_0_4163,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2224]),
[final] ).
cnf(i_0_4164,plain,
( X3 = bot_bot_fun_nat_bool
| hAPP_f22106695ol_nat(X2,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4),X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(X1,X4),hAPP_f22106695ol_nat(X2,X3))
| ~ hBOOL(finite795500164em_nat(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2360]),
[final] ).
cnf(i_0_4165,plain,
( X3 = bot_bot_fun_int_bool
| hAPP_f1594865479ol_int(X2,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4),X3)) = hAPP_int_int(hAPP_int_fun_int_int(X1,X4),hAPP_f1594865479ol_int(X2,X3))
| ~ hBOOL(finite1432773856em_int(X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2361]),
[final] ).
cnf(i_0_4166,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
| X1 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2181]),
[final] ).
cnf(i_0_4167,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2074]),
[final] ).
cnf(i_0_4168,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2362]),
[final] ).
cnf(i_0_4169,plain,
( X2 = X1
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2363]),
[final] ).
cnf(i_0_4170,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2364]),
[final] ).
cnf(i_0_4171,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2365]),
[final] ).
cnf(i_0_4172,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2366]),
[final] ).
cnf(i_0_4173,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2367]),
[final] ).
cnf(i_0_4174,plain,
( X1 = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2368]),
[final] ).
cnf(i_0_4175,plain,
( X2 = X1
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2369]),
[final] ).
cnf(i_0_4176,plain,
( X1 = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2370]),
[final] ).
cnf(i_0_4177,plain,
( X1 = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2371]),
[final] ).
cnf(i_0_4178,plain,
( X1 = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2372]),
[final] ).
cnf(i_0_4179,plain,
( X1 = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2373]),
[final] ).
cnf(i_0_4180,plain,
( X2 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2374]),
[final] ).
cnf(i_0_4181,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2375]),
[final] ).
cnf(i_0_4182,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2376]),
[final] ).
cnf(i_0_4183,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2377]),
[final] ).
cnf(i_0_4184,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2378]),
[final] ).
cnf(i_0_4185,plain,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2379]),
[final] ).
cnf(i_0_4186,plain,
( X2 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2380]),
[final] ).
cnf(i_0_4187,plain,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2381]),
[final] ).
cnf(i_0_4188,plain,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2382]),
[final] ).
cnf(i_0_4189,plain,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2383]),
[final] ).
cnf(i_0_4190,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk181_2(X1,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2384]),
[final] ).
cnf(i_0_4191,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2385]),
[final] ).
cnf(i_0_4192,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2322]),
[final] ).
cnf(i_0_4193,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2386]),
[final] ).
cnf(i_0_4194,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2323]),
[final] ).
cnf(i_0_4195,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2271]),
[final] ).
cnf(i_0_4196,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2387]),
[final] ).
cnf(i_0_4197,hypothesis,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
inference(split_conjunct,[status(thm)],[i_0_2388]),
[final] ).
cnf(i_0_4198,plain,
( number_number_of_nat(X1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,number_number_of_nat(X1)),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2389]),
[final] ).
cnf(i_0_4199,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2332]),
[final] ).
cnf(i_0_4200,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
| hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2390]),
[final] ).
cnf(i_0_4201,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2333]),
[final] ).
cnf(i_0_4202,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2391]),
[final] ).
cnf(i_0_4203,plain,
( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X1),X2))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X1),X2)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2334]),
[final] ).
cnf(i_0_4204,plain,
( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2),X1))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X2),X1)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2392]),
[final] ).
cnf(i_0_4205,plain,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X1),X2))
| hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X1),X2)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2335]),
[final] ).
cnf(i_0_4206,plain,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2),X1))
| hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X2),X1)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2393]),
[final] ).
cnf(i_0_4207,plain,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1),X2))
| hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X1),X2)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2336]),
[final] ).
cnf(i_0_4208,plain,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2),X1))
| hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X2),X1)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2394]),
[final] ).
cnf(i_0_4209,plain,
( hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X1),X2))
| hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X1),X2)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X2))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2337]),
[final] ).
cnf(i_0_4210,plain,
( hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X2),X1))
| hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X2),X1)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,X1))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2395]),
[final] ).
cnf(i_0_4211,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2338]),
[final] ).
cnf(i_0_4212,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2396]),
[final] ).
cnf(i_0_4213,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2339]),
[final] ).
cnf(i_0_4214,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2397]),
[final] ).
cnf(i_0_4215,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
| X1 != X2
| ~ is_pname(X1)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2016]),
[final] ).
cnf(i_0_4216,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
| X1 != X2
| ~ is_a(X1)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2018]),
[final] ).
cnf(i_0_4217,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X2)),X3)
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[i_0_2398,c_0_1649]),
[final] ).
cnf(i_0_4218,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3,X1),X2))
| X2 = X1
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2399]),
[final] ).
cnf(i_0_4219,plain,
( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X1),X2))
| ~ hBOOL(hAPP_a_bool(X1,X2))
| ~ is_a(X3)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2191]),
[final] ).
cnf(i_0_4220,plain,
( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(suc,zero_zero_nat))) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2400]),
[final] ).
cnf(i_0_4221,plain,
( hBOOL(hAPP_a_bool(X1,X2))
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),X1)) = bot_bot_fun_a_bool ),
inference(split_conjunct,[status(thm)],[i_0_2264]),
[final] ).
cnf(i_0_4222,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(suc,X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)),X2),
inference(split_conjunct,[status(thm)],[i_0_2401]),
[final] ).
cnf(i_0_4223,plain,
( X1 = hAPP_nat_nat(suc,esk176_2(X1,X2))
| X1 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_4224,plain,
( X2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,esk204_2(X1,X2)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2402]),
[final] ).
cnf(i_0_4225,plain,
( hBOOL(hAPP_nat_bool(X2,X3))
| ~ hBOOL(hAPP_nat_bool(nat_case_bool(X1,X2),hAPP_nat_nat(suc,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_2403]),
[final] ).
cnf(i_0_4226,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),bot_bo844097828e_bool)))
| X1 != X2
| ~ is_pname(X1)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2120]),
[final] ).
cnf(i_0_4227,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)))
| X1 != X2
| ~ is_a(X1)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2122]),
[final] ).
cnf(i_0_4228,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2404]),
[final] ).
cnf(i_0_4229,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2405]),
[final] ).
cnf(i_0_4230,plain,
( X2 = X3
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2406]),
[final] ).
cnf(i_0_4231,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2352]),
[final] ).
cnf(i_0_4232,plain,
hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2) = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X1)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X2))),
inference(rw,[status(thm)],[i_0_2407,c_0_1684]),
[final] ).
cnf(i_0_4233,plain,
hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))),
inference(rw,[status(thm)],[i_0_2408,c_0_1678]),
[final] ).
cnf(i_0_4234,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2029]),
[final] ).
cnf(i_0_4235,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2146]),
[final] ).
cnf(i_0_4236,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2031]),
[final] ).
cnf(i_0_4237,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_4238,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2152]),
[final] ).
cnf(i_0_4239,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2155]),
[final] ).
cnf(i_0_4240,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_2409]),
[final] ).
cnf(i_0_4241,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1))),
inference(split_conjunct,[status(thm)],[i_0_2410]),
[final] ).
cnf(i_0_4242,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_2411]),
[final] ).
cnf(i_0_4243,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1))),
inference(split_conjunct,[status(thm)],[i_0_2412]),
[final] ).
cnf(i_0_4244,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_2413]),
[final] ).
cnf(i_0_4245,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1))),
inference(split_conjunct,[status(thm)],[i_0_2414]),
[final] ).
cnf(i_0_4246,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_2415]),
[final] ).
cnf(i_0_4247,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X1))),
inference(split_conjunct,[status(thm)],[i_0_2416]),
[final] ).
cnf(i_0_4248,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_2417]),
[final] ).
cnf(i_0_4249,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1))),
inference(split_conjunct,[status(thm)],[i_0_2418]),
[final] ).
cnf(i_0_4250,plain,
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X4),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool))
| X1 != X2
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[i_0_2175]),
[final] ).
cnf(i_0_4251,plain,
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X4),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool))
| X1 != X2
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[i_0_2176]),
[final] ).
cnf(i_0_4252,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X3) = X2
| X1 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2419]),
[final] ).
cnf(i_0_4253,plain,
( X1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) != X3
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2419]),
[final] ).
cnf(i_0_4254,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X3)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_2420]),
[final] ).
cnf(i_0_4255,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_2421]),
[final] ).
cnf(i_0_4256,plain,
hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X3)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_2422]),
[final] ).
cnf(i_0_4257,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2167]),
[final] ).
cnf(i_0_4258,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2169]),
[final] ).
cnf(i_0_4259,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2044]),
[final] ).
cnf(i_0_4260,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X2),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_4261,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X2),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2423]),
[final] ).
cnf(i_0_4262,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X2),X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2243]),
[final] ).
cnf(i_0_4263,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X2),X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2424]),
[final] ).
cnf(i_0_4264,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X2),X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2244]),
[final] ).
cnf(i_0_4265,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X2),X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2425]),
[final] ).
cnf(i_0_4266,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X2),X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2245]),
[final] ).
cnf(i_0_4267,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X2),X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2426]),
[final] ).
cnf(i_0_4268,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2427,c_0_1678]),c_0_1678]),
[final] ).
cnf(i_0_4269,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X2),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2428,c_0_1678]),c_0_1678]),
[final] ).
cnf(i_0_4270,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2429]),
[final] ).
cnf(i_0_4271,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2248]),
[final] ).
cnf(i_0_4272,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2430]),
[final] ).
cnf(i_0_4273,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X1),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2431,c_0_1684]),c_0_1684]),
[final] ).
cnf(i_0_4274,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,X2),X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2432,c_0_1684]),c_0_1684]),
[final] ).
cnf(i_0_4275,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X2)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2433]),
[final] ).
cnf(i_0_4276,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2251]),
[final] ).
cnf(i_0_4277,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2434]),
[final] ).
cnf(i_0_4278,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X1),X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2435]),
[final] ).
cnf(i_0_4279,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2252]),
[final] ).
cnf(i_0_4280,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2436]),
[final] ).
cnf(i_0_4281,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2253]),
[final] ).
cnf(i_0_4282,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2437]),
[final] ).
cnf(i_0_4283,plain,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2438]),
[final] ).
cnf(i_0_4284,plain,
( hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),X1))))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2439]),
[final] ).
cnf(i_0_4285,plain,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2440]),
[final] ).
cnf(i_0_4286,plain,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2441]),
[final] ).
cnf(i_0_4287,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2442]),
[final] ).
cnf(i_0_4288,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),X1))))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2443]),
[final] ).
cnf(i_0_4289,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2444]),
[final] ).
cnf(i_0_4290,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2445]),
[final] ).
cnf(i_0_4291,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| X1 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2345]),
[final] ).
cnf(i_0_4292,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk164_2(X1,X2)),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2229]),
[final] ).
cnf(i_0_4293,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk85_2(X1,X2)),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2230]),
[final] ).
cnf(i_0_4294,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk170_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2231]),
[final] ).
cnf(i_0_4295,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk206_1(X1)))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2341]),
[final] ).
cnf(i_0_4296,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2321]),
[final] ).
cnf(i_0_4297,plain,
( hBOOL(hAPP_f54304608l_bool(X1,esk114_2(X1,X2)))
| hBOOL(hAPP_f54304608l_bool(X1,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1714]),
[final] ).
cnf(i_0_4298,plain,
( hBOOL(hAPP_f448129468l_bool(X1,esk112_2(X1,X2)))
| hBOOL(hAPP_f448129468l_bool(X1,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1715]),
[final] ).
cnf(i_0_4299,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,esk116_2(X1,X2)))
| hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_4300,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,esk110_2(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1717]),
[final] ).
cnf(i_0_4301,plain,
image_nat_int(X1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X1,X2)),image_nat_int(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_2446]),
[final] ).
cnf(i_0_4302,plain,
image_pname_a(X1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X3)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X1,X2)),image_pname_a(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_2447]),
[final] ).
cnf(i_0_4303,plain,
( hBOOL(hAPP_f54304608l_bool(X1,esk122_2(X1,X2)))
| hBOOL(hAPP_f54304608l_bool(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(X1,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1771]),
[final] ).
cnf(i_0_4304,plain,
( hBOOL(hAPP_f448129468l_bool(X1,esk120_2(X1,X2)))
| hBOOL(hAPP_f448129468l_bool(X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(X1,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1772]),
[final] ).
cnf(i_0_4305,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,esk124_2(X1,X2)))
| hBOOL(hAPP_f1664156314l_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_4306,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,esk118_2(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_4307,plain,
( X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2448]),
[final] ).
cnf(i_0_4308,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2449]),
[final] ).
cnf(i_0_4309,plain,
( X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2450]),
[final] ).
cnf(i_0_4310,plain,
( X1 = X2
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2451]),
[final] ).
cnf(i_0_4311,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),hAPP_nat_nat(suc,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2227]),
[final] ).
cnf(i_0_4312,plain,
( hBOOL(hAPP_a_bool(X1,X2))
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X2)),X1)) = bot_bot_fun_a_bool ),
inference(split_conjunct,[status(thm)],[i_0_2355]),
[final] ).
cnf(i_0_4313,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk114_2(X1,X2)))
| hBOOL(hAPP_f54304608l_bool(X1,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1714]),
[final] ).
cnf(i_0_4314,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk112_2(X1,X2)))
| hBOOL(hAPP_f448129468l_bool(X1,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1715]),
[final] ).
cnf(i_0_4315,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk116_2(X1,X2)))
| hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_4316,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk110_2(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1717]),
[final] ).
cnf(i_0_4317,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk122_2(X1,X2)))
| hBOOL(hAPP_f54304608l_bool(X1,X2))
| ~ hBOOL(hAPP_f54304608l_bool(X1,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1771]),
[final] ).
cnf(i_0_4318,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk120_2(X1,X2)))
| hBOOL(hAPP_f448129468l_bool(X1,X2))
| ~ hBOOL(hAPP_f448129468l_bool(X1,bot_bot_fun_int_bool))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1772]),
[final] ).
cnf(i_0_4319,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk124_2(X1,X2)))
| hBOOL(hAPP_f1664156314l_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_4320,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk118_2(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_4321,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2452]),
[final] ).
cnf(i_0_4322,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2453]),
[final] ).
cnf(i_0_4323,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2454]),
[final] ).
cnf(i_0_4324,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2449]),
[final] ).
cnf(i_0_4325,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2450]),
[final] ).
cnf(i_0_4326,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2451]),
[final] ).
cnf(i_0_4327,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,esk161_2(X1,X2)))
| hBOOL(hAPP_f1664156314l_bool(X1,X2))
| is_pname(esk159_2(X1,X2))
| X2 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_4328,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,esk152_2(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| is_a(esk150_2(X1,X2))
| X2 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_4329,plain,
( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X2),X1) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2455]),
[final] ).
cnf(i_0_4330,plain,
( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X2),X1) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),X1)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2456]),
[final] ).
cnf(i_0_4331,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2457,c_0_2014]),c_0_1640]),
[final] ).
cnf(i_0_4332,hypothesis,
hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
inference(split_conjunct,[status(thm)],[conj_3]),
[final] ).
cnf(i_0_4333,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk210_1(X1)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2458]),
[final] ).
cnf(i_0_4334,plain,
( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2459]),
[final] ).
cnf(i_0_4335,plain,
( X1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2460]),
[final] ).
cnf(i_0_4336,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk161_2(X1,X2)))
| hBOOL(hAPP_f1664156314l_bool(X1,X2))
| is_pname(esk159_2(X1,X2))
| X2 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_4337,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk152_2(X1,X2)))
| hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| is_a(esk150_2(X1,X2))
| X2 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_4338,plain,
( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X3),X2))
| X1 != X2
| ~ is_a(X1)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2191]),
[final] ).
cnf(i_0_4339,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2461]),
[final] ).
cnf(i_0_4340,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2462]),
[final] ).
cnf(i_0_4341,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2463]),
[final] ).
cnf(i_0_4342,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X1),X2))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2464]),
[final] ).
cnf(i_0_4343,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X2))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1))
| ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2465]),
[final] ).
cnf(i_0_4344,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2466]),
[final] ).
cnf(i_0_4345,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2467]),
[final] ).
cnf(i_0_4346,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2468]),
[final] ).
cnf(i_0_4347,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2469]),
[final] ).
cnf(i_0_4348,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2470]),
[final] ).
cnf(i_0_4349,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2471]),
[final] ).
cnf(i_0_4350,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2472]),
[final] ).
cnf(i_0_4351,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X2))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2473]),
[final] ).
cnf(i_0_4352,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2474]),
[final] ).
cnf(i_0_4353,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2475]),
[final] ).
cnf(i_0_4354,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2476]),
[final] ).
cnf(i_0_4355,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2477]),
[final] ).
cnf(i_0_4356,plain,
hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2478]),
[final] ).
cnf(i_0_4357,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2479]),
[final] ).
cnf(i_0_4358,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2480]),
[final] ).
cnf(i_0_4359,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2481]),
[final] ).
cnf(i_0_4360,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2482]),
[final] ).
cnf(i_0_4361,plain,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X2)),
inference(split_conjunct,[status(thm)],[i_0_2483]),
[final] ).
cnf(i_0_4362,plain,
( X1 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk140_1(X1)),esk141_1(X1)))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2484]),
[final] ).
cnf(i_0_4363,plain,
( X1 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk134_1(X1)),esk135_1(X1)))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2485]),
[final] ).
cnf(i_0_4364,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X1)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(rw,[status(thm)],[i_0_2486,c_0_2014]),
[final] ).
cnf(i_0_4365,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)) = X1 ),
inference(split_conjunct,[status(thm)],[i_0_2487]),
[final] ).
cnf(i_0_4366,plain,
( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(X1)),X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X2)
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[i_0_2488,c_0_1649]),
[final] ).
cnf(i_0_4367,plain,
( cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X2)),X1) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2489,c_0_1684]),
[final] ).
cnf(i_0_4368,plain,
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),X1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2490,c_0_1678]),
[final] ).
cnf(i_0_4369,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),esk181_2(X1,X2)) = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2384]),
[final] ).
cnf(i_0_4370,plain,
( X2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),esk162_2(X1,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2491]),
[final] ).
cnf(i_0_4371,plain,
( X1 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,zero_zero_nat))) ),
inference(split_conjunct,[status(thm)],[i_0_2492]),
[final] ).
cnf(i_0_4372,plain,
( is_pname(esk62_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1655]),
[final] ).
cnf(i_0_4373,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X2)),X2) = X1,
inference(split_conjunct,[status(thm)],[i_0_2493]),
[final] ).
cnf(i_0_4374,plain,
hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2)),X2) = X1,
inference(split_conjunct,[status(thm)],[i_0_2494]),
[final] ).
cnf(i_0_4375,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X1) = X2,
inference(split_conjunct,[status(thm)],[i_0_2495]),
[final] ).
cnf(i_0_4376,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X2) = X1,
inference(split_conjunct,[status(thm)],[i_0_2496]),
[final] ).
cnf(i_0_4377,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2497]),
[final] ).
cnf(i_0_4378,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2497]),
[final] ).
cnf(i_0_4379,plain,
( X1 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk138_1(X1)),esk139_1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2498]),
[final] ).
cnf(i_0_4380,plain,
( X1 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk136_1(X1)),esk137_1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2499]),
[final] ).
cnf(i_0_4381,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,esk184_1(X1))))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2500]),
[final] ).
cnf(i_0_4382,plain,
( hBOOL(hAPP_nat_bool(nat_case_bool(X3,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2403]),
[final] ).
cnf(i_0_4383,plain,
( image_nat_int(cOMBK_int_nat(X3),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2501]),
[final] ).
cnf(i_0_4384,plain,
( image_pname_a(cOMBK_a_pname(X3),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2502]),
[final] ).
cnf(i_0_4385,plain,
( X1 = hAPP_nat_nat(suc,esk173_2(X2,X1))
| X1 = hAPP_nat_nat(suc,X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2330]),
[final] ).
cnf(i_0_4386,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| X1 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),hAPP_nat_int(semiri1621563631at_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2402]),
[final] ).
cnf(i_0_4387,plain,
( X1 = one_one_int
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2) != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2503]),
[final] ).
cnf(i_0_4388,plain,
( X1 = one_one_int
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2),X1) != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2503]),
[final] ).
cnf(i_0_4389,plain,
hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X2)),
inference(rw,[status(thm)],[i_0_2504,c_0_1684]),
[final] ).
cnf(i_0_4390,plain,
hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) = cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X1)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),X2)),
inference(rw,[status(thm)],[i_0_2505,c_0_1684]),
[final] ).
cnf(i_0_4391,plain,
hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2)),
inference(rw,[status(thm)],[i_0_2506,c_0_1678]),
[final] ).
cnf(i_0_4392,plain,
hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2)),
inference(rw,[status(thm)],[i_0_2507,c_0_1678]),
[final] ).
cnf(i_0_4393,plain,
( number_number_of_nat(X1) = number_number_of_nat(X2)
| X2 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(nat_neg,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2508,c_0_1649]),c_0_1649]),c_0_1649]),
[final] ).
cnf(i_0_4394,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),hAPP_nat_nat(suc,X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2509]),
[final] ).
cnf(i_0_4395,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int))
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2331]),
[final] ).
cnf(i_0_4396,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X1)),X2) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2510]),
[final] ).
cnf(i_0_4397,plain,
( number_number_of_nat(X1) = number_number_of_nat(X2)
| ~ hBOOL(hAPP_int_bool(nat_neg,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2511,c_0_1649]),c_0_1649]),
[final] ).
cnf(i_0_4398,plain,
( cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X2)),X1) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool)
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2512,c_0_1684]),
[final] ).
cnf(i_0_4399,plain,
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X2)),X1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool)
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2513,c_0_1678]),
[final] ).
cnf(i_0_4400,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(suc,X2)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2514]),
[final] ).
cnf(i_0_4401,plain,
( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1) = X1
| ~ is_fun_pname_bool(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2515]),
[final] ).
cnf(i_0_4402,plain,
( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1) = X1
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2516]),
[final] ).
cnf(i_0_4403,plain,
( hBOOL(hAPP_fun_a_bool_bool(p(X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2517]),
[final] ).
cnf(i_0_4404,plain,
( hBOOL(hAPP_int_bool(X1,esk206_1(X1)))
| ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2341]),
[final] ).
cnf(i_0_4405,plain,
( hBOOL(wt(the_com(body(X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),u)) ),
inference(split_conjunct,[status(thm)],[i_0_2518]),
[final] ).
cnf(i_0_4406,plain,
one_one_int = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),pls)),pls),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2519,c_0_1649]),c_0_1640]),
[final] ).
cnf(i_0_4407,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ is_pname(X1)
| ~ is_fun_pname_bool(X2)
| X3 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)
| X3 != bot_bo844097828e_bool
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2484]),
[final] ).
cnf(i_0_4408,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ is_a(X1)
| ~ is_fun_a_bool(X2)
| X3 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)
| X3 != bot_bot_fun_a_bool
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2485]),
[final] ).
cnf(i_0_4409,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk207_1(X1)))
| hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_2240]),
[final] ).
cnf(i_0_4410,plain,
( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2520]),
[final] ).
cnf(i_0_4411,plain,
( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2521]),
[final] ).
cnf(i_0_4412,plain,
( hBOOL(hAPP_nat_bool(X1,esk180_2(X2,X1)))
| hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_4413,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2522]),
[final] ).
cnf(i_0_4414,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2523]),
[final] ).
cnf(i_0_4415,plain,
( hBOOL(hAPP_nat_bool(X1,esk186_2(X2,X1)))
| hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,zero_zero_nat)) ),
inference(split_conjunct,[status(thm)],[i_0_2115]),
[final] ).
cnf(i_0_4416,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X1)) = one_one_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls)) ),
inference(split_conjunct,[status(thm)],[i_0_1556]),
[final] ).
cnf(i_0_4417,plain,
( X1 = zero_zero_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X1)),one_one_int)) ),
inference(split_conjunct,[status(thm)],[i_0_2524]),
[final] ).
cnf(i_0_4418,plain,
( X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2525]),
[final] ).
cnf(i_0_4419,plain,
( X1 = X2
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2526]),
[final] ).
cnf(i_0_4420,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X1 = X2
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2527]),
[final] ).
cnf(i_0_4421,plain,
hAPP_f1594865479ol_int(the_elem_int,X1) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,X1),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))),
inference(split_conjunct,[status(thm)],[i_0_2528]),
[final] ).
cnf(i_0_4422,plain,
hAPP_f22106695ol_nat(the_elem_nat,X1) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))),
inference(split_conjunct,[status(thm)],[i_0_2529]),
[final] ).
cnf(i_0_4423,plain,
hAPP_fun_a_bool_a(the_elem_a,X1) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))),
inference(split_conjunct,[status(thm)],[i_0_2530]),
[final] ).
cnf(i_0_4424,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2531]),
[final] ).
cnf(i_0_4425,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2532]),
[final] ).
cnf(i_0_4426,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2533]),
[final] ).
cnf(i_0_4427,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2534]),
[final] ).
cnf(i_0_4428,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2535]),
[final] ).
cnf(i_0_4429,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2536]),
[final] ).
cnf(i_0_4430,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2537]),
[final] ).
cnf(i_0_4431,plain,
( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2) = one_one_int
| X1 != one_one_int
| X2 != one_one_int
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2503]),
[final] ).
cnf(i_0_4432,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ is_fun_pname_bool(X1)
| ~ is_pname(X2)
| X3 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X2),X1)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2538]),
[final] ).
cnf(i_0_4433,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3))
| ~ is_fun_a_bool(X1)
| ~ is_a(X2)
| X3 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2539]),
[final] ).
cnf(i_0_4434,plain,
( hBOOL(hAPP_nat_bool(X2,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2540]),
[final] ).
cnf(i_0_4435,plain,
( hBOOL(hAPP_int_bool(X2,X1))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2541]),
[final] ).
cnf(i_0_4436,plain,
( hBOOL(hAPP_pname_bool(X2,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2542]),
[final] ).
cnf(i_0_4437,plain,
( hBOOL(hAPP_a_bool(X2,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2543]),
[final] ).
cnf(i_0_4438,plain,
( is_pname(esk115_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_4439,plain,
( is_a(esk109_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1717]),
[final] ).
cnf(i_0_4440,plain,
( is_fun_pname_bool(esk116_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_4441,plain,
( is_fun_a_bool(esk110_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1717]),
[final] ).
cnf(i_0_4442,plain,
( is_pname(esk123_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_4443,plain,
( is_a(esk117_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_4444,plain,
( is_fun_pname_bool(esk124_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(X1,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_4445,plain,
( is_fun_a_bool(esk118_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_4446,plain,
hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_2544]),
[final] ).
cnf(i_0_4447,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(suc,X2)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2545]),
[final] ).
cnf(i_0_4448,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| X1 != hAPP_nat_nat(suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2271]),
[final] ).
cnf(i_0_4449,plain,
( is_pname(esk160_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(X1,X2))
| is_pname(esk159_2(X1,X2))
| X2 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_4450,plain,
( is_fun_pname_bool(esk161_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(X1,X2))
| is_pname(esk159_2(X1,X2))
| X2 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_4451,plain,
( is_a(esk151_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| is_a(esk150_2(X1,X2))
| X2 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_4452,plain,
( is_fun_a_bool(esk152_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| is_a(esk150_2(X1,X2))
| X2 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_4453,plain,
( hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_int_bool(X1,esk207_1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2240]),
[final] ).
cnf(i_0_4454,plain,
X1 = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,esk214_1(X1))),hAPP_nat_int(semiri1621563631at_int,esk215_1(X1))),
inference(split_conjunct,[status(thm)],[i_0_2546]),
[final] ).
cnf(i_0_4455,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_2547]),
[final] ).
cnf(i_0_4456,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X1)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(suc,X2)),
inference(split_conjunct,[status(thm)],[i_0_2548]),
[final] ).
cnf(i_0_4457,plain,
( hBOOL(hAPP_nat_bool(X1,zero_zero_nat))
| ~ hBOOL(hAPP_nat_bool(X1,esk184_1(X1)))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2500]),
[final] ).
cnf(i_0_4458,plain,
( hBOOL(hAPP_int_bool(nat_neg,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[i_0_2549]),
[final] ).
cnf(i_0_4459,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_2550]),
[final] ).
cnf(i_0_4460,plain,
( hAPP_fun_a_bool_a(X3,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) = X1
| ~ is_a(X1)
| ~ hBOOL(finite_folding_one_a(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2551]),
[final] ).
cnf(i_0_4461,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3))
| X1 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)
| X1 != bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_2498]),
[final] ).
cnf(i_0_4462,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X3))
| X1 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)
| X1 != bot_bot_fun_int_bool ),
inference(split_conjunct,[status(thm)],[i_0_2499]),
[final] ).
cnf(i_0_4463,plain,
( X1 != bot_bo844097828e_bool
| ~ is_pname(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2552]),
[final] ).
cnf(i_0_4464,plain,
( X1 != bot_bot_fun_a_bool
| ~ is_a(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2553]),
[final] ).
cnf(i_0_4465,plain,
( ~ is_pname(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| X2 != bot_bo844097828e_bool
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2554]),
[final] ).
cnf(i_0_4466,plain,
( ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| X2 != bot_bot_fun_a_bool
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2555]),
[final] ).
cnf(i_0_4467,plain,
( X1 = X2
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2556]),
[final] ).
cnf(i_0_4468,plain,
( X1 = X2
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2557]),
[final] ).
cnf(i_0_4469,plain,
( X1 = X2
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2558]),
[final] ).
cnf(i_0_4470,plain,
( X1 = X2
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2559]),
[final] ).
cnf(i_0_4471,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| X1 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2491]),
[final] ).
cnf(i_0_4472,plain,
is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_]),
[final] ).
cnf(i_0_4473,plain,
is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool]),
[final] ).
cnf(i_0_4474,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X2))
| is_pname(esk159_2(X1,X2))
| X2 = bot_bo844097828e_bool
| esk161_2(X1,X2) != bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1735]),
[final] ).
cnf(i_0_4475,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| is_a(esk150_2(X1,X2))
| X2 = bot_bot_fun_a_bool
| esk152_2(X1,X2) != bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1736]),
[final] ).
cnf(i_0_4476,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2523]),
[final] ).
cnf(i_0_4477,plain,
( hAPP_nat_int(semiri1621563631at_int,X2) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X1),X2),X3))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2560]),
[final] ).
cnf(i_0_4478,plain,
( cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X2)),X1) = bot_bot_fun_int_bool
| hBOOL(hAPP_int_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2561,c_0_1684]),
[final] ).
cnf(i_0_4479,plain,
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),X1) = bot_bot_fun_nat_bool
| hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2562,c_0_1678]),
[final] ).
cnf(i_0_4480,plain,
( hBOOL(X1)
| hAPP_nat_int(semiri1621563631at_int,X2) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(X1),X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2560]),
[final] ).
cnf(i_0_4481,plain,
( hAPP_f1594865479ol_int(X2,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool)) = X3
| ~ hBOOL(finite1626084323ne_int(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2563]),
[final] ).
cnf(i_0_4482,plain,
( hAPP_f22106695ol_nat(X2,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),bot_bot_fun_nat_bool)) = X3
| ~ hBOOL(finite988810631ne_nat(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2564]),
[final] ).
cnf(i_0_4483,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2565]),
[final] ).
cnf(i_0_4484,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| X1 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2566]),
[final] ).
cnf(i_0_4485,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| X1 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X3)
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_2567]),
[final] ).
cnf(i_0_4486,plain,
( X1 = hAPP_nat_int(semiri1621563631at_int,esk213_1(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2568]),
[final] ).
cnf(i_0_4487,plain,
( X1 = hAPP_nat_int(semiri1621563631at_int,esk212_1(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2569]),
[final] ).
cnf(i_0_4488,plain,
( X1 = hAPP_nat_int(semiri1621563631at_int,esk211_1(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2570]),
[final] ).
cnf(i_0_4489,plain,
( X1 = hAPP_nat_int(semiri1621563631at_int,esk210_1(X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2458]),
[final] ).
cnf(i_0_4490,plain,
( X1 = hAPP_nat_nat(suc,esk182_1(X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2571]),
[final] ).
cnf(i_0_4491,plain,
( X1 = hAPP_nat_nat(suc,esk175_1(X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2572]),
[final] ).
cnf(i_0_4492,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),zero_zero_int))
| number_number_of_nat(X1) != number_number_of_nat(X2)
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2573,c_0_1649]),c_0_1649]),
[final] ).
cnf(i_0_4493,plain,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2574]),
[final] ).
cnf(i_0_4494,plain,
( X1 = X2
| ~ is_a(X1)
| ~ is_a(X2)
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2575]),
[final] ).
cnf(i_0_4495,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2322]),
[final] ).
cnf(i_0_4496,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_4497,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2576]),
[final] ).
cnf(i_0_4498,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2577]),
[final] ).
cnf(i_0_4499,plain,
( abs_abs_int(X1) = one_one_int
| abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2)) != one_one_int ),
inference(split_conjunct,[status(thm)],[i_0_2578]),
[final] ).
cnf(i_0_4500,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2540]),
[final] ).
cnf(i_0_4501,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2541]),
[final] ).
cnf(i_0_4502,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| ~ hBOOL(hAPP_pname_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2542]),
[final] ).
cnf(i_0_4503,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| ~ hBOOL(hAPP_a_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2543]),
[final] ).
cnf(i_0_4504,plain,
( X1 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),bot_bot_fun_a_bool))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2579]),
[final] ).
cnf(i_0_4505,plain,
( X1 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),bot_bot_fun_a_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2580]),
[final] ).
cnf(i_0_4506,plain,
( X1 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),bot_bot_fun_a_bool))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2581]),
[final] ).
cnf(i_0_4507,plain,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2450]),
[final] ).
cnf(i_0_4508,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2582]),
[final] ).
cnf(i_0_4509,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2583]),
[final] ).
cnf(i_0_4510,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2526]),
[final] ).
cnf(i_0_4511,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2526]),
[final] ).
cnf(i_0_4512,plain,
( X1 != X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2451]),
[final] ).
cnf(i_0_4513,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(X2,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2584]),
[final] ).
cnf(i_0_4514,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2585]),
[final] ).
cnf(i_0_4515,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2586]),
[final] ).
cnf(i_0_4516,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(X2,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2587]),
[final] ).
cnf(i_0_4517,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2588]),
[final] ).
cnf(i_0_4518,plain,
( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2589]),
[final] ).
cnf(i_0_4519,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2590]),
[final] ).
cnf(i_0_4520,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(X2,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2591]),
[final] ).
cnf(i_0_4521,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2592]),
[final] ).
cnf(i_0_4522,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2593]),
[final] ).
cnf(i_0_4523,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(X2,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2594]),
[final] ).
cnf(i_0_4524,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2595]),
[final] ).
cnf(i_0_4525,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X2,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2596]),
[final] ).
cnf(i_0_4526,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X2,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2597]),
[final] ).
cnf(i_0_4527,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X2,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2598]),
[final] ).
cnf(i_0_4528,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(X2,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2599]),
[final] ).
cnf(i_0_4529,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X2,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2600]),
[final] ).
cnf(i_0_4530,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2601]),
[final] ).
cnf(i_0_4531,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(X2,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2602]),
[final] ).
cnf(i_0_4532,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(X2,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2603]),
[final] ).
cnf(i_0_4533,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(X2,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2604]),
[final] ).
cnf(i_0_4534,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(X2,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2605]),
[final] ).
cnf(i_0_4535,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(X2,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2606]),
[final] ).
cnf(i_0_4536,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X2,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2607]),
[final] ).
cnf(i_0_4537,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(X2,X1)))
| ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2608]),
[final] ).
cnf(i_0_4538,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X2,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2609]),
[final] ).
cnf(i_0_4539,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X2,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2610]),
[final] ).
cnf(i_0_4540,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X2,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2611]),
[final] ).
cnf(i_0_4541,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2612]),
[final] ).
cnf(i_0_4542,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(X2,X1)))
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2613]),
[final] ).
cnf(i_0_4543,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2614]),
[final] ).
cnf(i_0_4544,plain,
( X1 != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2615]),
[final] ).
cnf(i_0_4545,plain,
( X1 != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2616]),
[final] ).
cnf(i_0_4546,plain,
( X1 != bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2617]),
[final] ).
cnf(i_0_4547,plain,
( X1 != bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2618]),
[final] ).
cnf(i_0_4548,plain,
( X1 != bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2619]),
[final] ).
cnf(i_0_4549,plain,
( X1 != bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2620]),
[final] ).
cnf(i_0_4550,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2621]),
[final] ).
cnf(i_0_4551,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| X2 != bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_2622]),
[final] ).
cnf(i_0_4552,plain,
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| X2 != bot_bot_fun_int_bool ),
inference(split_conjunct,[status(thm)],[i_0_2623]),
[final] ).
cnf(i_0_4553,plain,
( X3 = X4
| X1 != X2
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X2) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_2624]),
[final] ).
cnf(i_0_4554,plain,
( X3 = X4
| X1 != X2
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X3),X4) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2624]),
[final] ).
cnf(i_0_4555,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2625]),
[final] ).
cnf(i_0_4556,plain,
( X1 = X2
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2626]),
[final] ).
cnf(i_0_4557,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2627]),
[final] ).
cnf(i_0_4558,plain,
( X1 = X2
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2628]),
[final] ).
cnf(i_0_4559,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X1))),
inference(split_conjunct,[status(thm)],[i_0_2629]),
[final] ).
cnf(i_0_4560,plain,
( X1 = X3
| X2 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2630]),
[final] ).
cnf(i_0_4561,plain,
( X1 = zero_zero_nat
| X2 = X3
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2631]),
[final] ).
cnf(i_0_4562,plain,
( X2 = X3
| X1 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2632]),
[final] ).
cnf(i_0_4563,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2633]),
[final] ).
cnf(i_0_4564,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2634]),
[final] ).
cnf(i_0_4565,plain,
( X1 = X2
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) != zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2635]),
[final] ).
cnf(i_0_4566,plain,
( hAPP_nat_nat(suc,number_number_of_nat(X1)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))
| hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2636,c_0_1649]),c_0_2014]),
[final] ).
cnf(i_0_4567,plain,
( X1 = X3
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2637]),
[final] ).
cnf(i_0_4568,plain,
( X1 = X3
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2638]),
[final] ).
cnf(i_0_4569,plain,
( X1 = X3
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2639]),
[final] ).
cnf(i_0_4570,plain,
( X1 = X3
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2640]),
[final] ).
cnf(i_0_4571,plain,
( X1 = X3
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2641]),
[final] ).
cnf(i_0_4572,plain,
( X2 = X3
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2642]),
[final] ).
cnf(i_0_4573,plain,
( X2 = X3
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2643]),
[final] ).
cnf(i_0_4574,plain,
( X2 = X3
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2644]),
[final] ).
cnf(i_0_4575,plain,
( X2 = X3
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2645]),
[final] ).
cnf(i_0_4576,plain,
( X2 = X3
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2646]),
[final] ).
cnf(i_0_4577,plain,
( X2 = X3
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2647]),
[final] ).
cnf(i_0_4578,plain,
( X2 = X3
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2648]),
[final] ).
cnf(i_0_4579,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,zero_zero_nat)))
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2492]),
[final] ).
cnf(i_0_4580,plain,
( X1 = zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat)) ),
inference(split_conjunct,[status(thm)],[i_0_2649]),
[final] ).
cnf(i_0_4581,plain,
( X1 = bot_bot_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),bot_bot_nat)) ),
inference(split_conjunct,[status(thm)],[i_0_2650]),
[final] ).
cnf(i_0_4582,plain,
( X1 = bot_bot_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),bot_bot_nat)) ),
inference(split_conjunct,[status(thm)],[i_0_2651]),
[final] ).
cnf(i_0_4583,plain,
( X1 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),bot_bot_fun_nat_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2652]),
[final] ).
cnf(i_0_4584,plain,
( X1 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),bot_bot_fun_nat_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2653]),
[final] ).
cnf(i_0_4585,plain,
( X1 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),bot_bot_fun_nat_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2654]),
[final] ).
cnf(i_0_4586,plain,
( X1 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),bot_bot_fun_int_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2655]),
[final] ).
cnf(i_0_4587,plain,
( X1 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),bot_bot_fun_int_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2656]),
[final] ).
cnf(i_0_4588,plain,
( X1 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),bot_bot_fun_int_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_2657]),
[final] ).
cnf(i_0_4589,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2549]),
[final] ).
cnf(i_0_4590,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2550]),
[final] ).
cnf(i_0_4591,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X1))),
inference(split_conjunct,[status(thm)],[i_0_2658]),
[final] ).
cnf(i_0_4592,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
inference(split_conjunct,[status(thm)],[i_0_2659]),
[final] ).
cnf(i_0_4593,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
inference(split_conjunct,[status(thm)],[i_0_2660]),
[final] ).
cnf(i_0_4594,plain,
~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),bot_bot_fun_nat_bool)),
inference(split_conjunct,[status(thm)],[i_0_2661]),
[final] ).
cnf(i_0_4595,plain,
~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),bot_bot_fun_nat_bool)),
inference(split_conjunct,[status(thm)],[i_0_2662]),
[final] ).
cnf(i_0_4596,plain,
~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),bot_bot_fun_int_bool)),
inference(split_conjunct,[status(thm)],[i_0_2663]),
[final] ).
cnf(i_0_4597,plain,
~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),bot_bot_fun_int_bool)),
inference(split_conjunct,[status(thm)],[i_0_2664]),
[final] ).
cnf(i_0_4598,plain,
~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),bot_bo844097828e_bool)),
inference(split_conjunct,[status(thm)],[i_0_2665]),
[final] ).
cnf(i_0_4599,plain,
~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),bot_bo844097828e_bool)),
inference(split_conjunct,[status(thm)],[i_0_2666]),
[final] ).
cnf(i_0_4600,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),bot_bot_fun_a_bool)),
inference(split_conjunct,[status(thm)],[i_0_2667]),
[final] ).
cnf(i_0_4601,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),bot_bot_fun_a_bool)),
inference(split_conjunct,[status(thm)],[i_0_2668]),
[final] ).
cnf(i_0_4602,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
inference(split_conjunct,[status(thm)],[i_0_2669]),
[final] ).
cnf(i_0_4603,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
inference(split_conjunct,[status(thm)],[i_0_2670]),
[final] ).
cnf(i_0_4604,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
inference(split_conjunct,[status(thm)],[i_0_2671]),
[final] ).
cnf(i_0_4605,plain,
~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,X1))),
inference(split_conjunct,[status(thm)],[i_0_2672]),
[final] ).
cnf(i_0_4606,plain,
( X1 = X2
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2673]),
[final] ).
cnf(i_0_4607,plain,
( X1 = X2
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),bot_bot_fun_nat_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2674]),
[final] ).
cnf(i_0_4608,plain,
( cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,X2)),X1) = bot_bot_fun_int_bool
| hBOOL(hAPP_int_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2675,c_0_1684]),
[final] ).
cnf(i_0_4609,plain,
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X2)),X1) = bot_bot_fun_nat_bool
| hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2676,c_0_1678]),
[final] ).
cnf(i_0_4610,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X2),X1) = zero_zero_int ),
inference(split_conjunct,[status(thm)],[i_0_2456]),
[final] ).
cnf(i_0_4611,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2677]),
[final] ).
cnf(i_0_4612,plain,
cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),X1) = image_nat_int(semiri1621563631at_int,cOMBB_int_bool_nat(X1,semiri1621563631at_int)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2678,c_0_1678]),c_0_1684]),
[final] ).
cnf(i_0_4613,hypothesis,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
inference(split_conjunct,[status(thm)],[conj_1]),
[final] ).
cnf(i_0_4614,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk100_1(X1)),X1))
| X1 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2552]),
[final] ).
cnf(i_0_4615,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk96_1(X1)),X1))
| X1 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2554]),
[final] ).
cnf(i_0_4616,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk99_1(X1)),X1))
| X1 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2553]),
[final] ).
cnf(i_0_4617,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk95_1(X1)),X1))
| X1 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2555]),
[final] ).
cnf(i_0_4618,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)) = zero_zero_nat,
inference(split_conjunct,[status(thm)],[i_0_2679]),
[final] ).
cnf(i_0_4619,plain,
( X1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk132_1(X1)),esk131_1(X1))
| X1 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2538]),
[final] ).
cnf(i_0_4620,plain,
( X1 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk126_1(X1)),esk125_1(X1))
| X1 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2539]),
[final] ).
cnf(i_0_4621,plain,
( is_pname(esk78_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2108]),
[final] ).
cnf(i_0_4622,plain,
( is_a(esk83_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1763]),
[final] ).
cnf(i_0_4623,plain,
( is_a(esk77_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2109]),
[final] ).
cnf(i_0_4624,plain,
( is_a(esk70_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1764]),
[final] ).
cnf(i_0_4625,plain,
hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X1,X2),X3) = hAPP_bool_bool(hAPP_f1748468828l_bool(X1,X3),hAPP_f54304608l_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2680]),
[final] ).
cnf(i_0_4626,plain,
hAPP_f448129468l_bool(cOMBS_1912792529l_bool(X1,X2),X3) = hAPP_bool_bool(hAPP_f1721100032l_bool(X1,X3),hAPP_f448129468l_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2681]),
[final] ).
cnf(i_0_4627,plain,
hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X1,X2),X3) = hAPP_bool_bool(hAPP_f1476298914l_bool(X1,X3),hAPP_f1664156314l_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2682]),
[final] ).
cnf(i_0_4628,plain,
hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X1,X2),X3) = hAPP_bool_bool(hAPP_f198738859l_bool(X1,X3),hAPP_fun_a_bool_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2683]),
[final] ).
cnf(i_0_4629,plain,
hAPP_nat_bool(cOMBS_nat_bool_bool(X1,X2),X3) = hAPP_bool_bool(hAPP_n1006566506l_bool(X1,X3),hAPP_nat_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2684]),
[final] ).
cnf(i_0_4630,plain,
hAPP_int_bool(cOMBS_int_bool_bool(X1,X2),X3) = hAPP_bool_bool(hAPP_i68813070l_bool(X1,X3),hAPP_int_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2685]),
[final] ).
cnf(i_0_4631,plain,
hAPP_pname_bool(cOMBS_568398431l_bool(X1,X2),X3) = hAPP_bool_bool(hAPP_p393069232l_bool(X1,X3),hAPP_pname_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2686]),
[final] ).
cnf(i_0_4632,plain,
hAPP_a_bool(cOMBS_a_bool_bool(X1,X2),X3) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X1,X3),hAPP_a_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2687]),
[final] ).
cnf(i_0_4633,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(split_conjunct,[status(thm)],[i_0_2688]),
[final] ).
cnf(i_0_4634,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk98_1(X1)),X1))
| X1 = bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_2615]),
[final] ).
cnf(i_0_4635,plain,
( X1 = bot_bot_fun_nat_bool
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk94_1(X1)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2622]),
[final] ).
cnf(i_0_4636,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk97_1(X1)),X1))
| X1 = bot_bot_fun_int_bool ),
inference(split_conjunct,[status(thm)],[i_0_2617]),
[final] ).
cnf(i_0_4637,plain,
( X1 = bot_bot_fun_int_bool
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk93_1(X1)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2623]),
[final] ).
cnf(i_0_4638,plain,
( X1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk130_1(X1)),esk129_1(X1))
| X1 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2566]),
[final] ).
cnf(i_0_4639,plain,
( X1 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk128_1(X1)),esk127_1(X1))
| X1 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2567]),
[final] ).
cnf(i_0_4640,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(X1)),one_one_int))
| X1 != zero_zero_int ),
inference(split_conjunct,[status(thm)],[i_0_2524]),
[final] ).
cnf(i_0_4641,plain,
( X1 = hAPP_nat_nat(suc,zero_zero_nat)
| X2 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) != hAPP_nat_nat(suc,zero_zero_nat) ),
inference(split_conjunct,[status(thm)],[i_0_2689]),
[final] ).
cnf(i_0_4642,plain,
( X1 = hAPP_nat_nat(suc,zero_zero_nat)
| X2 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2690]),
[final] ).
cnf(i_0_4643,plain,
( hBOOL(hAPP_int_bool(nat_neg,X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2531]),
[final] ).
cnf(i_0_4644,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2346]),
[final] ).
cnf(i_0_4645,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X2 != X1
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2346]),
[final] ).
cnf(i_0_4646,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2
| ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2350]),
[final] ).
cnf(i_0_4647,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X2 != X1
| ~ is_fun_a_bool(X2)
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2350]),
[final] ).
cnf(i_0_4648,plain,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X1)),
inference(split_conjunct,[status(thm)],[i_0_2691]),
[final] ).
cnf(i_0_4649,plain,
hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(X1),X2),X3) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2692]),
[final] ).
cnf(i_0_4650,plain,
hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(X1),X2),X3) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2693]),
[final] ).
cnf(i_0_4651,plain,
hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X1),X2),X3) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2694]),
[final] ).
cnf(i_0_4652,plain,
hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(X1),X2),X3) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2695]),
[final] ).
cnf(i_0_4653,plain,
hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X1),X2),X3) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2696]),
[final] ).
cnf(i_0_4654,plain,
hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X1),X2),X3) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2697]),
[final] ).
cnf(i_0_4655,plain,
hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X1),X2),X3) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2698]),
[final] ).
cnf(i_0_4656,plain,
hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(X1),X2),X3) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2699]),
[final] ).
cnf(i_0_4657,plain,
hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X1),X2),X3) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2700]),
[final] ).
cnf(i_0_4658,plain,
hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X1),X2),X3) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2701]),
[final] ).
cnf(i_0_4659,plain,
hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(X1),X2),X3) = hAPP_int_bool(hAPP_n1082236369t_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2702]),
[final] ).
cnf(i_0_4660,plain,
hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(X1),X2),X3) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2703]),
[final] ).
cnf(i_0_4661,plain,
hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(X1),X2),X3) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2704]),
[final] ).
cnf(i_0_4662,plain,
hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(X1),X2),X3) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2705]),
[final] ).
cnf(i_0_4663,plain,
hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X1),X2),X3) = hAPP_nat_bool(hAPP_n1699378549t_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2706]),
[final] ).
cnf(i_0_4664,plain,
hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X1),X2),X3) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2707]),
[final] ).
cnf(i_0_4665,plain,
hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(X1),X2),X3) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2708]),
[final] ).
cnf(i_0_4666,plain,
hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(X1),X2),X3) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2709]),
[final] ).
cnf(i_0_4667,plain,
hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(X1),X2),X3) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2710]),
[final] ).
cnf(i_0_4668,plain,
hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(X1),X2),X3) = hAPP_a_bool(hAPP_int_fun_a_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2711]),
[final] ).
cnf(i_0_4669,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(X1),X2),X3) = hAPP_int_bool(hAPP_i1948725293t_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2712]),
[final] ).
cnf(i_0_4670,plain,
hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(X1),X2),X3) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2713]),
[final] ).
cnf(i_0_4671,plain,
hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X1),X2),X3) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2714]),
[final] ).
cnf(i_0_4672,plain,
hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X1),X2),X3) = hAPP_pname_bool(hAPP_p61793385e_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2715]),
[final] ).
cnf(i_0_4673,plain,
hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X1),X2),X3) = hAPP_a_bool(hAPP_p1534023578a_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2716]),
[final] ).
cnf(i_0_4674,plain,
hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(X1),X2),X3) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2717]),
[final] ).
cnf(i_0_4675,plain,
hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X1),X2),X3) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2718]),
[final] ).
cnf(i_0_4676,plain,
hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X1),X2),X3) = hAPP_a_bool(hAPP_a_fun_a_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2719]),
[final] ).
cnf(i_0_4677,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X1 != hAPP_nat_nat(suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2572]),
[final] ).
cnf(i_0_4678,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk131_1(X1)))
| X1 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2538]),
[final] ).
cnf(i_0_4679,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk125_1(X1)))
| X1 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2539]),
[final] ).
cnf(i_0_4680,plain,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X1))),
inference(rw,[status(thm)],[i_0_2720,c_0_1678]),
[final] ).
cnf(i_0_4681,plain,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X1))),
inference(rw,[status(thm)],[i_0_2721,c_0_1678]),
[final] ).
cnf(i_0_4682,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2722]),
[final] ).
cnf(i_0_4683,plain,
( hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool)) = X1
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2723]),
[final] ).
cnf(i_0_4684,plain,
( X1 = zero_zero_nat
| X1 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(suc,zero_zero_nat) ),
inference(split_conjunct,[status(thm)],[i_0_2689]),
[final] ).
cnf(i_0_4685,plain,
( X1 = hAPP_nat_nat(suc,zero_zero_nat)
| X1 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) != hAPP_nat_nat(suc,zero_zero_nat) ),
inference(split_conjunct,[status(thm)],[i_0_2689]),
[final] ).
cnf(i_0_4686,plain,
( X1 = zero_zero_nat
| X1 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2690]),
[final] ).
cnf(i_0_4687,plain,
( X1 = hAPP_nat_nat(suc,zero_zero_nat)
| X1 = zero_zero_nat
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2690]),
[final] ).
cnf(i_0_4688,plain,
( X1 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) != hAPP_nat_nat(suc,zero_zero_nat) ),
inference(split_conjunct,[status(thm)],[i_0_2724]),
[final] ).
cnf(i_0_4689,plain,
( X1 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) != hAPP_nat_nat(suc,zero_zero_nat) ),
inference(split_conjunct,[status(thm)],[i_0_2724]),
[final] ).
cnf(i_0_4690,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) = hAPP_nat_nat(suc,zero_zero_nat)
| X1 != hAPP_nat_nat(suc,zero_zero_nat)
| X2 != hAPP_nat_nat(suc,zero_zero_nat) ),
inference(split_conjunct,[status(thm)],[i_0_2724]),
[final] ).
cnf(i_0_4691,plain,
( X2 = zero_zero_int
| hBOOL(hAPP_int_bool(nat_neg,X2))
| number_number_of_nat(X1) != number_number_of_nat(X2)
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2725,c_0_1649]),c_0_1649]),c_0_1649]),
[final] ).
cnf(i_0_4692,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk129_1(X1)))
| X1 = bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2566]),
[final] ).
cnf(i_0_4693,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,esk127_1(X1)))
| X1 = bot_bot_fun_int_bool
| ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2567]),
[final] ).
cnf(i_0_4694,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2726]),
[final] ).
cnf(i_0_4695,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2727]),
[final] ).
cnf(i_0_4696,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2728]),
[final] ).
cnf(i_0_4697,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),bot_bot_fun_a_bool))
| X1 != bot_bot_fun_a_bool
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2579]),
[final] ).
cnf(i_0_4698,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),bot_bot_fun_a_bool))
| X1 != bot_bot_fun_a_bool
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2581]),
[final] ).
cnf(i_0_4699,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),one_one_nat) = X1,
inference(split_conjunct,[status(thm)],[i_0_2729]),
[final] ).
cnf(i_0_4700,plain,
hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2730]),
[final] ).
cnf(i_0_4701,plain,
hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2731]),
[final] ).
cnf(i_0_4702,plain,
( number_number_of_nat(X1) = number_number_of_nat(X2)
| hBOOL(hAPP_int_bool(nat_neg,X2))
| X2 != zero_zero_int
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2732,c_0_1649]),c_0_1649]),c_0_1649]),
[final] ).
cnf(i_0_4703,plain,
( hBOOL(X1)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2733]),
[final] ).
cnf(i_0_4704,plain,
hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_f1664156314l_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2734]),
[final] ).
cnf(i_0_4705,plain,
hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_f54304608l_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2735]),
[final] ).
cnf(i_0_4706,plain,
hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_f448129468l_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2736]),
[final] ).
cnf(i_0_4707,plain,
hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(X1,X2),X3) = hAPP_f284875647l_bool(X1,hAPP_n1082236369t_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2737]),
[final] ).
cnf(i_0_4708,plain,
hAPP_i1718399025l_bool(cOMBB_516767136ol_int(X1,X2),X3) = hAPP_f103356543l_bool(X1,hAPP_i418383825t_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2738]),
[final] ).
cnf(i_0_4709,plain,
hAPP_f198738859l_bool(cOMBB_338059395a_bool(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_fun_a_bool_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2739]),
[final] ).
cnf(i_0_4710,plain,
hAPP_p393069232l_bool(cOMBB_675860798_pname(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_pname_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2740]),
[final] ).
cnf(i_0_4711,plain,
hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_nat_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2741]),
[final] ).
cnf(i_0_4712,plain,
hAPP_i68813070l_bool(cOMBB_1652995168ol_int(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_int_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2742]),
[final] ).
cnf(i_0_4713,plain,
hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X1,X2),X3) = hAPP_b589554111l_bool(X1,hAPP_a_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2743]),
[final] ).
cnf(i_0_4714,plain,
hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(X1,X2),X3) = hAPP_i1948725293t_bool(X1,hAPP_nat_int(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2744]),
[final] ).
cnf(i_0_4715,plain,
hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(X1,X2),X3) = hAPP_f284875647l_bool(X1,hAPP_i1948725293t_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2745]),
[final] ).
cnf(i_0_4716,plain,
hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(X1,X2),X3) = hAPP_n215258509l_bool(X1,hAPP_nat_nat(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2746]),
[final] ).
cnf(i_0_4717,plain,
hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(X1,X2),X3) = hAPP_f103356543l_bool(X1,hAPP_n1699378549t_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2747]),
[final] ).
cnf(i_0_4718,plain,
hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(X1,X2),X3) = hAPP_n1699378549t_bool(X1,hAPP_nat_nat(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2748]),
[final] ).
cnf(i_0_4719,plain,
hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(X1,X2),X3) = hAPP_f434788991l_bool(X1,hAPP_n1025906991e_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2749]),
[final] ).
cnf(i_0_4720,plain,
hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(X1,X2),X3) = hAPP_f1631501043l_bool(X1,hAPP_nat_fun_a_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2750]),
[final] ).
cnf(i_0_4721,plain,
hAPP_nat_bool(cOMBB_int_bool_nat(X1,X2),X3) = hAPP_int_bool(X1,hAPP_nat_int(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2751]),
[final] ).
cnf(i_0_4722,plain,
hAPP_nat_bool(cOMBB_955900739ol_nat(X1,X2),X3) = hAPP_f54304608l_bool(X1,hAPP_n1699378549t_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2752]),
[final] ).
cnf(i_0_4723,plain,
hAPP_nat_bool(cOMBB_bool_bool_nat(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_nat_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2753]),
[final] ).
cnf(i_0_4724,plain,
hAPP_i1587699435l_bool(cOMBB_607112096ol_int(X1,X2),X3) = hAPP_f434788991l_bool(X1,hAPP_i7355787e_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2754]),
[final] ).
cnf(i_0_4725,plain,
hAPP_i888906320l_bool(cOMBB_313729068ol_int(X1,X2),X3) = hAPP_f1631501043l_bool(X1,hAPP_int_fun_a_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2755]),
[final] ).
cnf(i_0_4726,plain,
hAPP_int_fun_a_bool(cOMBB_375279840ol_int(X1,X2),X3) = hAPP_a_fun_a_bool(X1,hAPP_int_a(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2756]),
[final] ).
cnf(i_0_4727,plain,
hAPP_int_bool(cOMBB_1418110531ol_int(X1,X2),X3) = hAPP_f448129468l_bool(X1,hAPP_i1948725293t_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2757]),
[final] ).
cnf(i_0_4728,plain,
hAPP_int_bool(cOMBB_bool_bool_int(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_int_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2758]),
[final] ).
cnf(i_0_4729,plain,
hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X1,X2),X3) = hAPP_a_fun_a_bool(X1,hAPP_pname_a(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2759]),
[final] ).
cnf(i_0_4730,plain,
hAPP_pname_bool(cOMBB_647938656_pname(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_pname_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2760]),
[final] ).
cnf(i_0_4731,plain,
hAPP_a_bool(cOMBB_1273333599bool_a(X1,X2),X3) = hAPP_fun_a_bool_bool(X1,hAPP_a_fun_a_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2761]),
[final] ).
cnf(i_0_4732,plain,
hAPP_a_bool(cOMBB_bool_bool_a(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_a_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2762]),
[final] ).
cnf(i_0_4733,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2763]),
[final] ).
cnf(i_0_4734,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2764]),
[final] ).
cnf(i_0_4735,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2764]),
[final] ).
cnf(i_0_4736,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2765]),
[final] ).
cnf(i_0_4737,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2362]),
[final] ).
cnf(i_0_4738,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2362]),
[final] ).
cnf(i_0_4739,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2766]),
[final] ).
cnf(i_0_4740,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2366]),
[final] ).
cnf(i_0_4741,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2366]),
[final] ).
cnf(i_0_4742,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2767]),
[final] ).
cnf(i_0_4743,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2768]),
[final] ).
cnf(i_0_4744,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2769]),
[final] ).
cnf(i_0_4745,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2769]),
[final] ).
cnf(i_0_4746,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2770]),
[final] ).
cnf(i_0_4747,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2368]),
[final] ).
cnf(i_0_4748,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2368]),
[final] ).
cnf(i_0_4749,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2771]),
[final] ).
cnf(i_0_4750,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2372]),
[final] ).
cnf(i_0_4751,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2372]),
[final] ).
cnf(i_0_4752,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2772]),
[final] ).
cnf(i_0_4753,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2773]),
[final] ).
cnf(i_0_4754,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2774]),
[final] ).
cnf(i_0_4755,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2775]),
[final] ).
cnf(i_0_4756,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2775]),
[final] ).
cnf(i_0_4757,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2776]),
[final] ).
cnf(i_0_4758,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2777]),
[final] ).
cnf(i_0_4759,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2778]),
[final] ).
cnf(i_0_4760,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2779]),
[final] ).
cnf(i_0_4761,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2453]),
[final] ).
cnf(i_0_4762,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2449]),
[final] ).
cnf(i_0_4763,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2780]),
[final] ).
cnf(i_0_4764,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2377]),
[final] ).
cnf(i_0_4765,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2377]),
[final] ).
cnf(i_0_4766,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2781]),
[final] ).
cnf(i_0_4767,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2782]),
[final] ).
cnf(i_0_4768,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2783]),
[final] ).
cnf(i_0_4769,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2383]),
[final] ).
cnf(i_0_4770,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2383]),
[final] ).
cnf(i_0_4771,plain,
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2784]),
[final] ).
cnf(i_0_4772,plain,
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2785]),
[final] ).
cnf(i_0_4773,plain,
( X1 = zero_zero_nat
| X2 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != hAPP_nat_nat(suc,zero_zero_nat) ),
inference(split_conjunct,[status(thm)],[i_0_2689]),
[final] ).
cnf(i_0_4774,plain,
( X1 = zero_zero_nat
| X2 = zero_zero_nat
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2690]),
[final] ).
cnf(i_0_4775,plain,
hAPP_nat_nat(nat_case_nat(X1,X2),hAPP_nat_nat(suc,X3)) = hAPP_nat_nat(X2,X3),
inference(split_conjunct,[status(thm)],[i_0_2786]),
[final] ).
cnf(i_0_4776,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2631]),
[final] ).
cnf(i_0_4777,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2632]),
[final] ).
cnf(i_0_4778,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X3),X1)
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2630]),
[final] ).
cnf(i_0_4779,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2787]),
[final] ).
cnf(i_0_4780,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2788]),
[final] ).
cnf(i_0_4781,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2789]),
[final] ).
cnf(i_0_4782,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2790]),
[final] ).
cnf(i_0_4783,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2791]),
[final] ).
cnf(i_0_4784,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2792]),
[final] ).
cnf(i_0_4785,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2793]),
[final] ).
cnf(i_0_4786,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2794]),
[final] ).
cnf(i_0_4787,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2795]),
[final] ).
cnf(i_0_4788,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_2796]),
[final] ).
cnf(i_0_4789,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),bot_bot_fun_nat_bool))
| X1 != bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_2652]),
[final] ).
cnf(i_0_4790,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),bot_bot_fun_nat_bool))
| X1 != bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_2654]),
[final] ).
cnf(i_0_4791,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),bot_bot_fun_int_bool))
| X1 != bot_bot_fun_int_bool ),
inference(split_conjunct,[status(thm)],[i_0_2655]),
[final] ).
cnf(i_0_4792,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),bot_bot_fun_int_bool))
| X1 != bot_bot_fun_int_bool ),
inference(split_conjunct,[status(thm)],[i_0_2657]),
[final] ).
cnf(i_0_4793,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),zero_zero_nat))
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2649]),
[final] ).
cnf(i_0_4794,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),bot_bot_nat))
| X1 != bot_bot_nat ),
inference(split_conjunct,[status(thm)],[i_0_2650]),
[final] ).
cnf(i_0_4795,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X2) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2797]),
[final] ).
cnf(i_0_4796,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2798]),
[final] ).
cnf(i_0_4797,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2799]),
[final] ).
cnf(i_0_4798,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2800]),
[final] ).
cnf(i_0_4799,plain,
( X1 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2677]),
[final] ).
cnf(i_0_4800,plain,
( X1 = zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2801]),
[final] ).
cnf(i_0_4801,plain,
collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool),
inference(split_conjunct,[status(thm)],[i_0_2802]),
[final] ).
cnf(i_0_4802,plain,
( X1 = X2
| hBOOL(hAPP_int_bool(nat_neg,X2))
| hBOOL(hAPP_int_bool(nat_neg,X1))
| number_number_of_nat(X1) != number_number_of_nat(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2803,c_0_1649]),c_0_1649]),
[final] ).
cnf(i_0_4803,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X1)),
inference(split_conjunct,[status(thm)],[i_0_2804]),
[final] ).
cnf(i_0_4804,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X1)),
inference(split_conjunct,[status(thm)],[i_0_2805]),
[final] ).
cnf(i_0_4805,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X1)),
inference(split_conjunct,[status(thm)],[i_0_2806]),
[final] ).
cnf(i_0_4806,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),X1)),
inference(split_conjunct,[status(thm)],[i_0_2807]),
[final] ).
cnf(i_0_4807,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X1)),
inference(split_conjunct,[status(thm)],[i_0_2808]),
[final] ).
cnf(i_0_4808,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X1)),
inference(split_conjunct,[status(thm)],[i_0_2809]),
[final] ).
cnf(i_0_4809,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)),
inference(split_conjunct,[status(thm)],[i_0_2810]),
[final] ).
cnf(i_0_4810,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)),
inference(split_conjunct,[status(thm)],[i_0_2811]),
[final] ).
cnf(i_0_4811,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),X1)),
inference(split_conjunct,[status(thm)],[i_0_2812]),
[final] ).
cnf(i_0_4812,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) = hAPP_nat_nat(suc,zero_zero_nat)
| X1 != zero_zero_nat
| X2 != hAPP_nat_nat(suc,zero_zero_nat) ),
inference(split_conjunct,[status(thm)],[i_0_2689]),
[final] ).
cnf(i_0_4813,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) = hAPP_nat_nat(suc,zero_zero_nat)
| X1 != hAPP_nat_nat(suc,zero_zero_nat)
| X2 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2689]),
[final] ).
cnf(i_0_4814,plain,
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)
| X1 != zero_zero_nat
| X2 != hAPP_nat_nat(suc,zero_zero_nat) ),
inference(split_conjunct,[status(thm)],[i_0_2690]),
[final] ).
cnf(i_0_4815,plain,
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)
| X1 != hAPP_nat_nat(suc,zero_zero_nat)
| X2 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2690]),
[final] ).
cnf(i_0_4816,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(split_conjunct,[status(thm)],[conj_4]),
[final] ).
cnf(i_0_4817,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
inference(split_conjunct,[status(thm)],[fact_1035_int__0__less__1]),
[final] ).
cnf(i_0_4818,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
inference(split_conjunct,[status(thm)],[fact_1189_rel__simps_I19_J]),
[final] ).
cnf(i_0_4819,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
inference(split_conjunct,[status(thm)],[fact_1084_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]),
[final] ).
cnf(i_0_4820,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(split_conjunct,[status(thm)],[fact_1086_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]),
[final] ).
cnf(i_0_4821,plain,
( X1 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,esk140_1(X1)),esk141_1(X1))
| X1 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2484]),
[final] ).
cnf(i_0_4822,plain,
( X1 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,esk134_1(X1)),esk135_1(X1))
| X1 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2485]),
[final] ).
cnf(i_0_4823,plain,
( X1 = bot_bo844097828e_bool
| image_pname_a(cOMBK_a_pname(X2),X1) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),bot_bot_fun_a_bool)
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2813]),
[final] ).
cnf(i_0_4824,plain,
( X2 = one_one_nat
| X1 = zero_zero_nat
| X1 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2814]),
[final] ).
cnf(i_0_4825,plain,
( is_pname(esk132_1(X1))
| X1 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2538]),
[final] ).
cnf(i_0_4826,plain,
( is_fun_pname_bool(esk131_1(X1))
| X1 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2538]),
[final] ).
cnf(i_0_4827,plain,
( is_a(esk126_1(X1))
| X1 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2539]),
[final] ).
cnf(i_0_4828,plain,
( is_fun_a_bool(esk125_1(X1))
| X1 = bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2539]),
[final] ).
cnf(i_0_4829,plain,
collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool),
inference(split_conjunct,[status(thm)],[i_0_2815]),
[final] ).
cnf(i_0_4830,plain,
( collect_a(X1) != bot_bot_fun_a_bool
| ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2816]),
[final] ).
cnf(i_0_4831,plain,
( bot_bot_fun_a_bool != collect_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2817]),
[final] ).
cnf(i_0_4832,plain,
( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X1)) = zero_zero_int
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[i_0_2818,c_0_1649]),
[final] ).
cnf(i_0_4833,plain,
( hAPP_nat_nat(suc,number_number_of_nat(X1)) = one_one_nat
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[i_0_2819,c_0_1649]),
[final] ).
cnf(i_0_4834,plain,
( X1 = zero_zero_nat
| X2 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2820]),
[final] ).
cnf(i_0_4835,plain,
( X2 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2821]),
[final] ).
cnf(i_0_4836,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2822]),
[final] ).
cnf(i_0_4837,plain,
( X1 = zero_zero_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2822]),
[final] ).
cnf(i_0_4838,plain,
( X1 = one_one_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) != one_one_nat ),
inference(split_conjunct,[status(thm)],[i_0_2823]),
[final] ).
cnf(i_0_4839,plain,
( X1 = one_one_nat
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) != one_one_nat ),
inference(split_conjunct,[status(thm)],[i_0_2823]),
[final] ).
cnf(i_0_4840,plain,
( X1 = one_one_nat
| one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2824]),
[final] ).
cnf(i_0_4841,plain,
( X1 = one_one_nat
| one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2824]),
[final] ).
cnf(i_0_4842,plain,
hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) != bot_bot_fun_int_bool,
inference(split_conjunct,[status(thm)],[i_0_2825]),
[final] ).
cnf(i_0_4843,plain,
hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) != bot_bot_fun_nat_bool,
inference(split_conjunct,[status(thm)],[i_0_2826]),
[final] ).
cnf(i_0_4844,plain,
hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2) != bot_bot_fun_a_bool,
inference(split_conjunct,[status(thm)],[i_0_2827]),
[final] ).
cnf(i_0_4845,plain,
bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_2828]),
[final] ).
cnf(i_0_4846,plain,
bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_2829]),
[final] ).
cnf(i_0_4847,plain,
bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2),
inference(split_conjunct,[status(thm)],[i_0_2830]),
[final] ).
cnf(i_0_4848,plain,
( X1 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,esk138_1(X1)),esk139_1(X1))
| X1 = bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_2498]),
[final] ).
cnf(i_0_4849,plain,
( X1 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,esk136_1(X1)),esk137_1(X1))
| X1 = bot_bot_fun_int_bool ),
inference(split_conjunct,[status(thm)],[i_0_2499]),
[final] ).
cnf(i_0_4850,plain,
( X1 = bot_bot_fun_nat_bool
| image_nat_int(cOMBK_int_nat(X2),X1) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),bot_bot_fun_int_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2831]),
[final] ).
cnf(i_0_4851,plain,
hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X1)) = hAPP_nat_nat(suc,X1),
inference(rw,[status(thm)],[i_0_2832,c_0_1678]),
[final] ).
cnf(i_0_4852,plain,
hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X1) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool),
inference(rw,[status(thm)],[i_0_2833,c_0_1684]),
[final] ).
cnf(i_0_4853,plain,
hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool),
inference(rw,[status(thm)],[i_0_2834,c_0_1678]),
[final] ).
cnf(i_0_4854,plain,
( ~ hBOOL(hAPP_bool_bool(fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2835]),
[final] ).
cnf(i_0_4855,plain,
( bot_bot_fun_nat_bool != X1
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2836,c_0_1678]),
[final] ).
cnf(i_0_4856,plain,
( bot_bot_fun_int_bool != X1
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2837,c_0_1684]),
[final] ).
cnf(i_0_4857,plain,
( X1 != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2838,c_0_1678]),
[final] ).
cnf(i_0_4858,plain,
( X1 != bot_bot_fun_int_bool
| ~ hBOOL(hAPP_int_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2839,c_0_1684]),
[final] ).
cnf(i_0_4859,plain,
is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]),
[final] ).
cnf(i_0_4860,plain,
is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_It__a_Mtc__HOL__Obool_J]),
[final] ).
cnf(i_0_4861,plain,
hAPP_i1948725293t_bool(fequal_int,X1) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool),
inference(rw,[status(thm)],[i_0_2840,c_0_1684]),
[final] ).
cnf(i_0_4862,plain,
hAPP_nat_nat(suc,X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),one_one_nat),
inference(split_conjunct,[status(thm)],[i_0_2841]),
[final] ).
cnf(i_0_4863,plain,
hAPP_n1699378549t_bool(fequal_nat,X1) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool),
inference(rw,[status(thm)],[i_0_2842,c_0_1678]),
[final] ).
cnf(i_0_4864,plain,
hAPP_f22106695ol_nat(finite_card_nat,X1) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,X1)),
inference(split_conjunct,[status(thm)],[i_0_2843]),
[final] ).
cnf(i_0_4865,plain,
hAPP_n1699378549t_bool(ord_less_nat,X1) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),
inference(split_conjunct,[status(thm)],[i_0_2844]),
[final] ).
cnf(i_0_4866,plain,
( number_number_of_nat(X1) = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[i_0_2845,c_0_1649]),
[final] ).
cnf(i_0_4867,plain,
( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X1)) = X1
| hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2846,c_0_1649]),c_0_1649]),
[final] ).
cnf(i_0_4868,plain,
( hBOOL(hAPP_a_bool(X1,esk89_1(X1)))
| collect_a(X1) = bot_bot_fun_a_bool ),
inference(split_conjunct,[status(thm)],[i_0_2816]),
[final] ).
cnf(i_0_4869,plain,
( hBOOL(hAPP_a_bool(X1,esk92_1(X1)))
| bot_bot_fun_a_bool = collect_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2817]),
[final] ).
cnf(i_0_4870,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X1),X2) = X1,
inference(split_conjunct,[status(thm)],[i_0_2847]),
[final] ).
cnf(i_0_4871,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X1),X2) = X2,
inference(split_conjunct,[status(thm)],[i_0_2848]),
[final] ).
cnf(i_0_4872,plain,
hAPP_nat_nat(suc,X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),X1),
inference(split_conjunct,[status(thm)],[i_0_2849]),
[final] ).
cnf(i_0_4873,plain,
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2850]),
[final] ).
cnf(i_0_4874,plain,
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2851]),
[final] ).
cnf(i_0_4875,plain,
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2852]),
[final] ).
cnf(i_0_4876,plain,
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2853]),
[final] ).
cnf(i_0_4877,plain,
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2854]),
[final] ).
cnf(i_0_4878,plain,
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2855]),
[final] ).
cnf(i_0_4879,plain,
hAPP_f22106695ol_nat(finite_card_nat,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X1)) = X1,
inference(rw,[status(thm)],[i_0_2856,c_0_1678]),
[final] ).
cnf(i_0_4880,hypothesis,
( is_bool(hAPP_f1664156314l_bool(X1,X2))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2857]),
[final] ).
cnf(i_0_4881,hypothesis,
( is_bool(hAPP_fun_a_bool_bool(X1,X2))
| ~ is_fun949378684l_bool(X1)
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2858]),
[final] ).
cnf(i_0_4882,plain,
( is_bool(hAPP_pname_bool(X1,X2))
| ~ is_fun_pname_bool(X1)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2859]),
[final] ).
cnf(i_0_4883,plain,
( is_bool(hAPP_a_bool(X1,X2))
| ~ is_fun_a_bool(X1)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2860]),
[final] ).
cnf(i_0_4884,plain,
( bot_bot_fun_nat_bool = X1
| hBOOL(hAPP_nat_bool(X1,esk91_1(X1))) ),
inference(rw,[status(thm)],[i_0_2861,c_0_1678]),
[final] ).
cnf(i_0_4885,plain,
( bot_bot_fun_int_bool = X1
| hBOOL(hAPP_int_bool(X1,esk90_1(X1))) ),
inference(rw,[status(thm)],[i_0_2862,c_0_1684]),
[final] ).
cnf(i_0_4886,plain,
( X1 = bot_bot_fun_nat_bool
| hBOOL(hAPP_nat_bool(X1,esk88_1(X1))) ),
inference(rw,[status(thm)],[i_0_2863,c_0_1678]),
[final] ).
cnf(i_0_4887,plain,
( X1 = bot_bot_fun_int_bool
| hBOOL(hAPP_int_bool(X1,esk87_1(X1))) ),
inference(rw,[status(thm)],[i_0_2864,c_0_1684]),
[final] ).
cnf(i_0_4888,plain,
( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),bot_bot_fun_a_bool) = X1
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2865]),
[final] ).
cnf(i_0_4889,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) = one_one_nat
| X1 != one_one_nat
| X2 != one_one_nat ),
inference(split_conjunct,[status(thm)],[i_0_2823]),
[final] ).
cnf(i_0_4890,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) = zero_zero_nat
| X1 != zero_zero_nat
| X2 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2822]),
[final] ).
cnf(i_0_4891,plain,
( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2)
| X1 != one_one_nat
| X2 != one_one_nat ),
inference(split_conjunct,[status(thm)],[i_0_2824]),
[final] ).
cnf(i_0_4892,plain,
( X1 = X2
| hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2866]),
[final] ).
cnf(i_0_4893,plain,
( X1 = X2
| hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2867]),
[final] ).
cnf(i_0_4894,plain,
( X1 = X2
| hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2868]),
[final] ).
cnf(i_0_4895,plain,
( X1 = X2
| hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2869]),
[final] ).
cnf(i_0_4896,plain,
( X1 = X2
| image_nat_int(semiri1621563631at_int,X1) != image_nat_int(semiri1621563631at_int,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2870]),
[final] ).
cnf(i_0_4897,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2) = X2
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2066]),
[final] ).
cnf(i_0_4898,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) = zero_zero_nat
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2033]),
[final] ).
cnf(i_0_4899,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X2) = zero_zero_nat
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2820]),
[final] ).
cnf(i_0_4900,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X1) = zero_zero_nat
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2820]),
[final] ).
cnf(i_0_4901,plain,
abs_abs_int(hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,X1),
inference(split_conjunct,[status(thm)],[i_0_2871]),
[final] ).
cnf(i_0_4902,plain,
~ hBOOL(hAPP_int_bool(nat_neg,pls)),
inference(rw,[status(thm)],[i_0_2872,c_0_1649]),
[final] ).
cnf(i_0_4903,plain,
~ hBOOL(hAPP_int_bool(nat_neg,zero_zero_int)),
inference(split_conjunct,[status(thm)],[i_0_2873]),
[final] ).
cnf(i_0_4904,plain,
~ hBOOL(hAPP_int_bool(nat_neg,one_one_int)),
inference(split_conjunct,[status(thm)],[i_0_2874]),
[final] ).
cnf(i_0_4905,plain,
( is_pname(hAPP_f1297739591_pname(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2875]),
[final] ).
cnf(i_0_4906,plain,
( is_pname(hAPP_pname_pname(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2876]),
[final] ).
cnf(i_0_4907,plain,
( is_a(hAPP_fun_a_bool_a(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2877]),
[final] ).
cnf(i_0_4908,hypothesis,
( is_a(hAPP_pname_a(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2878]),
[final] ).
cnf(i_0_4909,plain,
( is_a(hAPP_a_a(X2,X1))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2879]),
[final] ).
cnf(i_0_4910,plain,
( is_fun1661590463l_bool(hAPP_f559147733l_bool(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2880]),
[final] ).
cnf(i_0_4911,plain,
( is_fun1661590463l_bool(hAPP_f434788991l_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2881]),
[final] ).
cnf(i_0_4912,hypothesis,
( is_fun1661590463l_bool(hAPP_p338031245l_bool(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2882]),
[final] ).
cnf(i_0_4913,plain,
( is_fun1661590463l_bool(image_47868345e_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2883]),
[final] ).
cnf(i_0_4914,plain,
( is_fun1661590463l_bool(image_819518260e_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2884]),
[final] ).
cnf(i_0_4915,plain,
( is_fun1661590463l_bool(cOMBS_350070575l_bool(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2885]),
[final] ).
cnf(i_0_4916,plain,
( is_bool(hAPP_f1935102916l_bool(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2886]),
[final] ).
cnf(i_0_4917,plain,
( is_bool(hAPP_f621171935l_bool(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2887]),
[final] ).
cnf(i_0_4918,plain,
( is_bool(hAPP_bool_bool(X2,X1))
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2888]),
[final] ).
cnf(i_0_4919,plain,
( is_fun949378684l_bool(hAPP_f2117159681l_bool(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2889]),
[final] ).
cnf(i_0_4920,hypothesis,
( is_fun949378684l_bool(hAPP_f1631501043l_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2890]),
[final] ).
cnf(i_0_4921,hypothesis,
( is_fun949378684l_bool(hAPP_a85458249l_bool(X2,X1))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2891]),
[final] ).
cnf(i_0_4922,plain,
( is_fun949378684l_bool(image_112932426a_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2892]),
[final] ).
cnf(i_0_4923,plain,
( is_fun949378684l_bool(image_a_fun_a_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2893]),
[final] ).
cnf(i_0_4924,plain,
( is_fun949378684l_bool(cOMBS_1035972772l_bool(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2894]),
[final] ).
cnf(i_0_4925,plain,
( is_fun_pname_bool(hAPP_f759274231e_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2895]),
[final] ).
cnf(i_0_4926,plain,
( is_fun_pname_bool(hAPP_p61793385e_bool(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2896]),
[final] ).
cnf(i_0_4927,plain,
( is_fun_pname_bool(hAPP_a93125764e_bool(X2,X1))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2897]),
[final] ).
cnf(i_0_4928,plain,
( is_fun_pname_bool(image_1283814551_pname(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2898]),
[final] ).
cnf(i_0_4929,plain,
( is_fun_pname_bool(image_1854862208_pname(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2899]),
[final] ).
cnf(i_0_4930,plain,
( is_fun_pname_bool(image_pname_pname(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2900]),
[final] ).
cnf(i_0_4931,plain,
( is_fun_pname_bool(image_a_pname(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2901]),
[final] ).
cnf(i_0_4932,plain,
( is_fun_pname_bool(cOMBS_568398431l_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2902]),
[final] ).
cnf(i_0_4933,plain,
( is_fun_pname_bool(cOMBB_647938656_pname(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2903]),
[final] ).
cnf(i_0_4934,hypothesis,
( is_fun_a_bool(hAPP_f2050579477a_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2904]),
[final] ).
cnf(i_0_4935,plain,
( is_fun_a_bool(hAPP_p1534023578a_bool(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2905]),
[final] ).
cnf(i_0_4936,plain,
( is_fun_a_bool(hAPP_a_fun_a_bool(X2,X1))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2906]),
[final] ).
cnf(i_0_4937,plain,
( is_fun_a_bool(image_876012084bool_a(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2907]),
[final] ).
cnf(i_0_4938,plain,
( is_fun_a_bool(image_fun_a_bool_a(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2908]),
[final] ).
cnf(i_0_4939,hypothesis,
( is_fun_a_bool(image_pname_a(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2909]),
[final] ).
cnf(i_0_4940,plain,
( is_fun_a_bool(image_a_a(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2910]),
[final] ).
cnf(i_0_4941,plain,
( is_fun_a_bool(cOMBS_a_bool_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2911]),
[final] ).
cnf(i_0_4942,plain,
( is_fun_a_bool(cOMBB_1273333599bool_a(X1,X2))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2912]),
[final] ).
cnf(i_0_4943,plain,
( is_fun_a_bool(cOMBB_bool_bool_a(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2913]),
[final] ).
cnf(i_0_4944,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X1) = zero_zero_nat,
inference(split_conjunct,[status(thm)],[i_0_2914]),
[final] ).
cnf(i_0_4945,plain,
hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),X1) = bot_bot_fun_int_bool,
inference(split_conjunct,[status(thm)],[i_0_2915]),
[final] ).
cnf(i_0_4946,plain,
hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),X1) = bot_bot_fun_nat_bool,
inference(split_conjunct,[status(thm)],[i_0_2916]),
[final] ).
cnf(i_0_4947,plain,
hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X1),X1) = bot_bot_fun_a_bool,
inference(split_conjunct,[status(thm)],[i_0_2917]),
[final] ).
cnf(i_0_4948,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| X1 != bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2538]),
[final] ).
cnf(i_0_4949,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| X1 != bot_bot_fun_a_bool
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2539]),
[final] ).
cnf(i_0_4950,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),one_one_int) = X1,
inference(split_conjunct,[status(thm)],[i_0_2918]),
[final] ).
cnf(i_0_4951,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),pls) = X1,
inference(split_conjunct,[status(thm)],[i_0_2919]),
[final] ).
cnf(i_0_4952,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),zero_zero_int) = X1,
inference(split_conjunct,[status(thm)],[i_0_2920]),
[final] ).
cnf(i_0_4953,plain,
hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),pls) = X1,
inference(split_conjunct,[status(thm)],[i_0_2921]),
[final] ).
cnf(i_0_4954,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),one_one_nat) = X1,
inference(split_conjunct,[status(thm)],[i_0_2922]),
[final] ).
cnf(i_0_4955,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),zero_zero_nat) = X1,
inference(split_conjunct,[status(thm)],[i_0_2923]),
[final] ).
cnf(i_0_4956,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),zero_zero_nat) = X1,
inference(split_conjunct,[status(thm)],[i_0_2924]),
[final] ).
cnf(i_0_4957,plain,
hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X1),bot_bot_fun_int_bool) = X1,
inference(split_conjunct,[status(thm)],[i_0_2925]),
[final] ).
cnf(i_0_4958,plain,
hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X1),bot_bot_fun_nat_bool) = X1,
inference(split_conjunct,[status(thm)],[i_0_2926]),
[final] ).
cnf(i_0_4959,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),zero_zero_nat) = zero_zero_nat,
inference(split_conjunct,[status(thm)],[i_0_2927]),
[final] ).
cnf(i_0_4960,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2928]),
[final] ).
cnf(i_0_4961,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2929]),
[final] ).
cnf(i_0_4962,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2930]),
[final] ).
cnf(i_0_4963,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2931]),
[final] ).
cnf(i_0_4964,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2932]),
[final] ).
cnf(i_0_4965,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),X1) = pls,
inference(split_conjunct,[status(thm)],[i_0_2933]),
[final] ).
cnf(i_0_4966,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),X1) = zero_zero_nat,
inference(split_conjunct,[status(thm)],[i_0_2934]),
[final] ).
cnf(i_0_4967,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),X1) = zero_zero_nat,
inference(split_conjunct,[status(thm)],[i_0_2935]),
[final] ).
cnf(i_0_4968,plain,
hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),X1) = bot_bot_fun_int_bool,
inference(split_conjunct,[status(thm)],[i_0_2936]),
[final] ).
cnf(i_0_4969,plain,
hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),X1) = bot_bot_fun_nat_bool,
inference(split_conjunct,[status(thm)],[i_0_2937]),
[final] ).
cnf(i_0_4970,plain,
hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),X1) = bot_bot_fun_a_bool,
inference(split_conjunct,[status(thm)],[i_0_2938]),
[final] ).
cnf(i_0_4971,plain,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,zero_zero_nat)) = one_one_int,
inference(split_conjunct,[status(thm)],[fact_1122_int__Suc0__eq__1]),
[final] ).
cnf(i_0_4972,plain,
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1))
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2850]),
[final] ).
cnf(i_0_4973,plain,
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1))
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2851]),
[final] ).
cnf(i_0_4974,plain,
( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X1))
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2852]),
[final] ).
cnf(i_0_4975,plain,
( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X1))
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2853]),
[final] ).
cnf(i_0_4976,plain,
( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X1))
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2854]),
[final] ).
cnf(i_0_4977,plain,
( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X1))
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2855]),
[final] ).
cnf(i_0_4978,plain,
( hBOOL(X1)
| hBOOL(hAPP_bool_bool(fNot,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2939]),
[final] ).
cnf(i_0_4979,plain,
( X2 = bot_bo844097828e_bool
| image_pname_a(X1,X2) != bot_bot_fun_a_bool
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2940]),
[final] ).
cnf(i_0_4980,plain,
( X2 = bot_bo844097828e_bool
| bot_bot_fun_a_bool != image_pname_a(X1,X2)
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2941]),
[final] ).
cnf(i_0_4981,plain,
is_a(hAPP_int_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2942]),
[final] ).
cnf(i_0_4982,plain,
is_fun1661590463l_bool(hAPP_n850744903l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2943]),
[final] ).
cnf(i_0_4983,plain,
is_fun1661590463l_bool(hAPP_i1587699435l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2944]),
[final] ).
cnf(i_0_4984,plain,
is_fun1661590463l_bool(image_1655916159e_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2945]),
[final] ).
cnf(i_0_4985,plain,
is_fun1661590463l_bool(image_637364955e_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2946]),
[final] ).
cnf(i_0_4986,plain,
is_bool(hAPP_f937997336l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2947]),
[final] ).
cnf(i_0_4987,plain,
is_bool(hAPP_f1593524852l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2948]),
[final] ).
cnf(i_0_4988,plain,
is_bool(hAPP_f389811538l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2949]),
[final] ).
cnf(i_0_4989,plain,
is_bool(hAPP_f292226953l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2950]),
[final] ).
cnf(i_0_4990,plain,
is_bool(hAPP_f1637334154l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2951]),
[final] ).
cnf(i_0_4991,plain,
is_bool(hAPP_f215623910l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2952]),
[final] ).
cnf(i_0_4992,plain,
is_bool(hAPP_f54304608l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2953]),
[final] ).
cnf(i_0_4993,plain,
is_bool(hAPP_f448129468l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2954]),
[final] ).
cnf(i_0_4994,hypothesis,
is_bool(hAPP_nat_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2955]),
[final] ).
cnf(i_0_4995,plain,
is_bool(hAPP_int_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2956]),
[final] ).
cnf(i_0_4996,plain,
is_bool(finite795500164em_nat(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2957]),
[final] ).
cnf(i_0_4997,plain,
is_bool(finite1432773856em_int(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2958]),
[final] ).
cnf(i_0_4998,plain,
is_bool(finite89670078_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2959]),
[final] ).
cnf(i_0_4999,plain,
is_bool(finite1819937229idem_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2960]),
[final] ).
cnf(i_0_5000,plain,
is_bool(finite988810631ne_nat(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2961]),
[final] ).
cnf(i_0_5001,plain,
is_bool(finite1626084323ne_int(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2962]),
[final] ).
cnf(i_0_5002,plain,
is_bool(finite1282449217_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2963]),
[final] ).
cnf(i_0_5003,plain,
is_bool(finite_folding_one_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2964]),
[final] ).
cnf(i_0_5004,plain,
is_fun949378684l_bool(hAPP_n1414589940l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2965]),
[final] ).
cnf(i_0_5005,plain,
is_fun949378684l_bool(hAPP_i888906320l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2966]),
[final] ).
cnf(i_0_5006,plain,
is_fun949378684l_bool(image_nat_fun_a_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2967]),
[final] ).
cnf(i_0_5007,plain,
is_fun949378684l_bool(image_int_fun_a_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2968]),
[final] ).
cnf(i_0_5008,plain,
is_fun_pname_bool(hAPP_n1025906991e_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2969]),
[final] ).
cnf(i_0_5009,plain,
is_fun_pname_bool(hAPP_i7355787e_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2970]),
[final] ).
cnf(i_0_5010,plain,
is_fun_pname_bool(image_1921560913_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2971]),
[final] ).
cnf(i_0_5011,plain,
is_fun_pname_bool(image_62782965_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2972]),
[final] ).
cnf(i_0_5012,plain,
is_fun_pname_bool(image_nat_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2973]),
[final] ).
cnf(i_0_5013,plain,
is_fun_pname_bool(image_int_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2974]),
[final] ).
cnf(i_0_5014,plain,
is_fun_a_bool(hAPP_nat_fun_a_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2975]),
[final] ).
cnf(i_0_5015,plain,
is_fun_a_bool(hAPP_int_fun_a_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2976]),
[final] ).
cnf(i_0_5016,plain,
is_fun_a_bool(image_fun_nat_bool_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2977]),
[final] ).
cnf(i_0_5017,plain,
is_fun_a_bool(image_fun_int_bool_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2978]),
[final] ).
cnf(i_0_5018,plain,
is_fun_a_bool(image_nat_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2979]),
[final] ).
cnf(i_0_5019,plain,
is_fun_a_bool(image_int_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2980]),
[final] ).
cnf(i_0_5020,plain,
( image_pname_a(cOMBK_a_pname(X2),X1) = bot_bot_fun_a_bool
| X1 != bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2813]),
[final] ).
cnf(i_0_5021,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| X1 != bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_2566]),
[final] ).
cnf(i_0_5022,plain,
( hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| X1 != bot_bot_fun_int_bool ),
inference(split_conjunct,[status(thm)],[i_0_2567]),
[final] ).
cnf(i_0_5023,plain,
( hAPP_nat_bool(cOMBK_bool_nat(X1),X2) = X1
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2981]),
[final] ).
cnf(i_0_5024,plain,
( hAPP_int_bool(cOMBK_bool_int(X1),X2) = X1
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2982]),
[final] ).
cnf(i_0_5025,plain,
( hAPP_pname_a(cOMBK_a_pname(X1),X2) = X1
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2983]),
[final] ).
cnf(i_0_5026,plain,
( hAPP_a_bool(cOMBK_bool_a(X1),X2) = X1
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2984]),
[final] ).
cnf(i_0_5027,plain,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
inference(split_conjunct,[status(thm)],[fact_498_finite_OemptyI]),
[final] ).
cnf(i_0_5028,plain,
hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool)),
inference(split_conjunct,[status(thm)],[fact_497_finite_OemptyI]),
[final] ).
cnf(i_0_5029,hypothesis,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
inference(split_conjunct,[status(thm)],[conj_0]),
[final] ).
cnf(i_0_5030,plain,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
inference(split_conjunct,[status(thm)],[fact_499_finite_OemptyI]),
[final] ).
cnf(i_0_5031,plain,
hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
inference(split_conjunct,[status(thm)],[fact_500_finite_OemptyI]),
[final] ).
cnf(i_0_5032,plain,
( X2 = bot_bot_fun_nat_bool
| image_nat_int(X1,X2) != bot_bot_fun_int_bool ),
inference(split_conjunct,[status(thm)],[i_0_2985]),
[final] ).
cnf(i_0_5033,plain,
( X2 = bot_bot_fun_nat_bool
| bot_bot_fun_int_bool != image_nat_int(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2986]),
[final] ).
cnf(i_0_5034,plain,
( image_pname_a(X2,X1) = bot_bot_fun_a_bool
| X1 != bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2940]),
[final] ).
cnf(i_0_5035,plain,
( bot_bot_fun_a_bool = image_pname_a(X2,X1)
| X1 != bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2941]),
[final] ).
cnf(i_0_5036,plain,
( image_nat_int(cOMBK_int_nat(X2),X1) = bot_bot_fun_int_bool
| X1 != bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_2831]),
[final] ).
cnf(i_0_5037,plain,
( X1 = zero_zero_nat
| hAPP_nat_int(semiri1621563631at_int,X1) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[i_0_2987]),
[final] ).
cnf(i_0_5038,plain,
hAPP_nat_nat(suc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_2988]),
[final] ).
cnf(i_0_5039,plain,
X1 != hAPP_nat_nat(suc,X1),
inference(split_conjunct,[status(thm)],[i_0_2989]),
[final] ).
cnf(i_0_5040,plain,
( X1 = zero_zero_nat
| X1 = hAPP_nat_nat(suc,esk185_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2990]),
[final] ).
cnf(i_0_5041,plain,
( X1 = zero_zero_nat
| X1 = hAPP_nat_nat(suc,esk183_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2991]),
[final] ).
cnf(i_0_5042,plain,
hAPP_nat_int(cOMBK_int_nat(X1),X2) = X1,
inference(split_conjunct,[status(thm)],[i_0_2992]),
[final] ).
cnf(i_0_5043,plain,
hAPP_nat_nat(suc,X1) != zero_zero_nat,
inference(split_conjunct,[status(thm)],[i_0_2993]),
[final] ).
cnf(i_0_5044,plain,
hAPP_nat_nat(suc,X1) != zero_zero_nat,
inference(split_conjunct,[status(thm)],[i_0_2994]),
[final] ).
cnf(i_0_5045,plain,
hAPP_nat_nat(suc,X1) != zero_zero_nat,
inference(split_conjunct,[status(thm)],[i_0_2995]),
[final] ).
cnf(i_0_5046,plain,
zero_zero_nat != hAPP_nat_nat(suc,X1),
inference(split_conjunct,[status(thm)],[i_0_2996]),
[final] ).
cnf(i_0_5047,plain,
zero_zero_nat != hAPP_nat_nat(suc,X1),
inference(split_conjunct,[status(thm)],[i_0_2997]),
[final] ).
cnf(i_0_5048,plain,
zero_zero_nat != hAPP_nat_nat(suc,X1),
inference(split_conjunct,[status(thm)],[i_0_2998]),
[final] ).
cnf(i_0_5049,plain,
( is_pname(esk140_1(X1))
| X1 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2484]),
[final] ).
cnf(i_0_5050,plain,
( is_pname(esk100_1(X1))
| X1 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2552]),
[final] ).
cnf(i_0_5051,plain,
( is_pname(esk96_1(X1))
| X1 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2554]),
[final] ).
cnf(i_0_5052,plain,
( is_fun_pname_bool(esk141_1(X1))
| X1 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2484]),
[final] ).
cnf(i_0_5053,plain,
( is_a(esk134_1(X1))
| X1 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2485]),
[final] ).
cnf(i_0_5054,plain,
( is_a(esk99_1(X1))
| X1 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2553]),
[final] ).
cnf(i_0_5055,plain,
( is_a(esk95_1(X1))
| X1 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2555]),
[final] ).
cnf(i_0_5056,plain,
( is_fun_a_bool(esk135_1(X1))
| X1 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2485]),
[final] ).
cnf(i_0_5057,plain,
( is_fun1661590463l_bool(collec1974731493e_bool(X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2999]),
[final] ).
cnf(i_0_5058,plain,
( is_fun949378684l_bool(p(X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_3000]),
[final] ).
cnf(i_0_5059,plain,
( is_fun949378684l_bool(collect_fun_a_bool(X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_3001]),
[final] ).
cnf(i_0_5060,plain,
( is_fun_pname_bool(collect_pname(X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_3002]),
[final] ).
cnf(i_0_5061,plain,
( is_fun_a_bool(collect_a(X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_3003]),
[final] ).
cnf(i_0_5062,plain,
( is_fun_a_bool(cOMBK_bool_a(X1))
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_3004]),
[final] ).
cnf(i_0_5063,plain,
( image_nat_int(X2,X1) = bot_bot_fun_int_bool
| X1 != bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_2985]),
[final] ).
cnf(i_0_5064,plain,
( bot_bot_fun_int_bool = image_nat_int(X2,X1)
| X1 != bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_2986]),
[final] ).
cnf(i_0_5065,plain,
( hAPP_nat_int(semiri1621563631at_int,X1) = zero_zero_int
| X1 != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_2987]),
[final] ).
cnf(i_0_5066,plain,
( is_a(esk89_1(X1))
| collect_a(X1) = bot_bot_fun_a_bool ),
inference(split_conjunct,[status(thm)],[i_0_2816]),
[final] ).
cnf(i_0_5067,plain,
( is_a(esk92_1(X1))
| bot_bot_fun_a_bool = collect_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2817]),
[final] ).
cnf(i_0_5068,plain,
hAPP_nat_nat(cOMBI_nat,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_3005]),
[final] ).
cnf(i_0_5069,plain,
image_nat_int(X1,bot_bot_fun_nat_bool) = bot_bot_fun_int_bool,
inference(split_conjunct,[status(thm)],[i_0_3006]),
[final] ).
cnf(i_0_5070,plain,
image_pname_a(X1,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
inference(split_conjunct,[status(thm)],[i_0_3007]),
[final] ).
cnf(i_0_5071,plain,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_1099_int__0]),
[final] ).
cnf(i_0_5072,plain,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
inference(split_conjunct,[status(thm)],[fact_1098_int__1]),
[final] ).
cnf(i_0_5073,plain,
zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(split_conjunct,[status(thm)],[fact_1116_transfer__int__nat__numerals_I1_J]),
[final] ).
cnf(i_0_5074,plain,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
inference(split_conjunct,[status(thm)],[fact_1115_transfer__int__nat__numerals_I2_J]),
[final] ).
cnf(i_0_5075,plain,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
inference(split_conjunct,[status(thm)],[fact_957_One__nat__def]),
[final] ).
cnf(i_0_5076,plain,
bot_bot_fun_int_bool = image_nat_int(semiri1621563631at_int,bot_bot_fun_nat_bool),
inference(split_conjunct,[status(thm)],[fact_1135_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J]),
[final] ).
cnf(i_0_5077,plain,
is_a(mgt(X1)),
inference(split_conjunct,[status(thm)],[i_0_3008]),
[final] ).
cnf(i_0_5078,plain,
is_bool(wt(X1)),
inference(split_conjunct,[status(thm)],[i_0_3009]),
[final] ).
cnf(i_0_5079,plain,
( X1 = fTrue
| X1 = fFalse
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_3010]),
[final] ).
cnf(i_0_5080,plain,
( X1 = fTrue
| X1 = fFalse
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_3011]),
[final] ).
cnf(i_0_5081,plain,
is_pname(undefined_pname(pname)),
inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Com__Opname]),
[final] ).
cnf(i_0_5082,plain,
is_a(undefined_a(x_a)),
inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000t__a]),
[final] ).
cnf(i_0_5083,plain,
bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
inference(split_conjunct,[status(thm)],[fact_540_empty__def]),
[final] ).
cnf(i_0_5084,plain,
~ hBOOL(fFalse),
inference(split_conjunct,[status(thm)],[i_0_3012]),
[final] ).
cnf(i_0_5085,hypothesis,
is_pname(pn),
inference(split_conjunct,[status(thm)],[gsy_v_pn]),
[final] ).
cnf(i_0_5086,hypothesis,
is_fun1661590463l_bool(finite_finite_pname),
inference(split_conjunct,[status(thm)],[gsy_c_Finite__Set_Ofinite_000tc__Com__Opname]),
[final] ).
cnf(i_0_5087,plain,
is_bool(fTrue),
inference(split_conjunct,[status(thm)],[gsy_c_fTrue]),
[final] ).
cnf(i_0_5088,plain,
is_bool(fFalse),
inference(split_conjunct,[status(thm)],[gsy_c_fFalse]),
[final] ).
cnf(i_0_5089,plain,
is_bool(bot_bot_bool),
inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool]),
[final] ).
cnf(i_0_5090,plain,
is_fun949378684l_bool(finite_finite_a),
inference(split_conjunct,[status(thm)],[gsy_c_Finite__Set_Ofinite_000t__a]),
[final] ).
cnf(i_0_5091,hypothesis,
is_fun_pname_bool(u),
inference(split_conjunct,[status(thm)],[gsy_v_U]),
[final] ).
cnf(i_0_5092,plain,
is_fun_pname_bool(bot_bo844097828e_bool),
inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]),
[final] ).
cnf(i_0_5093,hypothesis,
is_fun_a_bool(g),
inference(split_conjunct,[status(thm)],[gsy_v_G]),
[final] ).
cnf(i_0_5094,plain,
is_fun_a_bool(bot_bot_fun_a_bool),
inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__fun_It__a_Mtc__HOL__Obool_J]),
[final] ).
cnf(i_0_5095,plain,
number_number_of_nat(pls) = zero_zero_nat,
inference(split_conjunct,[status(thm)],[fact_1178_nat__number__of__Pls]),
[final] ).
cnf(i_0_5096,plain,
zero_zero_nat = number_number_of_nat(pls),
inference(split_conjunct,[status(thm)],[fact_1179_semiring__norm_I113_J]),
[final] ).
cnf(i_0_5097,plain,
bot_bot_fun_nat_bool = cOMBK_bool_nat(fFalse),
inference(rw,[status(thm)],[i_0_3013,c_0_1678]),
[final] ).
cnf(i_0_5098,plain,
bot_bot_fun_int_bool = cOMBK_bool_int(fFalse),
inference(rw,[status(thm)],[i_0_3014,c_0_1684]),
[final] ).
cnf(i_0_5099,plain,
zero_zero_int != one_one_int,
inference(split_conjunct,[status(thm)],[fact_1072_int__0__neq__1]),
[final] ).
cnf(i_0_5100,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_1180_Pls__def]),
[final] ).
cnf(i_0_5101,plain,
pls = zero_zero_int,
inference(rw,[status(thm)],[i_0_3015,c_0_1649]),
[final] ).
cnf(i_0_5102,plain,
bot_bot_nat = zero_zero_nat,
inference(split_conjunct,[status(thm)],[fact_930_bot__nat__def]),
[final] ).
cnf(i_0_5103,axiom,
X1 = X1 ).
cnf(i_0_5104,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_5105,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_5106,axiom,
( X1 != X2
| hAPP_nat_bool(X1,X3) = hAPP_nat_bool(X2,X3) ) ).
cnf(i_0_5107,axiom,
( X1 != X2
| hAPP_nat_bool(X3,X1) = hAPP_nat_bool(X3,X2) ) ).
cnf(i_0_5108,axiom,
( X1 != X2
| hAPP_nat_nat(X1,X3) = hAPP_nat_nat(X2,X3) ) ).
cnf(i_0_5109,axiom,
( X1 != X2
| hAPP_nat_nat(X3,X1) = hAPP_nat_nat(X3,X2) ) ).
cnf(i_0_5110,axiom,
( X1 != X2
| hAPP_f215623910l_bool(X1,X3) = hAPP_f215623910l_bool(X2,X3) ) ).
cnf(i_0_5111,axiom,
( X1 != X2
| hAPP_f215623910l_bool(X3,X1) = hAPP_f215623910l_bool(X3,X2) ) ).
cnf(i_0_5112,axiom,
( X1 != X2
| image_1556378401t_bool(X1,X3) = image_1556378401t_bool(X2,X3) ) ).
cnf(i_0_5113,axiom,
( X1 != X2
| image_1556378401t_bool(X3,X1) = image_1556378401t_bool(X3,X2) ) ).
cnf(i_0_5114,axiom,
( X1 != X2
| hAPP_f1935102916l_bool(X1,X3) = hAPP_f1935102916l_bool(X2,X3) ) ).
cnf(i_0_5115,axiom,
( X1 != X2
| hAPP_f1935102916l_bool(X3,X1) = hAPP_f1935102916l_bool(X3,X2) ) ).
cnf(i_0_5116,axiom,
( X1 != X2
| image_1655916159e_bool(X1,X3) = image_1655916159e_bool(X2,X3) ) ).
cnf(i_0_5117,axiom,
( X1 != X2
| image_1655916159e_bool(X3,X1) = image_1655916159e_bool(X3,X2) ) ).
cnf(i_0_5118,axiom,
( X1 != X2
| hAPP_f621171935l_bool(X1,X3) = hAPP_f621171935l_bool(X2,X3) ) ).
cnf(i_0_5119,axiom,
( X1 != X2
| hAPP_f621171935l_bool(X3,X1) = hAPP_f621171935l_bool(X3,X2) ) ).
cnf(i_0_5120,axiom,
( X1 != X2
| image_nat_fun_a_bool(X1,X3) = image_nat_fun_a_bool(X2,X3) ) ).
cnf(i_0_5121,axiom,
( X1 != X2
| image_nat_fun_a_bool(X3,X1) = image_nat_fun_a_bool(X3,X2) ) ).
cnf(i_0_5122,axiom,
( X1 != X2
| image_nat_int(X1,X3) = image_nat_int(X2,X3) ) ).
cnf(i_0_5123,axiom,
( X1 != X2
| image_nat_int(X3,X1) = image_nat_int(X3,X2) ) ).
cnf(i_0_5124,axiom,
( X1 != X2
| image_892525857t_bool(X1,X3) = image_892525857t_bool(X2,X3) ) ).
cnf(i_0_5125,axiom,
( X1 != X2
| image_892525857t_bool(X3,X1) = image_892525857t_bool(X3,X2) ) ).
cnf(i_0_5126,axiom,
( X1 != X2
| cOMBS_int_bool_bool(X1,X3) = cOMBS_int_bool_bool(X2,X3) ) ).
cnf(i_0_5127,axiom,
( X1 != X2
| cOMBS_int_bool_bool(X3,X1) = cOMBS_int_bool_bool(X3,X2) ) ).
cnf(i_0_5128,axiom,
( X1 != X2
| image_275383677t_bool(X1,X3) = image_275383677t_bool(X2,X3) ) ).
cnf(i_0_5129,axiom,
( X1 != X2
| image_275383677t_bool(X3,X1) = image_275383677t_bool(X3,X2) ) ).
cnf(i_0_5130,axiom,
( X1 != X2
| image_637364955e_bool(X1,X3) = image_637364955e_bool(X2,X3) ) ).
cnf(i_0_5131,axiom,
( X1 != X2
| image_637364955e_bool(X3,X1) = image_637364955e_bool(X3,X2) ) ).
cnf(i_0_5132,axiom,
( X1 != X2
| image_int_fun_a_bool(X1,X3) = image_int_fun_a_bool(X2,X3) ) ).
cnf(i_0_5133,axiom,
( X1 != X2
| image_int_fun_a_bool(X3,X1) = image_int_fun_a_bool(X3,X2) ) ).
cnf(i_0_5134,axiom,
( X1 != X2
| hAPP_int_fun_a_bool(X1,X3) = hAPP_int_fun_a_bool(X2,X3) ) ).
cnf(i_0_5135,axiom,
( X1 != X2
| hAPP_int_fun_a_bool(X3,X1) = hAPP_int_fun_a_bool(X3,X2) ) ).
cnf(i_0_5136,axiom,
( X1 != X2
| image_int_a(X1,X3) = image_int_a(X2,X3) ) ).
cnf(i_0_5137,axiom,
( X1 != X2
| image_int_a(X3,X1) = image_int_a(X3,X2) ) ).
cnf(i_0_5138,axiom,
( X1 != X2
| hAPP_f957591787ol_nat(X1,X3) = hAPP_f957591787ol_nat(X2,X3) ) ).
cnf(i_0_5139,axiom,
( X1 != X2
| hAPP_f957591787ol_nat(X3,X1) = hAPP_f957591787ol_nat(X3,X2) ) ).
cnf(i_0_5140,axiom,
( X1 != X2
| number_number_of_nat(X1) = number_number_of_nat(X2) ) ).
cnf(i_0_5141,axiom,
( X1 != X2
| hAPP_fun_a_bool_nat(X1,X3) = hAPP_fun_a_bool_nat(X2,X3) ) ).
cnf(i_0_5142,axiom,
( X1 != X2
| hAPP_fun_a_bool_nat(X3,X1) = hAPP_fun_a_bool_nat(X3,X2) ) ).
cnf(i_0_5143,axiom,
( X1 != X2
| hAPP_f921600141ol_nat(X1,X3) = hAPP_f921600141ol_nat(X2,X3) ) ).
cnf(i_0_5144,axiom,
( X1 != X2
| hAPP_f921600141ol_nat(X3,X1) = hAPP_f921600141ol_nat(X3,X2) ) ).
cnf(i_0_5145,axiom,
( X1 != X2
| hAPP_f1664156314l_bool(X1,X3) = hAPP_f1664156314l_bool(X2,X3) ) ).
cnf(i_0_5146,axiom,
( X1 != X2
| hAPP_f1664156314l_bool(X3,X1) = hAPP_f1664156314l_bool(X3,X2) ) ).
cnf(i_0_5147,axiom,
( X1 != X2
| esk161_2(X1,X3) = esk161_2(X2,X3) ) ).
cnf(i_0_5148,axiom,
( X1 != X2
| esk161_2(X3,X1) = esk161_2(X3,X2) ) ).
cnf(i_0_5149,axiom,
( X1 != X2
| esk152_2(X1,X3) = esk152_2(X2,X3) ) ).
cnf(i_0_5150,axiom,
( X1 != X2
| esk152_2(X3,X1) = esk152_2(X3,X2) ) ).
cnf(i_0_5151,axiom,
( X1 != X2
| esk158_2(X1,X3) = esk158_2(X2,X3) ) ).
cnf(i_0_5152,axiom,
( X1 != X2
| esk158_2(X3,X1) = esk158_2(X3,X2) ) ).
cnf(i_0_5153,axiom,
( X1 != X2
| hAPP_n1699378549t_bool(X1,X3) = hAPP_n1699378549t_bool(X2,X3) ) ).
cnf(i_0_5154,axiom,
( X1 != X2
| hAPP_n1699378549t_bool(X3,X1) = hAPP_n1699378549t_bool(X3,X2) ) ).
cnf(i_0_5155,axiom,
( X1 != X2
| hAPP_f1297739591_pname(X1,X3) = hAPP_f1297739591_pname(X2,X3) ) ).
cnf(i_0_5156,axiom,
( X1 != X2
| hAPP_f1297739591_pname(X3,X1) = hAPP_f1297739591_pname(X3,X2) ) ).
cnf(i_0_5157,axiom,
( X1 != X2
| esk155_2(X1,X3) = esk155_2(X2,X3) ) ).
cnf(i_0_5158,axiom,
( X1 != X2
| esk155_2(X3,X1) = esk155_2(X3,X2) ) ).
cnf(i_0_5159,axiom,
( X1 != X2
| hAPP_a_bool(X1,X3) = hAPP_a_bool(X2,X3) ) ).
cnf(i_0_5160,axiom,
( X1 != X2
| hAPP_a_bool(X3,X1) = hAPP_a_bool(X3,X2) ) ).
cnf(i_0_5161,axiom,
( X1 != X2
| hAPP_pname_pname(X1,X3) = hAPP_pname_pname(X2,X3) ) ).
cnf(i_0_5162,axiom,
( X1 != X2
| hAPP_pname_pname(X3,X1) = hAPP_pname_pname(X3,X2) ) ).
cnf(i_0_5163,axiom,
( X1 != X2
| image_1921560913_pname(X1,X3) = image_1921560913_pname(X2,X3) ) ).
cnf(i_0_5164,axiom,
( X1 != X2
| image_1921560913_pname(X3,X1) = image_1921560913_pname(X3,X2) ) ).
cnf(i_0_5165,axiom,
( X1 != X2
| image_fun_nat_bool_a(X1,X3) = image_fun_nat_bool_a(X2,X3) ) ).
cnf(i_0_5166,axiom,
( X1 != X2
| image_fun_nat_bool_a(X3,X1) = image_fun_nat_bool_a(X3,X2) ) ).
cnf(i_0_5167,axiom,
( X1 != X2
| image_62782965_pname(X1,X3) = image_62782965_pname(X2,X3) ) ).
cnf(i_0_5168,axiom,
( X1 != X2
| image_62782965_pname(X3,X1) = image_62782965_pname(X3,X2) ) ).
cnf(i_0_5169,axiom,
( X1 != X2
| image_fun_int_bool_a(X1,X3) = image_fun_int_bool_a(X2,X3) ) ).
cnf(i_0_5170,axiom,
( X1 != X2
| image_fun_int_bool_a(X3,X1) = image_fun_int_bool_a(X3,X2) ) ).
cnf(i_0_5171,axiom,
( X1 != X2
| image_1283814551_pname(X1,X3) = image_1283814551_pname(X2,X3) ) ).
cnf(i_0_5172,axiom,
( X1 != X2
| image_1283814551_pname(X3,X1) = image_1283814551_pname(X3,X2) ) ).
cnf(i_0_5173,axiom,
( X1 != X2
| image_876012084bool_a(X1,X3) = image_876012084bool_a(X2,X3) ) ).
cnf(i_0_5174,axiom,
( X1 != X2
| image_876012084bool_a(X3,X1) = image_876012084bool_a(X3,X2) ) ).
cnf(i_0_5175,axiom,
( X1 != X2
| image_1854862208_pname(X1,X3) = image_1854862208_pname(X2,X3) ) ).
cnf(i_0_5176,axiom,
( X1 != X2
| image_1854862208_pname(X3,X1) = image_1854862208_pname(X3,X2) ) ).
cnf(i_0_5177,axiom,
( X1 != X2
| image_fun_a_bool_a(X1,X3) = image_fun_a_bool_a(X2,X3) ) ).
cnf(i_0_5178,axiom,
( X1 != X2
| image_fun_a_bool_a(X3,X1) = image_fun_a_bool_a(X3,X2) ) ).
cnf(i_0_5179,axiom,
( X1 != X2
| image_nat_pname(X1,X3) = image_nat_pname(X2,X3) ) ).
cnf(i_0_5180,axiom,
( X1 != X2
| image_nat_pname(X3,X1) = image_nat_pname(X3,X2) ) ).
cnf(i_0_5181,axiom,
( X1 != X2
| image_nat_a(X1,X3) = image_nat_a(X2,X3) ) ).
cnf(i_0_5182,axiom,
( X1 != X2
| image_nat_a(X3,X1) = image_nat_a(X3,X2) ) ).
cnf(i_0_5183,axiom,
( X1 != X2
| image_int_pname(X1,X3) = image_int_pname(X2,X3) ) ).
cnf(i_0_5184,axiom,
( X1 != X2
| image_int_pname(X3,X1) = image_int_pname(X3,X2) ) ).
cnf(i_0_5185,axiom,
( X1 != X2
| hAPP_f759274231e_bool(X1,X3) = hAPP_f759274231e_bool(X2,X3) ) ).
cnf(i_0_5186,axiom,
( X1 != X2
| hAPP_f759274231e_bool(X3,X1) = hAPP_f759274231e_bool(X3,X2) ) ).
cnf(i_0_5187,axiom,
( X1 != X2
| image_pname_pname(X1,X3) = image_pname_pname(X2,X3) ) ).
cnf(i_0_5188,axiom,
( X1 != X2
| image_pname_pname(X3,X1) = image_pname_pname(X3,X2) ) ).
cnf(i_0_5189,axiom,
( X1 != X2
| image_112932426a_bool(X1,X3) = image_112932426a_bool(X2,X3) ) ).
cnf(i_0_5190,axiom,
( X1 != X2
| image_112932426a_bool(X3,X1) = image_112932426a_bool(X3,X2) ) ).
cnf(i_0_5191,axiom,
( X1 != X2
| image_47868345e_bool(X1,X3) = image_47868345e_bool(X2,X3) ) ).
cnf(i_0_5192,axiom,
( X1 != X2
| image_47868345e_bool(X3,X1) = image_47868345e_bool(X3,X2) ) ).
cnf(i_0_5193,axiom,
( X1 != X2
| image_a_pname(X1,X3) = image_a_pname(X2,X3) ) ).
cnf(i_0_5194,axiom,
( X1 != X2
| image_a_pname(X3,X1) = image_a_pname(X3,X2) ) ).
cnf(i_0_5195,axiom,
( X1 != X2
| image_a_fun_a_bool(X1,X3) = image_a_fun_a_bool(X2,X3) ) ).
cnf(i_0_5196,axiom,
( X1 != X2
| image_a_fun_a_bool(X3,X1) = image_a_fun_a_bool(X3,X2) ) ).
cnf(i_0_5197,axiom,
( X1 != X2
| image_819518260e_bool(X1,X3) = image_819518260e_bool(X2,X3) ) ).
cnf(i_0_5198,axiom,
( X1 != X2
| image_819518260e_bool(X3,X1) = image_819518260e_bool(X3,X2) ) ).
cnf(i_0_5199,axiom,
( X1 != X2
| image_a_a(X1,X3) = image_a_a(X2,X3) ) ).
cnf(i_0_5200,axiom,
( X1 != X2
| image_a_a(X3,X1) = image_a_a(X3,X2) ) ).
cnf(i_0_5201,axiom,
( X1 != X2
| image_1133522419ol_int(X1,X3) = image_1133522419ol_int(X2,X3) ) ).
cnf(i_0_5202,axiom,
( X1 != X2
| image_1133522419ol_int(X3,X1) = image_1133522419ol_int(X3,X2) ) ).
cnf(i_0_5203,axiom,
( X1 != X2
| image_496248727ol_nat(X1,X3) = image_496248727ol_nat(X2,X3) ) ).
cnf(i_0_5204,axiom,
( X1 != X2
| image_496248727ol_nat(X3,X1) = image_496248727ol_nat(X3,X2) ) ).
cnf(i_0_5205,axiom,
( X1 != X2
| image_2069007511ol_int(X1,X3) = image_2069007511ol_int(X2,X3) ) ).
cnf(i_0_5206,axiom,
( X1 != X2
| image_2069007511ol_int(X3,X1) = image_2069007511ol_int(X3,X2) ) ).
cnf(i_0_5207,axiom,
( X1 != X2
| image_1431733819ol_nat(X1,X3) = image_1431733819ol_nat(X2,X3) ) ).
cnf(i_0_5208,axiom,
( X1 != X2
| image_1431733819ol_nat(X3,X1) = image_1431733819ol_nat(X3,X2) ) ).
cnf(i_0_5209,axiom,
( X1 != X2
| image_41399353ol_int(X1,X3) = image_41399353ol_int(X2,X3) ) ).
cnf(i_0_5210,axiom,
( X1 != X2
| image_41399353ol_int(X3,X1) = image_41399353ol_int(X3,X2) ) ).
cnf(i_0_5211,axiom,
( X1 != X2
| image_1551609309ol_nat(X1,X3) = image_1551609309ol_nat(X2,X3) ) ).
cnf(i_0_5212,axiom,
( X1 != X2
| image_1551609309ol_nat(X3,X1) = image_1551609309ol_nat(X3,X2) ) ).
cnf(i_0_5213,axiom,
( X1 != X2
| hAPP_fun_a_bool_bool(X1,X3) = hAPP_fun_a_bool_bool(X2,X3) ) ).
cnf(i_0_5214,axiom,
( X1 != X2
| hAPP_fun_a_bool_bool(X3,X1) = hAPP_fun_a_bool_bool(X3,X2) ) ).
cnf(i_0_5215,axiom,
( X1 != X2
| image_fun_a_bool_int(X1,X3) = image_fun_a_bool_int(X2,X3) ) ).
cnf(i_0_5216,axiom,
( X1 != X2
| image_fun_a_bool_int(X3,X1) = image_fun_a_bool_int(X3,X2) ) ).
cnf(i_0_5217,axiom,
( X1 != X2
| image_fun_a_bool_nat(X1,X3) = image_fun_a_bool_nat(X2,X3) ) ).
cnf(i_0_5218,axiom,
( X1 != X2
| image_fun_a_bool_nat(X3,X1) = image_fun_a_bool_nat(X3,X2) ) ).
cnf(i_0_5219,axiom,
( X1 != X2
| image_2129980159t_bool(X1,X3) = image_2129980159t_bool(X2,X3) ) ).
cnf(i_0_5220,axiom,
( X1 != X2
| image_2129980159t_bool(X3,X1) = image_2129980159t_bool(X3,X2) ) ).
cnf(i_0_5221,axiom,
( X1 != X2
| image_1512837979t_bool(X1,X3) = image_1512837979t_bool(X2,X3) ) ).
cnf(i_0_5222,axiom,
( X1 != X2
| image_1512837979t_bool(X3,X1) = image_1512837979t_bool(X3,X2) ) ).
cnf(i_0_5223,axiom,
( X1 != X2
| image_pname_int(X1,X3) = image_pname_int(X2,X3) ) ).
cnf(i_0_5224,axiom,
( X1 != X2
| image_pname_int(X3,X1) = image_pname_int(X3,X2) ) ).
cnf(i_0_5225,axiom,
( X1 != X2
| image_pname_nat(X1,X3) = image_pname_nat(X2,X3) ) ).
cnf(i_0_5226,axiom,
( X1 != X2
| image_pname_nat(X3,X1) = image_pname_nat(X3,X2) ) ).
cnf(i_0_5227,axiom,
( X1 != X2
| image_a_int(X1,X3) = image_a_int(X2,X3) ) ).
cnf(i_0_5228,axiom,
( X1 != X2
| image_a_int(X3,X1) = image_a_int(X3,X2) ) ).
cnf(i_0_5229,axiom,
( X1 != X2
| image_a_nat(X1,X3) = image_a_nat(X2,X3) ) ).
cnf(i_0_5230,axiom,
( X1 != X2
| image_a_nat(X3,X1) = image_a_nat(X3,X2) ) ).
cnf(i_0_5231,axiom,
( X1 != X2
| hAPP_fun_a_bool_a(X1,X3) = hAPP_fun_a_bool_a(X2,X3) ) ).
cnf(i_0_5232,axiom,
( X1 != X2
| hAPP_fun_a_bool_a(X3,X1) = hAPP_fun_a_bool_a(X3,X2) ) ).
cnf(i_0_5233,axiom,
( X1 != X2
| image_a_fun_nat_bool(X1,X3) = image_a_fun_nat_bool(X2,X3) ) ).
cnf(i_0_5234,axiom,
( X1 != X2
| image_a_fun_nat_bool(X3,X1) = image_a_fun_nat_bool(X3,X2) ) ).
cnf(i_0_5235,axiom,
( X1 != X2
| image_a_fun_int_bool(X1,X3) = image_a_fun_int_bool(X2,X3) ) ).
cnf(i_0_5236,axiom,
( X1 != X2
| image_a_fun_int_bool(X3,X1) = image_a_fun_int_bool(X3,X2) ) ).
cnf(i_0_5237,axiom,
( X1 != X2
| hAPP_a_a(X1,X3) = hAPP_a_a(X2,X3) ) ).
cnf(i_0_5238,axiom,
( X1 != X2
| hAPP_a_a(X3,X1) = hAPP_a_a(X3,X2) ) ).
cnf(i_0_5239,axiom,
( X1 != X2
| collect_a(X1) = collect_a(X2) ) ).
cnf(i_0_5240,axiom,
( X1 != X2
| hAPP_f2009550088ol_nat(X1,X3) = hAPP_f2009550088ol_nat(X2,X3) ) ).
cnf(i_0_5241,axiom,
( X1 != X2
| hAPP_f2009550088ol_nat(X3,X1) = hAPP_f2009550088ol_nat(X3,X2) ) ).
cnf(i_0_5242,axiom,
( X1 != X2
| hAPP_f55526627ol_nat(X1,X3) = hAPP_f55526627ol_nat(X2,X3) ) ).
cnf(i_0_5243,axiom,
( X1 != X2
| hAPP_f55526627ol_nat(X3,X1) = hAPP_f55526627ol_nat(X3,X2) ) ).
cnf(i_0_5244,axiom,
( X1 != X2
| hAPP_f696928925ol_nat(X1,X3) = hAPP_f696928925ol_nat(X2,X3) ) ).
cnf(i_0_5245,axiom,
( X1 != X2
| hAPP_f696928925ol_nat(X3,X1) = hAPP_f696928925ol_nat(X3,X2) ) ).
cnf(i_0_5246,axiom,
( X1 != X2
| hAPP_f521865025ol_nat(X1,X3) = hAPP_f521865025ol_nat(X2,X3) ) ).
cnf(i_0_5247,axiom,
( X1 != X2
| hAPP_f521865025ol_nat(X3,X1) = hAPP_f521865025ol_nat(X3,X2) ) ).
cnf(i_0_5248,axiom,
( X1 != X2
| hAPP_a_fun_a_bool(X1,X3) = hAPP_a_fun_a_bool(X2,X3) ) ).
cnf(i_0_5249,axiom,
( X1 != X2
| hAPP_a_fun_a_bool(X3,X1) = hAPP_a_fun_a_bool(X3,X2) ) ).
cnf(i_0_5250,axiom,
( X1 != X2
| hAPP_f2050579477a_bool(X1,X3) = hAPP_f2050579477a_bool(X2,X3) ) ).
cnf(i_0_5251,axiom,
( X1 != X2
| hAPP_f2050579477a_bool(X3,X1) = hAPP_f2050579477a_bool(X3,X2) ) ).
cnf(i_0_5252,axiom,
( X1 != X2
| hAPP_f54304608l_bool(X1,X3) = hAPP_f54304608l_bool(X2,X3) ) ).
cnf(i_0_5253,axiom,
( X1 != X2
| hAPP_f54304608l_bool(X3,X1) = hAPP_f54304608l_bool(X3,X2) ) ).
cnf(i_0_5254,axiom,
( X1 != X2
| hAPP_n215258509l_bool(X1,X3) = hAPP_n215258509l_bool(X2,X3) ) ).
cnf(i_0_5255,axiom,
( X1 != X2
| hAPP_n215258509l_bool(X3,X1) = hAPP_n215258509l_bool(X3,X2) ) ).
cnf(i_0_5256,axiom,
( X1 != X2
| hAPP_int_bool(X1,X3) = hAPP_int_bool(X2,X3) ) ).
cnf(i_0_5257,axiom,
( X1 != X2
| hAPP_int_bool(X3,X1) = hAPP_int_bool(X3,X2) ) ).
cnf(i_0_5258,axiom,
( X1 != X2
| hAPP_f22106695ol_nat(X1,X3) = hAPP_f22106695ol_nat(X2,X3) ) ).
cnf(i_0_5259,axiom,
( X1 != X2
| hAPP_f22106695ol_nat(X3,X1) = hAPP_f22106695ol_nat(X3,X2) ) ).
cnf(i_0_5260,axiom,
( X1 != X2
| hAPP_pname_bool(X1,X3) = hAPP_pname_bool(X2,X3) ) ).
cnf(i_0_5261,axiom,
( X1 != X2
| hAPP_pname_bool(X3,X1) = hAPP_pname_bool(X3,X2) ) ).
cnf(i_0_5262,axiom,
( X1 != X2
| hAPP_f800510211t_bool(X1,X3) = hAPP_f800510211t_bool(X2,X3) ) ).
cnf(i_0_5263,axiom,
( X1 != X2
| hAPP_f800510211t_bool(X3,X1) = hAPP_f800510211t_bool(X3,X2) ) ).
cnf(i_0_5264,axiom,
( X1 != X2
| hAPP_f1748468828l_bool(X1,X3) = hAPP_f1748468828l_bool(X2,X3) ) ).
cnf(i_0_5265,axiom,
( X1 != X2
| hAPP_f1748468828l_bool(X3,X1) = hAPP_f1748468828l_bool(X3,X2) ) ).
cnf(i_0_5266,axiom,
( X1 != X2
| hAPP_f1721100032l_bool(X1,X3) = hAPP_f1721100032l_bool(X2,X3) ) ).
cnf(i_0_5267,axiom,
( X1 != X2
| hAPP_f1721100032l_bool(X3,X1) = hAPP_f1721100032l_bool(X3,X2) ) ).
cnf(i_0_5268,axiom,
( X1 != X2
| hAPP_f1476298914l_bool(X1,X3) = hAPP_f1476298914l_bool(X2,X3) ) ).
cnf(i_0_5269,axiom,
( X1 != X2
| hAPP_f1476298914l_bool(X3,X1) = hAPP_f1476298914l_bool(X3,X2) ) ).
cnf(i_0_5270,axiom,
( X1 != X2
| hAPP_f198738859l_bool(X1,X3) = hAPP_f198738859l_bool(X2,X3) ) ).
cnf(i_0_5271,axiom,
( X1 != X2
| hAPP_f198738859l_bool(X3,X1) = hAPP_f198738859l_bool(X3,X2) ) ).
cnf(i_0_5272,axiom,
( X1 != X2
| hAPP_n1006566506l_bool(X1,X3) = hAPP_n1006566506l_bool(X2,X3) ) ).
cnf(i_0_5273,axiom,
( X1 != X2
| hAPP_n1006566506l_bool(X3,X1) = hAPP_n1006566506l_bool(X3,X2) ) ).
cnf(i_0_5274,axiom,
( X1 != X2
| hAPP_i68813070l_bool(X1,X3) = hAPP_i68813070l_bool(X2,X3) ) ).
cnf(i_0_5275,axiom,
( X1 != X2
| hAPP_i68813070l_bool(X3,X1) = hAPP_i68813070l_bool(X3,X2) ) ).
cnf(i_0_5276,axiom,
( X1 != X2
| hAPP_p393069232l_bool(X1,X3) = hAPP_p393069232l_bool(X2,X3) ) ).
cnf(i_0_5277,axiom,
( X1 != X2
| hAPP_p393069232l_bool(X3,X1) = hAPP_p393069232l_bool(X3,X2) ) ).
cnf(i_0_5278,axiom,
( X1 != X2
| hAPP_a_fun_bool_bool(X1,X3) = hAPP_a_fun_bool_bool(X2,X3) ) ).
cnf(i_0_5279,axiom,
( X1 != X2
| hAPP_a_fun_bool_bool(X3,X1) = hAPP_a_fun_bool_bool(X3,X2) ) ).
cnf(i_0_5280,axiom,
( X1 != X2
| hAPP_f448129468l_bool(X1,X3) = hAPP_f448129468l_bool(X2,X3) ) ).
cnf(i_0_5281,axiom,
( X1 != X2
| hAPP_f448129468l_bool(X3,X1) = hAPP_f448129468l_bool(X3,X2) ) ).
cnf(i_0_5282,axiom,
( X1 != X2
| hAPP_n1414589940l_bool(X1,X3) = hAPP_n1414589940l_bool(X2,X3) ) ).
cnf(i_0_5283,axiom,
( X1 != X2
| hAPP_n1414589940l_bool(X3,X1) = hAPP_n1414589940l_bool(X3,X2) ) ).
cnf(i_0_5284,axiom,
( X1 != X2
| hAPP_n850744903l_bool(X1,X3) = hAPP_n850744903l_bool(X2,X3) ) ).
cnf(i_0_5285,axiom,
( X1 != X2
| hAPP_n850744903l_bool(X3,X1) = hAPP_n850744903l_bool(X3,X2) ) ).
cnf(i_0_5286,axiom,
( X1 != X2
| hAPP_n609083369l_bool(X1,X3) = hAPP_n609083369l_bool(X2,X3) ) ).
cnf(i_0_5287,axiom,
( X1 != X2
| hAPP_n609083369l_bool(X3,X1) = hAPP_n609083369l_bool(X3,X2) ) ).
cnf(i_0_5288,axiom,
( X1 != X2
| hAPP_i888906320l_bool(X1,X3) = hAPP_i888906320l_bool(X2,X3) ) ).
cnf(i_0_5289,axiom,
( X1 != X2
| hAPP_i888906320l_bool(X3,X1) = hAPP_i888906320l_bool(X3,X2) ) ).
cnf(i_0_5290,axiom,
( X1 != X2
| hAPP_i1587699435l_bool(X1,X3) = hAPP_i1587699435l_bool(X2,X3) ) ).
cnf(i_0_5291,axiom,
( X1 != X2
| hAPP_i1587699435l_bool(X3,X1) = hAPP_i1587699435l_bool(X3,X2) ) ).
cnf(i_0_5292,axiom,
( X1 != X2
| hAPP_i1718399025l_bool(X1,X3) = hAPP_i1718399025l_bool(X2,X3) ) ).
cnf(i_0_5293,axiom,
( X1 != X2
| hAPP_i1718399025l_bool(X3,X1) = hAPP_i1718399025l_bool(X3,X2) ) ).
cnf(i_0_5294,axiom,
( X1 != X2
| hAPP_p1534023578a_bool(X1,X3) = hAPP_p1534023578a_bool(X2,X3) ) ).
cnf(i_0_5295,axiom,
( X1 != X2
| hAPP_p1534023578a_bool(X3,X1) = hAPP_p1534023578a_bool(X3,X2) ) ).
cnf(i_0_5296,axiom,
( X1 != X2
| hAPP_i2112223885l_bool(X1,X3) = hAPP_i2112223885l_bool(X2,X3) ) ).
cnf(i_0_5297,axiom,
( X1 != X2
| hAPP_i2112223885l_bool(X3,X1) = hAPP_i2112223885l_bool(X3,X2) ) ).
cnf(i_0_5298,axiom,
( X1 != X2
| cOMBK_bool_nat(X1) = cOMBK_bool_nat(X2) ) ).
cnf(i_0_5299,axiom,
( X1 != X2
| cOMBK_bool_int(X1) = cOMBK_bool_int(X2) ) ).
cnf(i_0_5300,axiom,
( X1 != X2
| hAPP_f1594865479ol_int(X1,X3) = hAPP_f1594865479ol_int(X2,X3) ) ).
cnf(i_0_5301,axiom,
( X1 != X2
| hAPP_f1594865479ol_int(X3,X1) = hAPP_f1594865479ol_int(X3,X2) ) ).
cnf(i_0_5302,axiom,
( X1 != X2
| hAPP_i1948725293t_bool(X1,X3) = hAPP_i1948725293t_bool(X2,X3) ) ).
cnf(i_0_5303,axiom,
( X1 != X2
| hAPP_i1948725293t_bool(X3,X1) = hAPP_i1948725293t_bool(X3,X2) ) ).
cnf(i_0_5304,axiom,
( X1 != X2
| hAPP_f1805168059t_bool(X1,X3) = hAPP_f1805168059t_bool(X2,X3) ) ).
cnf(i_0_5305,axiom,
( X1 != X2
| hAPP_f1805168059t_bool(X3,X1) = hAPP_f1805168059t_bool(X3,X2) ) ).
cnf(i_0_5306,axiom,
( X1 != X2
| hAPP_nat_int(X1,X3) = hAPP_nat_int(X2,X3) ) ).
cnf(i_0_5307,axiom,
( X1 != X2
| hAPP_nat_int(X3,X1) = hAPP_nat_int(X3,X2) ) ).
cnf(i_0_5308,axiom,
( X1 != X2
| collect_pname(X1) = collect_pname(X2) ) ).
cnf(i_0_5309,axiom,
( X1 != X2
| hAPP_pname_a(X1,X3) = hAPP_pname_a(X2,X3) ) ).
cnf(i_0_5310,axiom,
( X1 != X2
| hAPP_pname_a(X3,X1) = hAPP_pname_a(X3,X2) ) ).
cnf(i_0_5311,axiom,
( X1 != X2
| abs_abs_int(X1) = abs_abs_int(X2) ) ).
cnf(i_0_5312,axiom,
( X1 != X2
| image_pname_a(X1,X3) = image_pname_a(X2,X3) ) ).
cnf(i_0_5313,axiom,
( X1 != X2
| image_pname_a(X3,X1) = image_pname_a(X3,X2) ) ).
cnf(i_0_5314,axiom,
( X1 != X2
| hAPP_f103356543l_bool(X1,X3) = hAPP_f103356543l_bool(X2,X3) ) ).
cnf(i_0_5315,axiom,
( X1 != X2
| hAPP_f103356543l_bool(X3,X1) = hAPP_f103356543l_bool(X3,X2) ) ).
cnf(i_0_5316,axiom,
( X1 != X2
| hAPP_f284875647l_bool(X1,X3) = hAPP_f284875647l_bool(X2,X3) ) ).
cnf(i_0_5317,axiom,
( X1 != X2
| hAPP_f284875647l_bool(X3,X1) = hAPP_f284875647l_bool(X3,X2) ) ).
cnf(i_0_5318,axiom,
( X1 != X2
| hAPP_n1082236369t_bool(X1,X3) = hAPP_n1082236369t_bool(X2,X3) ) ).
cnf(i_0_5319,axiom,
( X1 != X2
| hAPP_n1082236369t_bool(X3,X1) = hAPP_n1082236369t_bool(X3,X2) ) ).
cnf(i_0_5320,axiom,
( X1 != X2
| hAPP_f434788991l_bool(X1,X3) = hAPP_f434788991l_bool(X2,X3) ) ).
cnf(i_0_5321,axiom,
( X1 != X2
| hAPP_f434788991l_bool(X3,X1) = hAPP_f434788991l_bool(X3,X2) ) ).
cnf(i_0_5322,axiom,
( X1 != X2
| hAPP_int_int(X1,X3) = hAPP_int_int(X2,X3) ) ).
cnf(i_0_5323,axiom,
( X1 != X2
| hAPP_int_int(X3,X1) = hAPP_int_int(X3,X2) ) ).
cnf(i_0_5324,axiom,
( X1 != X2
| hAPP_f1631501043l_bool(X1,X3) = hAPP_f1631501043l_bool(X2,X3) ) ).
cnf(i_0_5325,axiom,
( X1 != X2
| hAPP_f1631501043l_bool(X3,X1) = hAPP_f1631501043l_bool(X3,X2) ) ).
cnf(i_0_5326,axiom,
( X1 != X2
| hAPP_bool_bool(X1,X3) = hAPP_bool_bool(X2,X3) ) ).
cnf(i_0_5327,axiom,
( X1 != X2
| hAPP_bool_bool(X3,X1) = hAPP_bool_bool(X3,X2) ) ).
cnf(i_0_5328,axiom,
( X1 != X2
| hAPP_b589554111l_bool(X1,X3) = hAPP_b589554111l_bool(X2,X3) ) ).
cnf(i_0_5329,axiom,
( X1 != X2
| hAPP_b589554111l_bool(X3,X1) = hAPP_b589554111l_bool(X3,X2) ) ).
cnf(i_0_5330,axiom,
( X1 != X2
| hAPP_f1637334154l_bool(X1,X3) = hAPP_f1637334154l_bool(X2,X3) ) ).
cnf(i_0_5331,axiom,
( X1 != X2
| hAPP_f1637334154l_bool(X3,X1) = hAPP_f1637334154l_bool(X3,X2) ) ).
cnf(i_0_5332,axiom,
( X1 != X2
| image_26036933t_bool(X1,X3) = image_26036933t_bool(X2,X3) ) ).
cnf(i_0_5333,axiom,
( X1 != X2
| image_26036933t_bool(X3,X1) = image_26036933t_bool(X3,X2) ) ).
cnf(i_0_5334,axiom,
( X1 != X2
| cOMBS_nat_bool_bool(X1,X3) = cOMBS_nat_bool_bool(X2,X3) ) ).
cnf(i_0_5335,axiom,
( X1 != X2
| cOMBS_nat_bool_bool(X3,X1) = cOMBS_nat_bool_bool(X3,X2) ) ).
cnf(i_0_5336,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_5337,axiom,
( X1 != X2
| ~ is_fun_pname_bool(X1)
| is_fun_pname_bool(X2) ) ).
cnf(i_0_5338,axiom,
( X1 != X2
| ~ is_fun_a_bool(X1)
| is_fun_a_bool(X2) ) ).
cnf(i_0_5339,axiom,
( X1 != X2
| ~ is_pname(X1)
| is_pname(X2) ) ).
cnf(i_0_5340,axiom,
( X1 != X2
| ~ is_a(X1)
| is_a(X2) ) ).
cnf(i_0_5341,axiom,
( X1 != X2
| ~ is_fun949378684l_bool(X1)
| is_fun949378684l_bool(X2) ) ).
cnf(i_0_5342,axiom,
( X1 != X2
| ~ is_fun1661590463l_bool(X1)
| is_fun1661590463l_bool(X2) ) ).
cnf(i_0_5343,axiom,
( X1 != X2
| ~ is_bool(X1)
| is_bool(X2) ) ).
cnf(i_0_5103_001,axiom,
X1 = X1 ).
cnf(i_0_5104_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_5105_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_5106_004,axiom,
( X1 != X2
| hAPP_nat_bool(X1,X3) = hAPP_nat_bool(X2,X3) ) ).
cnf(i_0_5107_005,axiom,
( X1 != X2
| hAPP_nat_bool(X3,X1) = hAPP_nat_bool(X3,X2) ) ).
cnf(i_0_5108_006,axiom,
( X1 != X2
| hAPP_nat_nat(X1,X3) = hAPP_nat_nat(X2,X3) ) ).
cnf(i_0_5109_007,axiom,
( X1 != X2
| hAPP_nat_nat(X3,X1) = hAPP_nat_nat(X3,X2) ) ).
cnf(i_0_5110_008,axiom,
( X1 != X2
| hAPP_f215623910l_bool(X1,X3) = hAPP_f215623910l_bool(X2,X3) ) ).
cnf(i_0_5111_009,axiom,
( X1 != X2
| hAPP_f215623910l_bool(X3,X1) = hAPP_f215623910l_bool(X3,X2) ) ).
cnf(i_0_5112_010,axiom,
( X1 != X2
| image_1556378401t_bool(X1,X3) = image_1556378401t_bool(X2,X3) ) ).
cnf(i_0_5113_011,axiom,
( X1 != X2
| image_1556378401t_bool(X3,X1) = image_1556378401t_bool(X3,X2) ) ).
cnf(i_0_5114_012,axiom,
( X1 != X2
| hAPP_f1935102916l_bool(X1,X3) = hAPP_f1935102916l_bool(X2,X3) ) ).
cnf(i_0_5115_013,axiom,
( X1 != X2
| hAPP_f1935102916l_bool(X3,X1) = hAPP_f1935102916l_bool(X3,X2) ) ).
cnf(i_0_5116_014,axiom,
( X1 != X2
| image_1655916159e_bool(X1,X3) = image_1655916159e_bool(X2,X3) ) ).
cnf(i_0_5117_015,axiom,
( X1 != X2
| image_1655916159e_bool(X3,X1) = image_1655916159e_bool(X3,X2) ) ).
cnf(i_0_5118_016,axiom,
( X1 != X2
| hAPP_f621171935l_bool(X1,X3) = hAPP_f621171935l_bool(X2,X3) ) ).
cnf(i_0_5119_017,axiom,
( X1 != X2
| hAPP_f621171935l_bool(X3,X1) = hAPP_f621171935l_bool(X3,X2) ) ).
cnf(i_0_5120_018,axiom,
( X1 != X2
| image_nat_fun_a_bool(X1,X3) = image_nat_fun_a_bool(X2,X3) ) ).
cnf(i_0_5121_019,axiom,
( X1 != X2
| image_nat_fun_a_bool(X3,X1) = image_nat_fun_a_bool(X3,X2) ) ).
cnf(i_0_5122_020,axiom,
( X1 != X2
| image_nat_int(X1,X3) = image_nat_int(X2,X3) ) ).
cnf(i_0_5123_021,axiom,
( X1 != X2
| image_nat_int(X3,X1) = image_nat_int(X3,X2) ) ).
cnf(i_0_5124_022,axiom,
( X1 != X2
| image_892525857t_bool(X1,X3) = image_892525857t_bool(X2,X3) ) ).
cnf(i_0_5125_023,axiom,
( X1 != X2
| image_892525857t_bool(X3,X1) = image_892525857t_bool(X3,X2) ) ).
cnf(i_0_5126_024,axiom,
( X1 != X2
| cOMBS_int_bool_bool(X1,X3) = cOMBS_int_bool_bool(X2,X3) ) ).
cnf(i_0_5127_025,axiom,
( X1 != X2
| cOMBS_int_bool_bool(X3,X1) = cOMBS_int_bool_bool(X3,X2) ) ).
cnf(i_0_5128_026,axiom,
( X1 != X2
| image_275383677t_bool(X1,X3) = image_275383677t_bool(X2,X3) ) ).
cnf(i_0_5129_027,axiom,
( X1 != X2
| image_275383677t_bool(X3,X1) = image_275383677t_bool(X3,X2) ) ).
cnf(i_0_5130_028,axiom,
( X1 != X2
| image_637364955e_bool(X1,X3) = image_637364955e_bool(X2,X3) ) ).
cnf(i_0_5131_029,axiom,
( X1 != X2
| image_637364955e_bool(X3,X1) = image_637364955e_bool(X3,X2) ) ).
cnf(i_0_5132_030,axiom,
( X1 != X2
| image_int_fun_a_bool(X1,X3) = image_int_fun_a_bool(X2,X3) ) ).
cnf(i_0_5133_031,axiom,
( X1 != X2
| image_int_fun_a_bool(X3,X1) = image_int_fun_a_bool(X3,X2) ) ).
cnf(i_0_5134_032,axiom,
( X1 != X2
| hAPP_int_fun_a_bool(X1,X3) = hAPP_int_fun_a_bool(X2,X3) ) ).
cnf(i_0_5135_033,axiom,
( X1 != X2
| hAPP_int_fun_a_bool(X3,X1) = hAPP_int_fun_a_bool(X3,X2) ) ).
cnf(i_0_5136_034,axiom,
( X1 != X2
| image_int_a(X1,X3) = image_int_a(X2,X3) ) ).
cnf(i_0_5137_035,axiom,
( X1 != X2
| image_int_a(X3,X1) = image_int_a(X3,X2) ) ).
cnf(i_0_5138_036,axiom,
( X1 != X2
| hAPP_f957591787ol_nat(X1,X3) = hAPP_f957591787ol_nat(X2,X3) ) ).
cnf(i_0_5139_037,axiom,
( X1 != X2
| hAPP_f957591787ol_nat(X3,X1) = hAPP_f957591787ol_nat(X3,X2) ) ).
cnf(i_0_5140_038,axiom,
( X1 != X2
| number_number_of_nat(X1) = number_number_of_nat(X2) ) ).
cnf(i_0_5141_039,axiom,
( X1 != X2
| hAPP_fun_a_bool_nat(X1,X3) = hAPP_fun_a_bool_nat(X2,X3) ) ).
cnf(i_0_5142_040,axiom,
( X1 != X2
| hAPP_fun_a_bool_nat(X3,X1) = hAPP_fun_a_bool_nat(X3,X2) ) ).
cnf(i_0_5143_041,axiom,
( X1 != X2
| hAPP_f921600141ol_nat(X1,X3) = hAPP_f921600141ol_nat(X2,X3) ) ).
cnf(i_0_5144_042,axiom,
( X1 != X2
| hAPP_f921600141ol_nat(X3,X1) = hAPP_f921600141ol_nat(X3,X2) ) ).
cnf(i_0_5145_043,axiom,
( X1 != X2
| hAPP_f1664156314l_bool(X1,X3) = hAPP_f1664156314l_bool(X2,X3) ) ).
cnf(i_0_5146_044,axiom,
( X1 != X2
| hAPP_f1664156314l_bool(X3,X1) = hAPP_f1664156314l_bool(X3,X2) ) ).
cnf(i_0_5147_045,axiom,
( X1 != X2
| esk161_2(X1,X3) = esk161_2(X2,X3) ) ).
cnf(i_0_5148_046,axiom,
( X1 != X2
| esk161_2(X3,X1) = esk161_2(X3,X2) ) ).
cnf(i_0_5149_047,axiom,
( X1 != X2
| esk152_2(X1,X3) = esk152_2(X2,X3) ) ).
cnf(i_0_5150_048,axiom,
( X1 != X2
| esk152_2(X3,X1) = esk152_2(X3,X2) ) ).
cnf(i_0_5151_049,axiom,
( X1 != X2
| esk158_2(X1,X3) = esk158_2(X2,X3) ) ).
cnf(i_0_5152_050,axiom,
( X1 != X2
| esk158_2(X3,X1) = esk158_2(X3,X2) ) ).
cnf(i_0_5153_051,axiom,
( X1 != X2
| hAPP_n1699378549t_bool(X1,X3) = hAPP_n1699378549t_bool(X2,X3) ) ).
cnf(i_0_5154_052,axiom,
( X1 != X2
| hAPP_n1699378549t_bool(X3,X1) = hAPP_n1699378549t_bool(X3,X2) ) ).
cnf(i_0_5155_053,axiom,
( X1 != X2
| hAPP_f1297739591_pname(X1,X3) = hAPP_f1297739591_pname(X2,X3) ) ).
cnf(i_0_5156_054,axiom,
( X1 != X2
| hAPP_f1297739591_pname(X3,X1) = hAPP_f1297739591_pname(X3,X2) ) ).
cnf(i_0_5157_055,axiom,
( X1 != X2
| esk155_2(X1,X3) = esk155_2(X2,X3) ) ).
cnf(i_0_5158_056,axiom,
( X1 != X2
| esk155_2(X3,X1) = esk155_2(X3,X2) ) ).
cnf(i_0_5159_057,axiom,
( X1 != X2
| hAPP_a_bool(X1,X3) = hAPP_a_bool(X2,X3) ) ).
cnf(i_0_5160_058,axiom,
( X1 != X2
| hAPP_a_bool(X3,X1) = hAPP_a_bool(X3,X2) ) ).
cnf(i_0_5161_059,axiom,
( X1 != X2
| hAPP_pname_pname(X1,X3) = hAPP_pname_pname(X2,X3) ) ).
cnf(i_0_5162_060,axiom,
( X1 != X2
| hAPP_pname_pname(X3,X1) = hAPP_pname_pname(X3,X2) ) ).
cnf(i_0_5163_061,axiom,
( X1 != X2
| image_1921560913_pname(X1,X3) = image_1921560913_pname(X2,X3) ) ).
cnf(i_0_5164_062,axiom,
( X1 != X2
| image_1921560913_pname(X3,X1) = image_1921560913_pname(X3,X2) ) ).
cnf(i_0_5165_063,axiom,
( X1 != X2
| image_fun_nat_bool_a(X1,X3) = image_fun_nat_bool_a(X2,X3) ) ).
cnf(i_0_5166_064,axiom,
( X1 != X2
| image_fun_nat_bool_a(X3,X1) = image_fun_nat_bool_a(X3,X2) ) ).
cnf(i_0_5167_065,axiom,
( X1 != X2
| image_62782965_pname(X1,X3) = image_62782965_pname(X2,X3) ) ).
cnf(i_0_5168_066,axiom,
( X1 != X2
| image_62782965_pname(X3,X1) = image_62782965_pname(X3,X2) ) ).
cnf(i_0_5169_067,axiom,
( X1 != X2
| image_fun_int_bool_a(X1,X3) = image_fun_int_bool_a(X2,X3) ) ).
cnf(i_0_5170_068,axiom,
( X1 != X2
| image_fun_int_bool_a(X3,X1) = image_fun_int_bool_a(X3,X2) ) ).
cnf(i_0_5171_069,axiom,
( X1 != X2
| image_1283814551_pname(X1,X3) = image_1283814551_pname(X2,X3) ) ).
cnf(i_0_5172_070,axiom,
( X1 != X2
| image_1283814551_pname(X3,X1) = image_1283814551_pname(X3,X2) ) ).
cnf(i_0_5173_071,axiom,
( X1 != X2
| image_876012084bool_a(X1,X3) = image_876012084bool_a(X2,X3) ) ).
cnf(i_0_5174_072,axiom,
( X1 != X2
| image_876012084bool_a(X3,X1) = image_876012084bool_a(X3,X2) ) ).
cnf(i_0_5175_073,axiom,
( X1 != X2
| image_1854862208_pname(X1,X3) = image_1854862208_pname(X2,X3) ) ).
cnf(i_0_5176_074,axiom,
( X1 != X2
| image_1854862208_pname(X3,X1) = image_1854862208_pname(X3,X2) ) ).
cnf(i_0_5177_075,axiom,
( X1 != X2
| image_fun_a_bool_a(X1,X3) = image_fun_a_bool_a(X2,X3) ) ).
cnf(i_0_5178_076,axiom,
( X1 != X2
| image_fun_a_bool_a(X3,X1) = image_fun_a_bool_a(X3,X2) ) ).
cnf(i_0_5179_077,axiom,
( X1 != X2
| image_nat_pname(X1,X3) = image_nat_pname(X2,X3) ) ).
cnf(i_0_5180_078,axiom,
( X1 != X2
| image_nat_pname(X3,X1) = image_nat_pname(X3,X2) ) ).
cnf(i_0_5181_079,axiom,
( X1 != X2
| image_nat_a(X1,X3) = image_nat_a(X2,X3) ) ).
cnf(i_0_5182_080,axiom,
( X1 != X2
| image_nat_a(X3,X1) = image_nat_a(X3,X2) ) ).
cnf(i_0_5183_081,axiom,
( X1 != X2
| image_int_pname(X1,X3) = image_int_pname(X2,X3) ) ).
cnf(i_0_5184_082,axiom,
( X1 != X2
| image_int_pname(X3,X1) = image_int_pname(X3,X2) ) ).
cnf(i_0_5185_083,axiom,
( X1 != X2
| hAPP_f759274231e_bool(X1,X3) = hAPP_f759274231e_bool(X2,X3) ) ).
cnf(i_0_5186_084,axiom,
( X1 != X2
| hAPP_f759274231e_bool(X3,X1) = hAPP_f759274231e_bool(X3,X2) ) ).
cnf(i_0_5187_085,axiom,
( X1 != X2
| image_pname_pname(X1,X3) = image_pname_pname(X2,X3) ) ).
cnf(i_0_5188_086,axiom,
( X1 != X2
| image_pname_pname(X3,X1) = image_pname_pname(X3,X2) ) ).
cnf(i_0_5189_087,axiom,
( X1 != X2
| image_112932426a_bool(X1,X3) = image_112932426a_bool(X2,X3) ) ).
cnf(i_0_5190_088,axiom,
( X1 != X2
| image_112932426a_bool(X3,X1) = image_112932426a_bool(X3,X2) ) ).
cnf(i_0_5191_089,axiom,
( X1 != X2
| image_47868345e_bool(X1,X3) = image_47868345e_bool(X2,X3) ) ).
cnf(i_0_5192_090,axiom,
( X1 != X2
| image_47868345e_bool(X3,X1) = image_47868345e_bool(X3,X2) ) ).
cnf(i_0_5193_091,axiom,
( X1 != X2
| image_a_pname(X1,X3) = image_a_pname(X2,X3) ) ).
cnf(i_0_5194_092,axiom,
( X1 != X2
| image_a_pname(X3,X1) = image_a_pname(X3,X2) ) ).
cnf(i_0_5195_093,axiom,
( X1 != X2
| image_a_fun_a_bool(X1,X3) = image_a_fun_a_bool(X2,X3) ) ).
cnf(i_0_5196_094,axiom,
( X1 != X2
| image_a_fun_a_bool(X3,X1) = image_a_fun_a_bool(X3,X2) ) ).
cnf(i_0_5197_095,axiom,
( X1 != X2
| image_819518260e_bool(X1,X3) = image_819518260e_bool(X2,X3) ) ).
cnf(i_0_5198_096,axiom,
( X1 != X2
| image_819518260e_bool(X3,X1) = image_819518260e_bool(X3,X2) ) ).
cnf(i_0_5199_097,axiom,
( X1 != X2
| image_a_a(X1,X3) = image_a_a(X2,X3) ) ).
cnf(i_0_5200_098,axiom,
( X1 != X2
| image_a_a(X3,X1) = image_a_a(X3,X2) ) ).
cnf(i_0_5201_099,axiom,
( X1 != X2
| image_1133522419ol_int(X1,X3) = image_1133522419ol_int(X2,X3) ) ).
cnf(i_0_5202_100,axiom,
( X1 != X2
| image_1133522419ol_int(X3,X1) = image_1133522419ol_int(X3,X2) ) ).
cnf(i_0_5203_101,axiom,
( X1 != X2
| image_496248727ol_nat(X1,X3) = image_496248727ol_nat(X2,X3) ) ).
cnf(i_0_5204_102,axiom,
( X1 != X2
| image_496248727ol_nat(X3,X1) = image_496248727ol_nat(X3,X2) ) ).
cnf(i_0_5205_103,axiom,
( X1 != X2
| image_2069007511ol_int(X1,X3) = image_2069007511ol_int(X2,X3) ) ).
cnf(i_0_5206_104,axiom,
( X1 != X2
| image_2069007511ol_int(X3,X1) = image_2069007511ol_int(X3,X2) ) ).
cnf(i_0_5207_105,axiom,
( X1 != X2
| image_1431733819ol_nat(X1,X3) = image_1431733819ol_nat(X2,X3) ) ).
cnf(i_0_5208_106,axiom,
( X1 != X2
| image_1431733819ol_nat(X3,X1) = image_1431733819ol_nat(X3,X2) ) ).
cnf(i_0_5209_107,axiom,
( X1 != X2
| image_41399353ol_int(X1,X3) = image_41399353ol_int(X2,X3) ) ).
cnf(i_0_5210_108,axiom,
( X1 != X2
| image_41399353ol_int(X3,X1) = image_41399353ol_int(X3,X2) ) ).
cnf(i_0_5211_109,axiom,
( X1 != X2
| image_1551609309ol_nat(X1,X3) = image_1551609309ol_nat(X2,X3) ) ).
cnf(i_0_5212_110,axiom,
( X1 != X2
| image_1551609309ol_nat(X3,X1) = image_1551609309ol_nat(X3,X2) ) ).
cnf(i_0_5213_111,axiom,
( X1 != X2
| hAPP_fun_a_bool_bool(X1,X3) = hAPP_fun_a_bool_bool(X2,X3) ) ).
cnf(i_0_5214_112,axiom,
( X1 != X2
| hAPP_fun_a_bool_bool(X3,X1) = hAPP_fun_a_bool_bool(X3,X2) ) ).
cnf(i_0_5215_113,axiom,
( X1 != X2
| image_fun_a_bool_int(X1,X3) = image_fun_a_bool_int(X2,X3) ) ).
cnf(i_0_5216_114,axiom,
( X1 != X2
| image_fun_a_bool_int(X3,X1) = image_fun_a_bool_int(X3,X2) ) ).
cnf(i_0_5217_115,axiom,
( X1 != X2
| image_fun_a_bool_nat(X1,X3) = image_fun_a_bool_nat(X2,X3) ) ).
cnf(i_0_5218_116,axiom,
( X1 != X2
| image_fun_a_bool_nat(X3,X1) = image_fun_a_bool_nat(X3,X2) ) ).
cnf(i_0_5219_117,axiom,
( X1 != X2
| image_2129980159t_bool(X1,X3) = image_2129980159t_bool(X2,X3) ) ).
cnf(i_0_5220_118,axiom,
( X1 != X2
| image_2129980159t_bool(X3,X1) = image_2129980159t_bool(X3,X2) ) ).
cnf(i_0_5221_119,axiom,
( X1 != X2
| image_1512837979t_bool(X1,X3) = image_1512837979t_bool(X2,X3) ) ).
cnf(i_0_5222_120,axiom,
( X1 != X2
| image_1512837979t_bool(X3,X1) = image_1512837979t_bool(X3,X2) ) ).
cnf(i_0_5223_121,axiom,
( X1 != X2
| image_pname_int(X1,X3) = image_pname_int(X2,X3) ) ).
cnf(i_0_5224_122,axiom,
( X1 != X2
| image_pname_int(X3,X1) = image_pname_int(X3,X2) ) ).
cnf(i_0_5225_123,axiom,
( X1 != X2
| image_pname_nat(X1,X3) = image_pname_nat(X2,X3) ) ).
cnf(i_0_5226_124,axiom,
( X1 != X2
| image_pname_nat(X3,X1) = image_pname_nat(X3,X2) ) ).
cnf(i_0_5227_125,axiom,
( X1 != X2
| image_a_int(X1,X3) = image_a_int(X2,X3) ) ).
cnf(i_0_5228_126,axiom,
( X1 != X2
| image_a_int(X3,X1) = image_a_int(X3,X2) ) ).
cnf(i_0_5229_127,axiom,
( X1 != X2
| image_a_nat(X1,X3) = image_a_nat(X2,X3) ) ).
cnf(i_0_5230_128,axiom,
( X1 != X2
| image_a_nat(X3,X1) = image_a_nat(X3,X2) ) ).
cnf(i_0_5231_129,axiom,
( X1 != X2
| hAPP_fun_a_bool_a(X1,X3) = hAPP_fun_a_bool_a(X2,X3) ) ).
cnf(i_0_5232_130,axiom,
( X1 != X2
| hAPP_fun_a_bool_a(X3,X1) = hAPP_fun_a_bool_a(X3,X2) ) ).
cnf(i_0_5233_131,axiom,
( X1 != X2
| image_a_fun_nat_bool(X1,X3) = image_a_fun_nat_bool(X2,X3) ) ).
cnf(i_0_5234_132,axiom,
( X1 != X2
| image_a_fun_nat_bool(X3,X1) = image_a_fun_nat_bool(X3,X2) ) ).
cnf(i_0_5235_133,axiom,
( X1 != X2
| image_a_fun_int_bool(X1,X3) = image_a_fun_int_bool(X2,X3) ) ).
cnf(i_0_5236_134,axiom,
( X1 != X2
| image_a_fun_int_bool(X3,X1) = image_a_fun_int_bool(X3,X2) ) ).
cnf(i_0_5237_135,axiom,
( X1 != X2
| hAPP_a_a(X1,X3) = hAPP_a_a(X2,X3) ) ).
cnf(i_0_5238_136,axiom,
( X1 != X2
| hAPP_a_a(X3,X1) = hAPP_a_a(X3,X2) ) ).
cnf(i_0_5239_137,axiom,
( X1 != X2
| collect_a(X1) = collect_a(X2) ) ).
cnf(i_0_5240_138,axiom,
( X1 != X2
| hAPP_f2009550088ol_nat(X1,X3) = hAPP_f2009550088ol_nat(X2,X3) ) ).
cnf(i_0_5241_139,axiom,
( X1 != X2
| hAPP_f2009550088ol_nat(X3,X1) = hAPP_f2009550088ol_nat(X3,X2) ) ).
cnf(i_0_5242_140,axiom,
( X1 != X2
| hAPP_f55526627ol_nat(X1,X3) = hAPP_f55526627ol_nat(X2,X3) ) ).
cnf(i_0_5243_141,axiom,
( X1 != X2
| hAPP_f55526627ol_nat(X3,X1) = hAPP_f55526627ol_nat(X3,X2) ) ).
cnf(i_0_5244_142,axiom,
( X1 != X2
| hAPP_f696928925ol_nat(X1,X3) = hAPP_f696928925ol_nat(X2,X3) ) ).
cnf(i_0_5245_143,axiom,
( X1 != X2
| hAPP_f696928925ol_nat(X3,X1) = hAPP_f696928925ol_nat(X3,X2) ) ).
cnf(i_0_5246_144,axiom,
( X1 != X2
| hAPP_f521865025ol_nat(X1,X3) = hAPP_f521865025ol_nat(X2,X3) ) ).
cnf(i_0_5247_145,axiom,
( X1 != X2
| hAPP_f521865025ol_nat(X3,X1) = hAPP_f521865025ol_nat(X3,X2) ) ).
cnf(i_0_5248_146,axiom,
( X1 != X2
| hAPP_a_fun_a_bool(X1,X3) = hAPP_a_fun_a_bool(X2,X3) ) ).
cnf(i_0_5249_147,axiom,
( X1 != X2
| hAPP_a_fun_a_bool(X3,X1) = hAPP_a_fun_a_bool(X3,X2) ) ).
cnf(i_0_5250_148,axiom,
( X1 != X2
| hAPP_f2050579477a_bool(X1,X3) = hAPP_f2050579477a_bool(X2,X3) ) ).
cnf(i_0_5251_149,axiom,
( X1 != X2
| hAPP_f2050579477a_bool(X3,X1) = hAPP_f2050579477a_bool(X3,X2) ) ).
cnf(i_0_5252_150,axiom,
( X1 != X2
| hAPP_f54304608l_bool(X1,X3) = hAPP_f54304608l_bool(X2,X3) ) ).
cnf(i_0_5253_151,axiom,
( X1 != X2
| hAPP_f54304608l_bool(X3,X1) = hAPP_f54304608l_bool(X3,X2) ) ).
cnf(i_0_5254_152,axiom,
( X1 != X2
| hAPP_n215258509l_bool(X1,X3) = hAPP_n215258509l_bool(X2,X3) ) ).
cnf(i_0_5255_153,axiom,
( X1 != X2
| hAPP_n215258509l_bool(X3,X1) = hAPP_n215258509l_bool(X3,X2) ) ).
cnf(i_0_5256_154,axiom,
( X1 != X2
| hAPP_int_bool(X1,X3) = hAPP_int_bool(X2,X3) ) ).
cnf(i_0_5257_155,axiom,
( X1 != X2
| hAPP_int_bool(X3,X1) = hAPP_int_bool(X3,X2) ) ).
cnf(i_0_5258_156,axiom,
( X1 != X2
| hAPP_f22106695ol_nat(X1,X3) = hAPP_f22106695ol_nat(X2,X3) ) ).
cnf(i_0_5259_157,axiom,
( X1 != X2
| hAPP_f22106695ol_nat(X3,X1) = hAPP_f22106695ol_nat(X3,X2) ) ).
cnf(i_0_5260_158,axiom,
( X1 != X2
| hAPP_pname_bool(X1,X3) = hAPP_pname_bool(X2,X3) ) ).
cnf(i_0_5261_159,axiom,
( X1 != X2
| hAPP_pname_bool(X3,X1) = hAPP_pname_bool(X3,X2) ) ).
cnf(i_0_5262_160,axiom,
( X1 != X2
| hAPP_f800510211t_bool(X1,X3) = hAPP_f800510211t_bool(X2,X3) ) ).
cnf(i_0_5263_161,axiom,
( X1 != X2
| hAPP_f800510211t_bool(X3,X1) = hAPP_f800510211t_bool(X3,X2) ) ).
cnf(i_0_5264_162,axiom,
( X1 != X2
| hAPP_f1748468828l_bool(X1,X3) = hAPP_f1748468828l_bool(X2,X3) ) ).
cnf(i_0_5265_163,axiom,
( X1 != X2
| hAPP_f1748468828l_bool(X3,X1) = hAPP_f1748468828l_bool(X3,X2) ) ).
cnf(i_0_5266_164,axiom,
( X1 != X2
| hAPP_f1721100032l_bool(X1,X3) = hAPP_f1721100032l_bool(X2,X3) ) ).
cnf(i_0_5267_165,axiom,
( X1 != X2
| hAPP_f1721100032l_bool(X3,X1) = hAPP_f1721100032l_bool(X3,X2) ) ).
cnf(i_0_5268_166,axiom,
( X1 != X2
| hAPP_f1476298914l_bool(X1,X3) = hAPP_f1476298914l_bool(X2,X3) ) ).
cnf(i_0_5269_167,axiom,
( X1 != X2
| hAPP_f1476298914l_bool(X3,X1) = hAPP_f1476298914l_bool(X3,X2) ) ).
cnf(i_0_5270_168,axiom,
( X1 != X2
| hAPP_f198738859l_bool(X1,X3) = hAPP_f198738859l_bool(X2,X3) ) ).
cnf(i_0_5271_169,axiom,
( X1 != X2
| hAPP_f198738859l_bool(X3,X1) = hAPP_f198738859l_bool(X3,X2) ) ).
cnf(i_0_5272_170,axiom,
( X1 != X2
| hAPP_n1006566506l_bool(X1,X3) = hAPP_n1006566506l_bool(X2,X3) ) ).
cnf(i_0_5273_171,axiom,
( X1 != X2
| hAPP_n1006566506l_bool(X3,X1) = hAPP_n1006566506l_bool(X3,X2) ) ).
cnf(i_0_5274_172,axiom,
( X1 != X2
| hAPP_i68813070l_bool(X1,X3) = hAPP_i68813070l_bool(X2,X3) ) ).
cnf(i_0_5275_173,axiom,
( X1 != X2
| hAPP_i68813070l_bool(X3,X1) = hAPP_i68813070l_bool(X3,X2) ) ).
cnf(i_0_5276_174,axiom,
( X1 != X2
| hAPP_p393069232l_bool(X1,X3) = hAPP_p393069232l_bool(X2,X3) ) ).
cnf(i_0_5277_175,axiom,
( X1 != X2
| hAPP_p393069232l_bool(X3,X1) = hAPP_p393069232l_bool(X3,X2) ) ).
cnf(i_0_5278_176,axiom,
( X1 != X2
| hAPP_a_fun_bool_bool(X1,X3) = hAPP_a_fun_bool_bool(X2,X3) ) ).
cnf(i_0_5279_177,axiom,
( X1 != X2
| hAPP_a_fun_bool_bool(X3,X1) = hAPP_a_fun_bool_bool(X3,X2) ) ).
cnf(i_0_5280_178,axiom,
( X1 != X2
| hAPP_f448129468l_bool(X1,X3) = hAPP_f448129468l_bool(X2,X3) ) ).
cnf(i_0_5281_179,axiom,
( X1 != X2
| hAPP_f448129468l_bool(X3,X1) = hAPP_f448129468l_bool(X3,X2) ) ).
cnf(i_0_5282_180,axiom,
( X1 != X2
| hAPP_n1414589940l_bool(X1,X3) = hAPP_n1414589940l_bool(X2,X3) ) ).
cnf(i_0_5283_181,axiom,
( X1 != X2
| hAPP_n1414589940l_bool(X3,X1) = hAPP_n1414589940l_bool(X3,X2) ) ).
cnf(i_0_5284_182,axiom,
( X1 != X2
| hAPP_n850744903l_bool(X1,X3) = hAPP_n850744903l_bool(X2,X3) ) ).
cnf(i_0_5285_183,axiom,
( X1 != X2
| hAPP_n850744903l_bool(X3,X1) = hAPP_n850744903l_bool(X3,X2) ) ).
cnf(i_0_5286_184,axiom,
( X1 != X2
| hAPP_n609083369l_bool(X1,X3) = hAPP_n609083369l_bool(X2,X3) ) ).
cnf(i_0_5287_185,axiom,
( X1 != X2
| hAPP_n609083369l_bool(X3,X1) = hAPP_n609083369l_bool(X3,X2) ) ).
cnf(i_0_5288_186,axiom,
( X1 != X2
| hAPP_i888906320l_bool(X1,X3) = hAPP_i888906320l_bool(X2,X3) ) ).
cnf(i_0_5289_187,axiom,
( X1 != X2
| hAPP_i888906320l_bool(X3,X1) = hAPP_i888906320l_bool(X3,X2) ) ).
cnf(i_0_5290_188,axiom,
( X1 != X2
| hAPP_i1587699435l_bool(X1,X3) = hAPP_i1587699435l_bool(X2,X3) ) ).
cnf(i_0_5291_189,axiom,
( X1 != X2
| hAPP_i1587699435l_bool(X3,X1) = hAPP_i1587699435l_bool(X3,X2) ) ).
cnf(i_0_5292_190,axiom,
( X1 != X2
| hAPP_i1718399025l_bool(X1,X3) = hAPP_i1718399025l_bool(X2,X3) ) ).
cnf(i_0_5293_191,axiom,
( X1 != X2
| hAPP_i1718399025l_bool(X3,X1) = hAPP_i1718399025l_bool(X3,X2) ) ).
cnf(i_0_5294_192,axiom,
( X1 != X2
| hAPP_p1534023578a_bool(X1,X3) = hAPP_p1534023578a_bool(X2,X3) ) ).
cnf(i_0_5295_193,axiom,
( X1 != X2
| hAPP_p1534023578a_bool(X3,X1) = hAPP_p1534023578a_bool(X3,X2) ) ).
cnf(i_0_5296_194,axiom,
( X1 != X2
| hAPP_i2112223885l_bool(X1,X3) = hAPP_i2112223885l_bool(X2,X3) ) ).
cnf(i_0_5297_195,axiom,
( X1 != X2
| hAPP_i2112223885l_bool(X3,X1) = hAPP_i2112223885l_bool(X3,X2) ) ).
cnf(i_0_5298_196,axiom,
( X1 != X2
| cOMBK_bool_nat(X1) = cOMBK_bool_nat(X2) ) ).
cnf(i_0_5299_197,axiom,
( X1 != X2
| cOMBK_bool_int(X1) = cOMBK_bool_int(X2) ) ).
cnf(i_0_5300_198,axiom,
( X1 != X2
| hAPP_f1594865479ol_int(X1,X3) = hAPP_f1594865479ol_int(X2,X3) ) ).
cnf(i_0_5301_199,axiom,
( X1 != X2
| hAPP_f1594865479ol_int(X3,X1) = hAPP_f1594865479ol_int(X3,X2) ) ).
cnf(i_0_5302_200,axiom,
( X1 != X2
| hAPP_i1948725293t_bool(X1,X3) = hAPP_i1948725293t_bool(X2,X3) ) ).
cnf(i_0_5303_201,axiom,
( X1 != X2
| hAPP_i1948725293t_bool(X3,X1) = hAPP_i1948725293t_bool(X3,X2) ) ).
cnf(i_0_5304_202,axiom,
( X1 != X2
| hAPP_f1805168059t_bool(X1,X3) = hAPP_f1805168059t_bool(X2,X3) ) ).
cnf(i_0_5305_203,axiom,
( X1 != X2
| hAPP_f1805168059t_bool(X3,X1) = hAPP_f1805168059t_bool(X3,X2) ) ).
cnf(i_0_5306_204,axiom,
( X1 != X2
| hAPP_nat_int(X1,X3) = hAPP_nat_int(X2,X3) ) ).
cnf(i_0_5307_205,axiom,
( X1 != X2
| hAPP_nat_int(X3,X1) = hAPP_nat_int(X3,X2) ) ).
cnf(i_0_5308_206,axiom,
( X1 != X2
| collect_pname(X1) = collect_pname(X2) ) ).
cnf(i_0_5309_207,axiom,
( X1 != X2
| hAPP_pname_a(X1,X3) = hAPP_pname_a(X2,X3) ) ).
cnf(i_0_5310_208,axiom,
( X1 != X2
| hAPP_pname_a(X3,X1) = hAPP_pname_a(X3,X2) ) ).
cnf(i_0_5311_209,axiom,
( X1 != X2
| abs_abs_int(X1) = abs_abs_int(X2) ) ).
cnf(i_0_5312_210,axiom,
( X1 != X2
| image_pname_a(X1,X3) = image_pname_a(X2,X3) ) ).
cnf(i_0_5313_211,axiom,
( X1 != X2
| image_pname_a(X3,X1) = image_pname_a(X3,X2) ) ).
cnf(i_0_5314_212,axiom,
( X1 != X2
| hAPP_f103356543l_bool(X1,X3) = hAPP_f103356543l_bool(X2,X3) ) ).
cnf(i_0_5315_213,axiom,
( X1 != X2
| hAPP_f103356543l_bool(X3,X1) = hAPP_f103356543l_bool(X3,X2) ) ).
cnf(i_0_5316_214,axiom,
( X1 != X2
| hAPP_f284875647l_bool(X1,X3) = hAPP_f284875647l_bool(X2,X3) ) ).
cnf(i_0_5317_215,axiom,
( X1 != X2
| hAPP_f284875647l_bool(X3,X1) = hAPP_f284875647l_bool(X3,X2) ) ).
cnf(i_0_5318_216,axiom,
( X1 != X2
| hAPP_n1082236369t_bool(X1,X3) = hAPP_n1082236369t_bool(X2,X3) ) ).
cnf(i_0_5319_217,axiom,
( X1 != X2
| hAPP_n1082236369t_bool(X3,X1) = hAPP_n1082236369t_bool(X3,X2) ) ).
cnf(i_0_5320_218,axiom,
( X1 != X2
| hAPP_f434788991l_bool(X1,X3) = hAPP_f434788991l_bool(X2,X3) ) ).
cnf(i_0_5321_219,axiom,
( X1 != X2
| hAPP_f434788991l_bool(X3,X1) = hAPP_f434788991l_bool(X3,X2) ) ).
cnf(i_0_5322_220,axiom,
( X1 != X2
| hAPP_int_int(X1,X3) = hAPP_int_int(X2,X3) ) ).
cnf(i_0_5323_221,axiom,
( X1 != X2
| hAPP_int_int(X3,X1) = hAPP_int_int(X3,X2) ) ).
cnf(i_0_5324_222,axiom,
( X1 != X2
| hAPP_f1631501043l_bool(X1,X3) = hAPP_f1631501043l_bool(X2,X3) ) ).
cnf(i_0_5325_223,axiom,
( X1 != X2
| hAPP_f1631501043l_bool(X3,X1) = hAPP_f1631501043l_bool(X3,X2) ) ).
cnf(i_0_5326_224,axiom,
( X1 != X2
| hAPP_bool_bool(X1,X3) = hAPP_bool_bool(X2,X3) ) ).
cnf(i_0_5327_225,axiom,
( X1 != X2
| hAPP_bool_bool(X3,X1) = hAPP_bool_bool(X3,X2) ) ).
cnf(i_0_5328_226,axiom,
( X1 != X2
| hAPP_b589554111l_bool(X1,X3) = hAPP_b589554111l_bool(X2,X3) ) ).
cnf(i_0_5329_227,axiom,
( X1 != X2
| hAPP_b589554111l_bool(X3,X1) = hAPP_b589554111l_bool(X3,X2) ) ).
cnf(i_0_5330_228,axiom,
( X1 != X2
| hAPP_f1637334154l_bool(X1,X3) = hAPP_f1637334154l_bool(X2,X3) ) ).
cnf(i_0_5331_229,axiom,
( X1 != X2
| hAPP_f1637334154l_bool(X3,X1) = hAPP_f1637334154l_bool(X3,X2) ) ).
cnf(i_0_5332_230,axiom,
( X1 != X2
| image_26036933t_bool(X1,X3) = image_26036933t_bool(X2,X3) ) ).
cnf(i_0_5333_231,axiom,
( X1 != X2
| image_26036933t_bool(X3,X1) = image_26036933t_bool(X3,X2) ) ).
cnf(i_0_5334_232,axiom,
( X1 != X2
| cOMBS_nat_bool_bool(X1,X3) = cOMBS_nat_bool_bool(X2,X3) ) ).
cnf(i_0_5335_233,axiom,
( X1 != X2
| cOMBS_nat_bool_bool(X3,X1) = cOMBS_nat_bool_bool(X3,X2) ) ).
cnf(i_0_5336_234,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_5337_235,axiom,
( X1 != X2
| ~ is_fun_pname_bool(X1)
| is_fun_pname_bool(X2) ) ).
cnf(i_0_5338_236,axiom,
( X1 != X2
| ~ is_fun_a_bool(X1)
| is_fun_a_bool(X2) ) ).
cnf(i_0_5339_237,axiom,
( X1 != X2
| ~ is_pname(X1)
| is_pname(X2) ) ).
cnf(i_0_5340_238,axiom,
( X1 != X2
| ~ is_a(X1)
| is_a(X2) ) ).
cnf(i_0_5341_239,axiom,
( X1 != X2
| ~ is_fun949378684l_bool(X1)
| is_fun949378684l_bool(X2) ) ).
cnf(i_0_5342_240,axiom,
( X1 != X2
| ~ is_fun1661590463l_bool(X1)
| is_fun1661590463l_bool(X2) ) ).
cnf(i_0_5343_241,axiom,
( X1 != X2
| ~ is_bool(X1)
| is_bool(X2) ) ).
cnf(i_0_5344,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X3)),X2)),zero_zero_int)) ),
inference(equality_inference,[],[3068]) ).
cnf(i_0_5345,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X2),X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X3),X3))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X1),X3)),X2))) ),
inference(equality_inference,[],[3095]) ).
cnf(i_0_5346,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X3)),X4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)),X3)),X4)) ),
inference(equality_inference,[],[3139]) ).
cnf(i_0_5347,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)),X3)),X4)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),X3)),X4) ),
inference(equality_inference,[],[3140]) ).
cnf(i_0_5348,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X1)),X2)),X3) = X3 ),
inference(equality_inference,[],[3148]) ).
cnf(i_0_5349,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1))
| X2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X1)),X3)),X2) ),
inference(equality_inference,[],[3149]) ).
cnf(i_0_5350,plain,
X1 = X1,
inference(equality_inference,[],[3462]) ).
cnf(i_0_5351,plain,
( ~ is_a(X1)
| ~ is_a(X2)
| ~ is_a(X1)
| ~ is_a(X2)
| X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[3771]) ).
cnf(i_0_5352,plain,
( ~ is_a(X1)
| ~ is_a(X2)
| ~ is_a(X1)
| ~ is_a(X2)
| X2 = X1
| X2 = X2 ),
inference(equality_inference,[],[3772]) ).
cnf(i_0_5353,plain,
( ~ is_a(X1)
| ~ is_a(X2)
| ~ is_a(X1)
| ~ is_a(X2)
| X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[3773]) ).
cnf(i_0_5354,plain,
( ~ is_a(X1)
| ~ is_a(X2)
| ~ is_a(X1)
| ~ is_a(X2)
| X2 = X1
| X1 = X1 ),
inference(equality_inference,[],[3774]) ).
cnf(i_0_5355,plain,
( hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)),X3))) ),
inference(equality_inference,[],[3780]) ).
cnf(i_0_5356,plain,
( X1 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(equality_inference,[],[3809]) ).
cnf(i_0_5357,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[3912]) ).
cnf(i_0_5358,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[3913]) ).
cnf(i_0_5359,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[3914]) ).
cnf(i_0_5360,plain,
( X1 = X2
| X1 = X1 ),
inference(equality_inference,[],[3915]) ).
cnf(i_0_5361,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[3916]) ).
cnf(i_0_5362,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[3917]) ).
cnf(i_0_5363,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[3918]) ).
cnf(i_0_5364,plain,
( X1 = X2
| X2 = X2 ),
inference(equality_inference,[],[3919]) ).
cnf(i_0_5365,plain,
( ~ is_fun_a_bool(image_pname_a(X1,X2))
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),image_pname_a(X1,X3))) ),
inference(equality_inference,[],[4050]) ).
cnf(i_0_5366,plain,
( ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X1)
| X1 = X1
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(equality_inference,[],[4052]) ).
cnf(i_0_5367,plain,
( ~ is_fun_a_bool(X1)
| ~ is_fun_a_bool(X1)
| X1 = X1
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(equality_inference,[],[4053]) ).
cnf(i_0_5368,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X1,X2)),image_nat_int(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3)) ),
inference(equality_inference,[],[4103]) ).
cnf(i_0_5369,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X1,X2)),image_nat_int(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
inference(equality_inference,[],[4104]) ).
cnf(i_0_5370,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,X2)),image_pname_a(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(equality_inference,[],[4106]) ).
cnf(i_0_5371,plain,
( X1 = X1
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1)) ),
inference(equality_inference,[],[4107]) ).
cnf(i_0_5372,plain,
( X1 = X1
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X2),X1)) ),
inference(equality_inference,[],[4108]) ).
cnf(i_0_5373,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2))) ),
inference(equality_inference,[],[4119]) ).
cnf(i_0_5374,plain,
X1 = X1,
inference(equality_inference,[],[4120]) ).
cnf(i_0_5375,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))))),
inference(equality_inference,[],[4166]) ).
cnf(i_0_5376,plain,
( X1 = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X2)) ),
inference(equality_inference,[],[4230]) ).
cnf(i_0_5377,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2))),
inference(equality_inference,[],[4235]) ).
cnf(i_0_5378,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2))),
inference(equality_inference,[],[4237]) ).
cnf(i_0_5379,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))),
inference(equality_inference,[],[4238]) ).
cnf(i_0_5380,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))),
inference(equality_inference,[],[4239]) ).
cnf(i_0_5381,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X2) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2))) ),
inference(equality_inference,[],[4252]) ).
cnf(i_0_5382,plain,
( X1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(equality_inference,[],[4253]) ).
cnf(i_0_5383,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))),
inference(equality_inference,[],[4259]) ).
cnf(i_0_5384,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)))),
inference(equality_inference,[],[4291]) ).
cnf(i_0_5385,plain,
( ~ is_a(X1)
| ~ is_a(X1)
| hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2),X1)) ),
inference(equality_inference,[],[4338]) ).
cnf(i_0_5386,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,X2)))),
inference(equality_inference,[],[4386]) ).
cnf(i_0_5387,plain,
( number_number_of_nat(X1) = number_number_of_nat(zero_zero_int)
| ~ hBOOL(hAPP_int_bool(nat_neg,X1))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
inference(equality_inference,[],[4393]) ).
cnf(i_0_5388,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,zero_zero_nat)),zero_zero_int)),
inference(equality_inference,[],[4395]) ).
cnf(i_0_5389,plain,
( ~ is_fun_pname_bool(hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))
| ~ is_fun_pname_bool(X2)
| ~ is_pname(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2))) ),
inference(equality_inference,[],[4432]) ).
cnf(i_0_5390,plain,
( ~ is_fun_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))
| ~ is_fun_a_bool(X2)
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2))) ),
inference(equality_inference,[],[4433]) ).
cnf(i_0_5391,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2))),
inference(equality_inference,[],[4471]) ).
cnf(i_0_5392,plain,
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1))) ),
inference(equality_inference,[],[4484]) ).
cnf(i_0_5393,plain,
( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,X1))
| hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1))) ),
inference(equality_inference,[],[4485]) ).
cnf(i_0_5394,plain,
( ~ hBOOL(hAPP_int_bool(nat_neg,X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),zero_zero_int)) ),
inference(equality_inference,[],[4492]) ).
cnf(i_0_5395,plain,
( ~ is_a(X1)
| ~ is_a(X1)
| X1 = X1 ),
inference(equality_inference,[],[4494]) ).
cnf(i_0_5396,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X1))),
inference(equality_inference,[],[4495]) ).
cnf(i_0_5397,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X1))),
inference(equality_inference,[],[4496]) ).
cnf(i_0_5398,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(equality_inference,[],[4510]) ).
cnf(i_0_5399,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(equality_inference,[],[4511]) ).
cnf(i_0_5400,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(equality_inference,[],[4512]) ).
cnf(i_0_5401,plain,
~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),bot_bo844097828e_bool)),
inference(equality_inference,[],[4548]) ).
cnf(i_0_5402,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),bot_bot_fun_a_bool)),
inference(equality_inference,[],[4549]) ).
cnf(i_0_5403,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
inference(equality_inference,[],[4550]) ).
cnf(i_0_5404,plain,
~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),bot_bot_fun_nat_bool)),
inference(equality_inference,[],[4551]) ).
cnf(i_0_5405,plain,
~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),bot_bot_fun_int_bool)),
inference(equality_inference,[],[4552]) ).
cnf(i_0_5406,plain,
( X1 = X1
| X2 = zero_zero_nat ),
inference(equality_inference,[],[4560]) ).
cnf(i_0_5407,plain,
( X1 = X1
| X2 = zero_zero_nat ),
inference(equality_inference,[],[4562]) ).
cnf(i_0_5408,plain,
X1 = X1,
inference(equality_inference,[],[4568]) ).
cnf(i_0_5409,plain,
X1 = X1,
inference(equality_inference,[],[4571]) ).
cnf(i_0_5410,plain,
X1 = X1,
inference(equality_inference,[],[4574]) ).
cnf(i_0_5411,plain,
X1 = X1,
inference(equality_inference,[],[4578]) ).
cnf(i_0_5412,plain,
X1 = X1,
inference(equality_inference,[],[4606]) ).
cnf(i_0_5413,plain,
X1 = X1,
inference(equality_inference,[],[4607]) ).
cnf(i_0_5414,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(zero_zero_int)),one_one_int)),
inference(equality_inference,[],[4640]) ).
cnf(i_0_5415,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X1))),
inference(equality_inference,[],[4677]) ).
cnf(i_0_5416,plain,
( X1 = zero_zero_int
| hBOOL(hAPP_int_bool(nat_neg,X1))
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(equality_inference,[],[4691]) ).
cnf(i_0_5417,plain,
( number_number_of_nat(X1) = number_number_of_nat(zero_zero_int)
| hBOOL(hAPP_int_bool(nat_neg,zero_zero_int))
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(equality_inference,[],[4702]) ).
cnf(i_0_5418,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X1)),
inference(equality_inference,[],[4733]) ).
cnf(i_0_5419,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(equality_inference,[],[4740]) ).
cnf(i_0_5420,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(equality_inference,[],[4742]) ).
cnf(i_0_5421,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X1),X1)),
inference(equality_inference,[],[4743]) ).
cnf(i_0_5422,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X1)),
inference(equality_inference,[],[4750]) ).
cnf(i_0_5423,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X1)),
inference(equality_inference,[],[4752]) ).
cnf(i_0_5424,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X1)),
inference(equality_inference,[],[4753]) ).
cnf(i_0_5425,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X1)),
inference(equality_inference,[],[4754]) ).
cnf(i_0_5426,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(equality_inference,[],[4758]) ).
cnf(i_0_5427,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(equality_inference,[],[4759]) ).
cnf(i_0_5428,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X1)),
inference(equality_inference,[],[4760]) ).
cnf(i_0_5429,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(equality_inference,[],[4765]) ).
cnf(i_0_5430,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(equality_inference,[],[4766]) ).
cnf(i_0_5431,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X1),X1)),
inference(equality_inference,[],[4767]) ).
cnf(i_0_5432,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X1)),
inference(equality_inference,[],[4769]) ).
cnf(i_0_5433,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X1)),
inference(equality_inference,[],[4770]) ).
cnf(i_0_5434,plain,
hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X1)),
inference(equality_inference,[],[4771]) ).
cnf(i_0_5435,plain,
hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X1)),
inference(equality_inference,[],[4772]) ).
cnf(i_0_5436,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),X2),
inference(equality_inference,[],[4777]) ).
cnf(i_0_5437,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X2),zero_zero_nat),
inference(equality_inference,[],[4778]) ).
cnf(i_0_5438,plain,
( X1 = X1
| hBOOL(hAPP_int_bool(nat_neg,X1))
| hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(equality_inference,[],[4802]) ).
cnf(i_0_5439,plain,
~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1)),
inference(equality_inference,[],[4855]) ).
cnf(i_0_5440,plain,
~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X1)),
inference(equality_inference,[],[4856]) ).
cnf(i_0_5441,plain,
~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1)),
inference(equality_inference,[],[4857]) ).
cnf(i_0_5442,plain,
~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X1)),
inference(equality_inference,[],[4858]) ).
cnf(i_0_5443,plain,
X1 = X1,
inference(equality_inference,[],[4893]) ).
cnf(i_0_5444,plain,
X1 = X1,
inference(equality_inference,[],[4895]) ).
cnf(i_0_5445,plain,
X1 = X1,
inference(equality_inference,[],[4896]) ).
cnf(i_0_5446,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X1) = X1,
inference(equality_inference,[],[4897]) ).
cnf(i_0_5447,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),X1) = zero_zero_nat,
inference(equality_inference,[],[4899]) ).
cnf(i_0_5448,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),zero_zero_nat) = zero_zero_nat,
inference(equality_inference,[],[4900]) ).
cnf(i_0_5449,plain,
( ~ is_fun_pname_bool(bot_bo844097828e_bool)
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)) ),
inference(equality_inference,[],[4948]) ).
cnf(i_0_5450,plain,
( ~ is_fun_a_bool(bot_bot_fun_a_bool)
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)) ),
inference(equality_inference,[],[4949]) ).
cnf(i_0_5451,plain,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
inference(equality_inference,[],[5021]) ).
cnf(i_0_5452,plain,
hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool)),
inference(equality_inference,[],[5022]) ).
cnf(i_0_5453,plain,
( ~ is_fun_pname_bool(bot_bo844097828e_bool)
| image_pname_a(X1,bot_bo844097828e_bool) = bot_bot_fun_a_bool ),
inference(equality_inference,[],[5034]) ).
cnf(i_0_5454,plain,
( ~ is_fun_pname_bool(bot_bo844097828e_bool)
| bot_bot_fun_a_bool = image_pname_a(X1,bot_bo844097828e_bool) ),
inference(equality_inference,[],[5035]) ).
cnf(i_0_5455,plain,
image_nat_int(X1,bot_bot_fun_nat_bool) = bot_bot_fun_int_bool,
inference(equality_inference,[],[5063]) ).
cnf(i_0_5456,plain,
bot_bot_fun_int_bool = image_nat_int(X1,bot_bot_fun_nat_bool),
inference(equality_inference,[],[5064]) ).
cnf(i_0_5457,plain,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
inference(equality_inference,[],[5065]) ).
cnf(i_0_5458,plain,
~ hBOOL(bot_bot_bool),
inference(scs_inference,[],[i_0_5439,i_0_4973]) ).
cnf(i_0_5459,plain,
~ hBOOL(bot_bot_bool),
inference(scs_inference,[],[i_0_5440,i_0_4975]) ).
cnf(i_0_5460,plain,
( ~ hBOOL(hAPP_int_bool(nat_neg,X1))
| number_number_of_nat(X1) = number_number_of_nat(zero_zero_int) ),
inference(scs_inference,[],[i_0_4903,i_0_5417]) ).
cnf(i_0_5461,plain,
bot_bot_fun_a_bool = image_pname_a(X1,bot_bo844097828e_bool),
inference(scs_inference,[],[i_0_5092,i_0_5454]) ).
cnf(i_0_5462,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),X1)))),
inference(scs_inference,[],[i_0_4245,i_0_3372]) ).
cnf(i_0_5463,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1))),
inference(rename_variables,[],[i_0_4245]) ).
cnf(i_0_5464,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3)) ),
inference(rename_variables,[],[i_0_3372]) ).
cnf(i_0_5465,plain,
is_a(esk83_2(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),
inference(scs_inference,[],[i_0_3177,i_0_4245,i_0_3372,i_0_4622]) ).
cnf(i_0_5466,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| is_a(esk83_2(X1,X2)) ),
inference(rename_variables,[],[i_0_4622]) ).
cnf(i_0_5467,plain,
is_a(esk77_2(image_pname_a(mgt_call,u),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g))),
inference(scs_inference,[],[i_0_3177,i_0_4245,i_0_3372,i_0_4622,i_0_4623]) ).
cnf(i_0_5468,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| is_a(esk77_2(X2,X1)) ),
inference(rename_variables,[],[i_0_4623]) ).
cnf(i_0_5469,plain,
is_a(esk70_2(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),image_pname_a(mgt_call,u))),
inference(scs_inference,[],[i_0_3177,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624]) ).
cnf(i_0_5470,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| is_a(esk70_2(X1,X2)) ),
inference(rename_variables,[],[i_0_4624]) ).
cnf(i_0_5471,plain,
hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g) != image_pname_a(mgt_call,u),
inference(scs_inference,[],[i_0_3177,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758]) ).
cnf(i_0_5472,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_4758]) ).
cnf(i_0_5473,plain,
image_pname_a(mgt_call,u) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g),
inference(scs_inference,[],[i_0_3177,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759]) ).
cnf(i_0_5474,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X2 != X1 ),
inference(rename_variables,[],[i_0_4759]) ).
cnf(i_0_5475,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X2)),
inference(scs_inference,[],[i_0_3177,i_0_4786,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675]) ).
cnf(i_0_5476,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2)),X1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)) ),
inference(rename_variables,[],[i_0_3675]) ).
cnf(i_0_5477,plain,
hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2),
inference(scs_inference,[],[i_0_3177,i_0_4786,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748]) ).
cnf(i_0_5478,plain,
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool))) = X2 ),
inference(rename_variables,[],[i_0_3748]) ).
cnf(i_0_5479,plain,
hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2),
inference(scs_inference,[],[i_0_3177,i_0_4786,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749]) ).
cnf(i_0_5480,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),bot_bot_fun_nat_bool))) = X2 ),
inference(rename_variables,[],[i_0_3749]) ).
cnf(i_0_5481,plain,
hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)),bot_bot_fun_int_bool) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X2),bot_bot_fun_int_bool)),
inference(scs_inference,[],[i_0_3177,i_0_4786,i_0_4597,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775]) ).
cnf(i_0_5482,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X3)),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,X3),X2)) ),
inference(rename_variables,[],[i_0_3775]) ).
cnf(i_0_5483,plain,
hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)),bot_bot_fun_nat_bool) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X2),bot_bot_fun_nat_bool)),
inference(scs_inference,[],[i_0_3177,i_0_4786,i_0_4595,i_0_4597,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776]) ).
cnf(i_0_5484,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X3)),X2) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,X3),X2)) ),
inference(rename_variables,[],[i_0_3776]) ).
cnf(i_0_5485,plain,
hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X2)),bot_bo844097828e_bool) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X2),bot_bo844097828e_bool)),
inference(scs_inference,[],[i_0_3177,i_0_4786,i_0_4595,i_0_4597,i_0_4599,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777]) ).
cnf(i_0_5486,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),X3)),X2) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,X3),X2)) ),
inference(rename_variables,[],[i_0_3777]) ).
cnf(i_0_5487,plain,
hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)),bot_bot_fun_a_bool) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X2),bot_bot_fun_a_bool)),
inference(scs_inference,[],[i_0_3177,i_0_4786,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778]) ).
cnf(i_0_5488,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X3)),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,X3),X2)) ),
inference(rename_variables,[],[i_0_3778]) ).
cnf(i_0_5489,plain,
image_nat_int(X1,X2) = image_nat_int(X1,esk71_3(image_nat_int(X1,X2),X1,X2)),
inference(scs_inference,[],[i_0_3177,i_0_4782,i_0_4786,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962]) ).
cnf(i_0_5490,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X1)),
inference(rename_variables,[],[i_0_4782]) ).
cnf(i_0_5491,plain,
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),image_nat_int(X2,X3)))
| X1 = image_nat_int(X2,esk71_3(X1,X2,X3)) ),
inference(rename_variables,[],[i_0_3962]) ).
cnf(i_0_5492,plain,
hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X1)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X1)),
inference(scs_inference,[],[i_0_3177,i_0_4782,i_0_4786,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012]) ).
cnf(i_0_5493,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X2)),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)) ),
inference(rename_variables,[],[i_0_4012]) ).
cnf(i_0_5494,plain,
hAPP_nat_nat(suc,hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(suc,esk174_2(X1,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X1)))),
inference(scs_inference,[],[i_0_3177,i_0_4782,i_0_4786,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017]) ).
cnf(i_0_5495,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X1))),
inference(rename_variables,[],[i_0_4559]) ).
cnf(i_0_5496,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X2))
| X2 = hAPP_nat_nat(suc,esk174_2(X1,X2)) ),
inference(rename_variables,[],[i_0_4017]) ).
cnf(i_0_5497,plain,
hAPP_nat_nat(suc,X1) = hAPP_nat_nat(suc,esk65_2(X1,hAPP_nat_nat(suc,X1))),
inference(scs_inference,[],[i_0_3177,i_0_4782,i_0_4786,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018]) ).
cnf(i_0_5498,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(rename_variables,[],[i_0_4786]) ).
cnf(i_0_5499,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| X2 = hAPP_nat_nat(suc,esk65_2(X1,X2)) ),
inference(rename_variables,[],[i_0_4018]) ).
cnf(i_0_5500,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X1)),X1) = X1,
inference(scs_inference,[],[i_0_3177,i_0_4782,i_0_4786,i_0_5498,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020]) ).
cnf(i_0_5501,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)),X1) = X2 ),
inference(rename_variables,[],[i_0_4020]) ).
cnf(i_0_5502,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),X1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X1)),
inference(scs_inference,[],[i_0_3177,i_0_4782,i_0_4786,i_0_5498,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049]) ).
cnf(i_0_5503,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X2)),X1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)) ),
inference(rename_variables,[],[i_0_4049]) ).
cnf(i_0_5504,plain,
hAPP_nat_nat(suc,X1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),esk169_2(zero_zero_nat,hAPP_nat_nat(suc,X1)))),
inference(scs_inference,[],[i_0_3177,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138]) ).
cnf(i_0_5505,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),esk169_2(X1,X2))) ),
inference(rename_variables,[],[i_0_4138]) ).
cnf(i_0_5506,plain,
hAPP_nat_nat(suc,X1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),esk165_2(zero_zero_nat,hAPP_nat_nat(suc,X1)))),
inference(scs_inference,[],[i_0_3177,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139]) ).
cnf(i_0_5507,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),esk165_2(X1,X2))) ),
inference(rename_variables,[],[i_0_4139]) ).
cnf(i_0_5508,plain,
hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X1,X2)),image_nat_int(X1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3))) = image_nat_int(X1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)),
inference(scs_inference,[],[i_0_3177,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158]) ).
cnf(i_0_5509,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(X3,X1)),image_nat_int(X3,X2)) = image_nat_int(X3,X2) ),
inference(rename_variables,[],[i_0_4158]) ).
cnf(i_0_5510,plain,
hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X1,pn)),image_pname_a(X1,u)) = image_pname_a(X1,u),
inference(scs_inference,[],[i_0_3177,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159]) ).
cnf(i_0_5511,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(X3,X1)),image_pname_a(X3,X2)) = image_pname_a(X3,X2) ),
inference(rename_variables,[],[i_0_4159]) ).
cnf(i_0_5512,plain,
hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,zero_zero_nat))) = hAPP_nat_nat(suc,X1),
inference(scs_inference,[],[i_0_3177,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220]) ).
cnf(i_0_5513,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(suc,zero_zero_nat))) = X1 ),
inference(rename_variables,[],[i_0_4220]) ).
cnf(i_0_5514,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,X2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,esk204_2(X1,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,X2))))),
inference(scs_inference,[],[i_0_3177,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224]) ).
cnf(i_0_5515,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,esk204_2(X1,X2))) ),
inference(rename_variables,[],[i_0_4224]) ).
cnf(i_0_5516,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X1)) = X1,
inference(scs_inference,[],[i_0_3177,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228]) ).
cnf(i_0_5517,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)) = X2 ),
inference(rename_variables,[],[i_0_4228]) ).
cnf(i_0_5518,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X1)) = X1,
inference(scs_inference,[],[i_0_3177,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229]) ).
cnf(i_0_5519,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)) = X1 ),
inference(rename_variables,[],[i_0_4229]) ).
cnf(i_0_5520,plain,
hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,X2))),X1) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,X2))),X1),
inference(scs_inference,[],[i_0_3177,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330]) ).
cnf(i_0_5521,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X2),X1) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),X1) ),
inference(rename_variables,[],[i_0_4330]) ).
cnf(i_0_5522,plain,
hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),one_one_nat)) = hAPP_nat_nat(suc,X1),
inference(scs_inference,[],[i_0_3177,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334]) ).
cnf(i_0_5523,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)) = X1 ),
inference(rename_variables,[],[i_0_4334]) ).
cnf(i_0_5524,plain,
hAPP_nat_nat(suc,X1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),one_one_nat)),
inference(scs_inference,[],[i_0_3177,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335]) ).
cnf(i_0_5525,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),one_one_nat)) ),
inference(rename_variables,[],[i_0_4335]) ).
cnf(i_0_5526,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(pls)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),one_one_int)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364]) ).
cnf(i_0_5527,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(rename_variables,[],[i_0_5400]) ).
cnf(i_0_5528,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),pls))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(X1)) = number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)) ),
inference(rename_variables,[],[i_0_4364]) ).
cnf(i_0_5529,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),zero_zero_nat)) = X1,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365]) ).
cnf(i_0_5530,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)) = X1 ),
inference(rename_variables,[],[i_0_4365]) ).
cnf(i_0_5531,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),esk181_2(zero_zero_nat,hAPP_nat_nat(suc,X1))) = hAPP_nat_nat(suc,X1),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369]) ).
cnf(i_0_5532,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),esk181_2(X1,X2)) = X2 ),
inference(rename_variables,[],[i_0_4369]) ).
cnf(i_0_5533,plain,
X1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),esk162_2(X1,X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370]) ).
cnf(i_0_5534,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),esk162_2(X1,X2)) ),
inference(rename_variables,[],[i_0_4370]) ).
cnf(i_0_5535,plain,
image_nat_int(cOMBK_int_nat(X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),bot_bot_fun_int_bool),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383]) ).
cnf(i_0_5536,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| image_nat_int(cOMBK_int_nat(X3),X2) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),bot_bot_fun_int_bool) ),
inference(rename_variables,[],[i_0_4383]) ).
cnf(i_0_5537,plain,
image_pname_a(cOMBK_a_pname(X1),u) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),bot_bot_fun_a_bool),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384]) ).
cnf(i_0_5538,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| image_pname_a(cOMBK_a_pname(X3),X2) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X3),bot_bot_fun_a_bool) ),
inference(rename_variables,[],[i_0_4384]) ).
cnf(i_0_5539,plain,
hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410]) ).
cnf(i_0_5540,plain,
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2) = X2 ),
inference(rename_variables,[],[i_0_4410]) ).
cnf(i_0_5541,plain,
hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411]) ).
cnf(i_0_5542,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2) = X2 ),
inference(rename_variables,[],[i_0_4411]) ).
cnf(i_0_5543,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,bot_bot_nat),X1) = zero_zero_nat,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414]) ).
cnf(i_0_5544,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) = zero_zero_nat ),
inference(rename_variables,[],[i_0_4414]) ).
cnf(i_0_5545,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,esk213_1(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486]) ).
cnf(i_0_5546,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,X2)))),
inference(rename_variables,[],[i_0_5386]) ).
cnf(i_0_5547,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| X1 = hAPP_nat_int(semiri1621563631at_int,esk213_1(X1)) ),
inference(rename_variables,[],[i_0_4486]) ).
cnf(i_0_5548,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,esk212_1(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487]) ).
cnf(i_0_5549,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,X2)))),
inference(rename_variables,[],[i_0_5386]) ).
cnf(i_0_5550,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| X1 = hAPP_nat_int(semiri1621563631at_int,esk212_1(X1)) ),
inference(rename_variables,[],[i_0_4487]) ).
cnf(i_0_5551,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)) = hAPP_nat_int(semiri1621563631at_int,esk211_1(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488]) ).
cnf(i_0_5552,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,X2)))),
inference(rename_variables,[],[i_0_5386]) ).
cnf(i_0_5553,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| X1 = hAPP_nat_int(semiri1621563631at_int,esk211_1(X1)) ),
inference(rename_variables,[],[i_0_4488]) ).
cnf(i_0_5554,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X1))) = hAPP_nat_int(semiri1621563631at_int,esk210_1(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X1))))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489]) ).
cnf(i_0_5555,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))))),
inference(rename_variables,[],[i_0_5375]) ).
cnf(i_0_5556,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| X1 = hAPP_nat_int(semiri1621563631at_int,esk210_1(X1)) ),
inference(rename_variables,[],[i_0_4489]) ).
cnf(i_0_5557,plain,
hAPP_nat_nat(suc,X1) = hAPP_nat_nat(suc,esk182_1(hAPP_nat_nat(suc,X1))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490]) ).
cnf(i_0_5558,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X1 = hAPP_nat_nat(suc,esk182_1(X1)) ),
inference(rename_variables,[],[i_0_4490]) ).
cnf(i_0_5559,plain,
hAPP_nat_nat(suc,X1) = hAPP_nat_nat(suc,esk175_1(hAPP_nat_nat(suc,X1))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491]) ).
cnf(i_0_5560,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X1 = hAPP_nat_nat(suc,esk175_1(X1)) ),
inference(rename_variables,[],[i_0_4491]) ).
cnf(i_0_5561,plain,
hAPP_nat_int(semiri1621563631at_int,X1) = hAPP_nat_int(semiri1621563631at_int,esk204_2(zero_zero_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574]) ).
cnf(i_0_5562,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X3)
| X2 = X3 ),
inference(rename_variables,[],[i_0_4574]) ).
cnf(i_0_5563,plain,
zero_zero_nat = bot_bot_nat,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582]) ).
cnf(i_0_5564,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)),
inference(rename_variables,[],[i_0_4810]) ).
cnf(i_0_5565,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),bot_bot_nat))
| X1 = bot_bot_nat ),
inference(rename_variables,[],[i_0_4582]) ).
cnf(i_0_5566,plain,
hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(pls)) = pls,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867]) ).
cnf(i_0_5567,plain,
( hBOOL(hAPP_int_bool(nat_neg,X1))
| hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(X1)) = X1 ),
inference(rename_variables,[],[i_0_4867]) ).
cnf(i_0_5568,plain,
X1 = esk204_2(zero_zero_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893]) ).
cnf(i_0_5569,plain,
( hAPP_nat_int(semiri1621563631at_int,X1) != hAPP_nat_int(semiri1621563631at_int,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_4893]) ).
cnf(i_0_5570,plain,
hAPP_nat_nat(suc,X1) = esk174_2(X1,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X1))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895]) ).
cnf(i_0_5571,plain,
( hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_4895]) ).
cnf(i_0_5572,plain,
X1 = esk71_3(image_nat_int(semiri1621563631at_int,X1),semiri1621563631at_int,X1),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896]) ).
cnf(i_0_5573,plain,
( image_nat_int(semiri1621563631at_int,X1) != image_nat_int(semiri1621563631at_int,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_4896]) ).
cnf(i_0_5574,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X1)),X2)),X3) = X3,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348]) ).
cnf(i_0_5575,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X1)),X2)),X3) = X3 ),
inference(rename_variables,[],[i_0_5348]) ).
cnf(i_0_5576,plain,
X1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X2)),X3)),X1),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349]) ).
cnf(i_0_5577,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1))
| X2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X1)),X3)),X2) ),
inference(rename_variables,[],[i_0_5349]) ).
cnf(i_0_5578,plain,
X1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X1)),X1),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382]) ).
cnf(i_0_5579,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X2),X1)),X1) ),
inference(rename_variables,[],[i_0_5382]) ).
cnf(i_0_5580,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2))),X2))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244]) ).
cnf(i_0_5581,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X1))),
inference(rename_variables,[],[i_0_4559]) ).
cnf(i_0_5582,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X2))) ),
inference(rename_variables,[],[i_0_3244]) ).
cnf(i_0_5583,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),X2))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245]) ).
cnf(i_0_5584,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(rename_variables,[],[i_0_4786]) ).
cnf(i_0_5585,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X3),X2))) ),
inference(rename_variables,[],[i_0_3245]) ).
cnf(i_0_5586,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X2))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4564,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339]) ).
cnf(i_0_5587,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(rename_variables,[],[i_0_4564]) ).
cnf(i_0_5588,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X3),X2))) ),
inference(rename_variables,[],[i_0_3339]) ).
cnf(i_0_5589,plain,
~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),image_nat_int(X2,bot_bot_fun_nat_bool))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4564,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341]) ).
cnf(i_0_5590,plain,
~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),bot_bot_fun_nat_bool)),
inference(rename_variables,[],[i_0_4595]) ).
cnf(i_0_5591,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk73_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),image_nat_int(X2,X3))) ),
inference(rename_variables,[],[i_0_3341]) ).
cnf(i_0_5592,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X3)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4564,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4241,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366]) ).
cnf(i_0_5593,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1))),
inference(rename_variables,[],[i_0_4241]) ).
cnf(i_0_5594,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3)) ),
inference(rename_variables,[],[i_0_3366]) ).
cnf(i_0_5595,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X3),X1)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4564,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367]) ).
cnf(i_0_5596,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X1))),
inference(rename_variables,[],[i_0_4241]) ).
cnf(i_0_5597,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2)),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
inference(rename_variables,[],[i_0_3367]) ).
cnf(i_0_5598,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X3)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4564,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368]) ).
cnf(i_0_5599,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1))),
inference(rename_variables,[],[i_0_4243]) ).
cnf(i_0_5600,plain,
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)),X3))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X3)) ),
inference(rename_variables,[],[i_0_3368]) ).
cnf(i_0_5601,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X3),X1)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4564,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369]) ).
cnf(i_0_5602,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X2),X1))),
inference(rename_variables,[],[i_0_4243]) ).
cnf(i_0_5603,plain,
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2)),X3))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X3)) ),
inference(rename_variables,[],[i_0_3369]) ).
cnf(i_0_5604,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X3)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4564,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373]) ).
cnf(i_0_5605,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X2),X1))),
inference(rename_variables,[],[i_0_4245]) ).
cnf(i_0_5606,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2)),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3)) ),
inference(rename_variables,[],[i_0_3373]) ).
cnf(i_0_5607,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4564,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374]) ).
cnf(i_0_5608,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)))),
inference(rename_variables,[],[i_0_3679]) ).
cnf(i_0_5609,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(rename_variables,[],[i_0_3374]) ).
cnf(i_0_5610,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4564,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377]) ).
cnf(i_0_5611,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X1))),
inference(rename_variables,[],[i_0_4247]) ).
cnf(i_0_5612,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(rename_variables,[],[i_0_3377]) ).
cnf(i_0_5613,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X1)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5375,i_0_4902,i_0_4564,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378]) ).
cnf(i_0_5614,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X1))),
inference(rename_variables,[],[i_0_4247]) ).
cnf(i_0_5615,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(rename_variables,[],[i_0_3378]) ).
cnf(i_0_5616,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)),hAPP_nat_int(semiri1621563631at_int,X2)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387]) ).
cnf(i_0_5617,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,X2)))),
inference(rename_variables,[],[i_0_5386]) ).
cnf(i_0_5618,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(rename_variables,[],[i_0_3387]) ).
cnf(i_0_5619,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4782,i_0_4786,i_0_5498,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530]) ).
cnf(i_0_5620,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(rename_variables,[],[i_0_4564]) ).
cnf(i_0_5621,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(rename_variables,[],[i_0_3530]) ).
cnf(i_0_5622,plain,
hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X1)),hAPP_nat_nat(suc,X1))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4782,i_0_4786,i_0_5498,i_0_5584,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620]) ).
cnf(i_0_5623,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(rename_variables,[],[i_0_4786]) ).
cnf(i_0_5624,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X1)),X2)) ),
inference(rename_variables,[],[i_0_3620]) ).
cnf(i_0_5625,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X1)),X2))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4782,i_0_4786,i_0_5498,i_0_5584,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666]) ).
cnf(i_0_5626,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)))),
inference(rename_variables,[],[i_0_3679]) ).
cnf(i_0_5627,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(rename_variables,[],[i_0_3666]) ).
cnf(i_0_5628,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int)),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4782,i_0_4786,i_0_5498,i_0_5584,i_0_4788,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673]) ).
cnf(i_0_5629,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X1)),
inference(rename_variables,[],[i_0_4788]) ).
cnf(i_0_5630,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),one_one_int)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(rename_variables,[],[i_0_3673]) ).
cnf(i_0_5631,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)),one_one_int)),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4782,i_0_4786,i_0_5498,i_0_5584,i_0_4788,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674]) ).
cnf(i_0_5632,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(rename_variables,[],[i_0_3674]) ).
cnf(i_0_5633,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),esk174_2(X1,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X1))))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4782,i_0_4786,i_0_5498,i_0_5584,i_0_4788,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691]) ).
cnf(i_0_5634,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X1))),
inference(rename_variables,[],[i_0_4559]) ).
cnf(i_0_5635,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),esk174_2(X1,X2))) ),
inference(rename_variables,[],[i_0_3691]) ).
cnf(i_0_5636,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X1))),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4782,i_0_4786,i_0_5498,i_0_5584,i_0_4788,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708]) ).
cnf(i_0_5637,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X1))),
inference(rename_variables,[],[i_0_4247]) ).
cnf(i_0_5638,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(rename_variables,[],[i_0_3708]) ).
cnf(i_0_5639,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X1,X2)),image_nat_int(X1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4782,i_0_4786,i_0_5498,i_0_5584,i_0_4788,i_0_4591,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843]) ).
cnf(i_0_5640,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(X3,X1)),image_nat_int(X3,X2))) ),
inference(rename_variables,[],[i_0_3843]) ).
cnf(i_0_5641,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X1,bot_bot_fun_nat_bool)),image_nat_int(X1,X2))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4782,i_0_4786,i_0_5498,i_0_5584,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844]) ).
cnf(i_0_5642,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X3,X1)),image_nat_int(X3,X2))) ),
inference(rename_variables,[],[i_0_3844]) ).
cnf(i_0_5643,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1,pn)),image_pname_a(X1,u))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4782,i_0_4786,i_0_5498,i_0_5584,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846]) ).
cnf(i_0_5644,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X3,X1)),image_pname_a(X3,X2))) ),
inference(rename_variables,[],[i_0_3846]) ).
cnf(i_0_5645,plain,
hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,X2)),hAPP_nat_bool(X1,X2))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_4786,i_0_5498,i_0_5584,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849]) ).
cnf(i_0_5646,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X1,X3)),hAPP_nat_bool(X2,X3))) ),
inference(rename_variables,[],[i_0_3849]) ).
cnf(i_0_5647,plain,
hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X1,X2)),hAPP_int_bool(X1,X2))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4786,i_0_5498,i_0_5584,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852]) ).
cnf(i_0_5648,plain,
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X1),X2))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(X1,X3)),hAPP_int_bool(X2,X3))) ),
inference(rename_variables,[],[i_0_3852]) ).
cnf(i_0_5649,plain,
hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X1,X2)),hAPP_a_bool(X1,X2))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854]) ).
cnf(i_0_5650,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X1,X3)),hAPP_a_bool(X2,X3))) ),
inference(rename_variables,[],[i_0_3854]) ).
cnf(i_0_5651,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(suc,X1)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871]) ).
cnf(i_0_5652,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X1))),
inference(rename_variables,[],[i_0_4559]) ).
cnf(i_0_5653,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(rename_variables,[],[i_0_3871]) ).
cnf(i_0_5654,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X1)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874]) ).
cnf(i_0_5655,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X1),X1))),
inference(rename_variables,[],[i_0_4247]) ).
cnf(i_0_5656,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(rename_variables,[],[i_0_3874]) ).
cnf(i_0_5657,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X1))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875]) ).
cnf(i_0_5658,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(rename_variables,[],[i_0_4786]) ).
cnf(i_0_5659,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(rename_variables,[],[i_0_3875]) ).
cnf(i_0_5660,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3)),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890]) ).
cnf(i_0_5661,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X1)),
inference(rename_variables,[],[i_0_3434]) ).
cnf(i_0_5662,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(rename_variables,[],[i_0_3890]) ).
cnf(i_0_5663,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3)),X2)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892]) ).
cnf(i_0_5664,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X1)),
inference(rename_variables,[],[i_0_3434]) ).
cnf(i_0_5665,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(rename_variables,[],[i_0_3892]) ).
cnf(i_0_5666,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2))),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894]) ).
cnf(i_0_5667,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X1)),
inference(rename_variables,[],[i_0_4118]) ).
cnf(i_0_5668,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(rename_variables,[],[i_0_3894]) ).
cnf(i_0_5669,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2))),X2)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896]) ).
cnf(i_0_5670,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X1)),
inference(rename_variables,[],[i_0_4118]) ).
cnf(i_0_5671,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X3)) ),
inference(rename_variables,[],[i_0_3896]) ).
cnf(i_0_5672,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X1)),X2)),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928]) ).
cnf(i_0_5673,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(rename_variables,[],[i_0_3928]) ).
cnf(i_0_5674,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X1))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933]) ).
cnf(i_0_5675,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(rename_variables,[],[i_0_3933]) ).
cnf(i_0_5676,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934]) ).
cnf(i_0_5677,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(rename_variables,[],[i_0_5400]) ).
cnf(i_0_5678,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(rename_variables,[],[i_0_3934]) ).
cnf(i_0_5679,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int)),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935]) ).
cnf(i_0_5680,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(rename_variables,[],[i_0_5400]) ).
cnf(i_0_5681,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(rename_variables,[],[i_0_3935]) ).
cnf(i_0_5682,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int)),one_one_int)),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936]) ).
cnf(i_0_5683,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X2),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2)) ),
inference(rename_variables,[],[i_0_3936]) ).
cnf(i_0_5684,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007]) ).
cnf(i_0_5685,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(rename_variables,[],[i_0_4007]) ).
cnf(i_0_5686,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X3))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113]) ).
cnf(i_0_5687,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(rename_variables,[],[i_0_4113]) ).
cnf(i_0_5688,plain,
hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(X1,bot_bot_fun_nat_bool)),X2)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147]) ).
cnf(i_0_5689,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,esk75_2(X1,X2)),X2))
| hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X2),X1)) ),
inference(rename_variables,[],[i_0_4147]) ).
cnf(i_0_5690,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148]) ).
cnf(i_0_5691,plain,
~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),bot_bo844097828e_bool)),
inference(rename_variables,[],[i_0_4599]) ).
cnf(i_0_5692,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk78_2(X1,X2)),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(rename_variables,[],[i_0_4148]) ).
cnf(i_0_5693,plain,
X1 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166]) ).
cnf(i_0_5694,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X2 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X3))) ),
inference(rename_variables,[],[i_0_4166]) ).
cnf(i_0_5695,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk181_2(zero_zero_nat,hAPP_nat_nat(suc,X1)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190]) ).
cnf(i_0_5696,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk181_2(X1,X2))) ),
inference(rename_variables,[],[i_0_4190]) ).
cnf(i_0_5697,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X1)),X2)),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192]) ).
cnf(i_0_5698,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X1)),
inference(rename_variables,[],[i_0_3434]) ).
cnf(i_0_5699,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(rename_variables,[],[i_0_4192]) ).
cnf(i_0_5700,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),hAPP_nat_nat(suc,X2))),X2)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194]) ).
cnf(i_0_5701,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X2)),
inference(rename_variables,[],[i_0_3435]) ).
cnf(i_0_5702,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(rename_variables,[],[i_0_4194]) ).
cnf(i_0_5703,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X1))),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196]) ).
cnf(i_0_5704,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X1)),
inference(rename_variables,[],[i_0_4118]) ).
cnf(i_0_5705,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(rename_variables,[],[i_0_4196]) ).
cnf(i_0_5706,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int) != X1,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259]) ).
cnf(i_0_5707,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(rename_variables,[],[i_0_5400]) ).
cnf(i_0_5708,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X2),one_one_int)))
| X1 != X2 ),
inference(rename_variables,[],[i_0_4259]) ).
cnf(i_0_5709,plain,
X1 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291]) ).
cnf(i_0_5710,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3)) ),
inference(rename_variables,[],[i_0_4291]) ).
cnf(i_0_5711,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk206_1(hAPP_i1948725293t_bool(fequal_int,hAPP_nat_int(semiri1621563631at_int,X1))))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5431,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295]) ).
cnf(i_0_5712,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X1),X1)),
inference(rename_variables,[],[i_0_5431]) ).
cnf(i_0_5713,plain,
( ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk206_1(X1))) ),
inference(rename_variables,[],[i_0_4295]) ).
cnf(i_0_5714,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),hAPP_nat_nat(suc,X1)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5431,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311]) ).
cnf(i_0_5715,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X2)),
inference(rename_variables,[],[i_0_3435]) ).
cnf(i_0_5716,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1)) ),
inference(rename_variables,[],[i_0_4311]) ).
cnf(i_0_5717,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2)),hAPP_nat_nat(suc,X1))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5431,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325]) ).
cnf(i_0_5718,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(rename_variables,[],[i_0_4325]) ).
cnf(i_0_5719,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5431,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326]) ).
cnf(i_0_5720,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2)) ),
inference(rename_variables,[],[i_0_4326]) ).
cnf(i_0_5721,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk210_1(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X1)))))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5431,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333]) ).
cnf(i_0_5722,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X2))))),
inference(rename_variables,[],[i_0_5375]) ).
cnf(i_0_5723,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),esk210_1(X1))) ),
inference(rename_variables,[],[i_0_4333]) ).
cnf(i_0_5724,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X1)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5431,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377]) ).
cnf(i_0_5725,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,X2)))),
inference(rename_variables,[],[i_0_5386]) ).
cnf(i_0_5726,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),X1))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),X1)) ),
inference(rename_variables,[],[i_0_4377]) ).
cnf(i_0_5727,plain,
hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X1),one_one_int)),one_one_int)),hAPP_nat_int(semiri1621563631at_int,X2)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5431,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386]) ).
cnf(i_0_5728,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),X2))
| X2 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,X3)) ),
inference(rename_variables,[],[i_0_4386]) ).
cnf(i_0_5729,plain,
hBOOL(hAPP_fun_a_bool_bool(p(X1),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5431,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403]) ).
cnf(i_0_5730,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(p(X2),X1)) ),
inference(rename_variables,[],[i_0_4403]) ).
cnf(i_0_5731,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,hAPP_nat_int(semiri1621563631at_int,X1)),esk206_1(hAPP_i1948725293t_bool(fequal_int,hAPP_nat_int(semiri1621563631at_int,X1))))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404]) ).
cnf(i_0_5732,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X1),X1)),
inference(rename_variables,[],[i_0_5431]) ).
cnf(i_0_5733,plain,
( ~ hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_int_bool(X1,esk206_1(X1))) ),
inference(rename_variables,[],[i_0_4404]) ).
cnf(i_0_5734,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk207_1(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1))))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409]) ).
cnf(i_0_5735,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(rename_variables,[],[i_0_5400]) ).
cnf(i_0_5736,plain,
( hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),esk207_1(X1))) ),
inference(rename_variables,[],[i_0_4409]) ).
cnf(i_0_5737,plain,
~ hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,X1)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424]) ).
cnf(i_0_5738,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),hAPP_nat_int(semiri1621563631at_int,X2)))),
inference(rename_variables,[],[i_0_5386]) ).
cnf(i_0_5739,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X1))
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rename_variables,[],[i_0_4424]) ).
cnf(i_0_5740,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X1)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427]) ).
cnf(i_0_5741,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(rename_variables,[],[i_0_4427]) ).
cnf(i_0_5742,plain,
hBOOL(hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X1),X2),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434]) ).
cnf(i_0_5743,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_nat_bool(X2,X1)) ),
inference(rename_variables,[],[i_0_4434]) ).
cnf(i_0_5744,plain,
hBOOL(hAPP_int_bool(hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X1),X2),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435]) ).
cnf(i_0_5745,plain,
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| hBOOL(hAPP_int_bool(X2,X1)) ),
inference(rename_variables,[],[i_0_4435]) ).
cnf(i_0_5746,plain,
hBOOL(hAPP_pname_bool(u,pn)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436]) ).
cnf(i_0_5747,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hBOOL(hAPP_pname_bool(X2,X1)) ),
inference(rename_variables,[],[i_0_4436]) ).
cnf(i_0_5748,plain,
hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X1),X2),X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437]) ).
cnf(i_0_5749,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hBOOL(hAPP_a_bool(X2,X1)) ),
inference(rename_variables,[],[i_0_4437]) ).
cnf(i_0_5750,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1)),esk207_1(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X1))))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453]) ).
cnf(i_0_5751,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(rename_variables,[],[i_0_5400]) ).
cnf(i_0_5752,plain,
( hBOOL(hAPP_int_bool(X1,hAPP_nat_int(semiri1621563631at_int,X2)))
| ~ hBOOL(hAPP_int_bool(X1,esk207_1(X1))) ),
inference(rename_variables,[],[i_0_4453]) ).
cnf(i_0_5753,plain,
X1 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X1)),X2),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471]) ).
cnf(i_0_5754,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X3) ),
inference(rename_variables,[],[i_0_4471]) ).
cnf(i_0_5755,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,X1)),X1) != zero_zero_nat,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476]) ).
cnf(i_0_5756,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) != zero_zero_nat ),
inference(rename_variables,[],[i_0_4476]) ).
cnf(i_0_5757,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X1)),X2) != X1,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495]) ).
cnf(i_0_5758,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X1)),
inference(rename_variables,[],[i_0_3434]) ).
cnf(i_0_5759,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| X1 != X2 ),
inference(rename_variables,[],[i_0_4495]) ).
cnf(i_0_5760,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,X1)),X2) != zero_zero_nat,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496]) ).
cnf(i_0_5761,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X1)),
inference(rename_variables,[],[i_0_3434]) ).
cnf(i_0_5762,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| X1 != zero_zero_nat ),
inference(rename_variables,[],[i_0_4496]) ).
cnf(i_0_5763,plain,
~ hBOOL(hAPP_int_bool(image_nat_int(X1,bot_bot_fun_nat_bool),esk75_2(X2,image_nat_int(X1,bot_bot_fun_nat_bool)))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501]) ).
cnf(i_0_5764,plain,
( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| ~ hBOOL(hAPP_int_bool(X2,X1)) ),
inference(rename_variables,[],[i_0_4501]) ).
cnf(i_0_5765,plain,
~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502]) ).
cnf(i_0_5766,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_pname_bool(X2,X1)) ),
inference(rename_variables,[],[i_0_4502]) ).
cnf(i_0_5767,plain,
~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503]) ).
cnf(i_0_5768,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| ~ hBOOL(hAPP_a_bool(X2,X1)) ),
inference(rename_variables,[],[i_0_4503]) ).
cnf(i_0_5769,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2) != hAPP_nat_nat(suc,X1),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510]) ).
cnf(i_0_5770,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_4510]) ).
cnf(i_0_5771,plain,
hAPP_nat_nat(suc,X1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X1),X2),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511]) ).
cnf(i_0_5772,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 != X1 ),
inference(rename_variables,[],[i_0_4511]) ).
cnf(i_0_5773,plain,
X1 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),one_one_int),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512]) ).
cnf(i_0_5774,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_4512]) ).
cnf(i_0_5775,plain,
u != bot_bo844097828e_bool,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548]) ).
cnf(i_0_5776,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| X2 != bot_bo844097828e_bool ),
inference(rename_variables,[],[i_0_4548]) ).
cnf(i_0_5777,plain,
image_pname_a(X1,u) != bot_bot_fun_a_bool,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549]) ).
cnf(i_0_5778,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| X2 != bot_bot_fun_a_bool ),
inference(rename_variables,[],[i_0_4549]) ).
cnf(i_0_5779,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2))),X2) != zero_zero_nat,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550]) ).
cnf(i_0_5780,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 != zero_zero_nat ),
inference(rename_variables,[],[i_0_4550]) ).
cnf(i_0_5781,plain,
image_nat_int(X1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X2),X3)) != bot_bot_fun_int_bool,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550,i_0_4552]) ).
cnf(i_0_5782,plain,
( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X1),X2))
| X2 != bot_bot_fun_int_bool ),
inference(rename_variables,[],[i_0_4552]) ).
cnf(i_0_5783,plain,
~ hBOOL(hAPP_int_bool(nat_neg,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),one_one_int))),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550,i_0_4552,i_0_4589]) ).
cnf(i_0_5784,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(nat_neg,X1)) ),
inference(rename_variables,[],[i_0_4589]) ).
cnf(i_0_5785,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),X1)),X1) != hAPP_nat_nat(suc,X2),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550,i_0_4552,i_0_4589,i_0_4677]) ).
cnf(i_0_5786,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),X1))
| X1 != hAPP_nat_nat(suc,X2) ),
inference(rename_variables,[],[i_0_4677]) ).
cnf(i_0_5787,plain,
X1 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X1)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550,i_0_4552,i_0_4589,i_0_4677,i_0_4765]) ).
cnf(i_0_5788,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 != X1 ),
inference(rename_variables,[],[i_0_4765]) ).
cnf(i_0_5789,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X1)) != X1,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550,i_0_4552,i_0_4589,i_0_4677,i_0_4765,i_0_4766]) ).
cnf(i_0_5790,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_4766]) ).
cnf(i_0_5791,plain,
bot_bot_fun_nat_bool != hAPP_n1699378549t_bool(fequal_nat,X1),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5428,i_0_5431,i_0_5712,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550,i_0_4552,i_0_4589,i_0_4677,i_0_4765,i_0_4766,i_0_4855]) ).
cnf(i_0_5792,plain,
( ~ hBOOL(hAPP_nat_bool(X1,X2))
| bot_bot_fun_nat_bool != X1 ),
inference(rename_variables,[],[i_0_4855]) ).
cnf(i_0_5793,plain,
bot_bot_fun_int_bool != hAPP_i1948725293t_bool(fequal_int,X1),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5428,i_0_5431,i_0_5712,i_0_5732,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550,i_0_4552,i_0_4589,i_0_4677,i_0_4765,i_0_4766,i_0_4855,i_0_4856]) ).
cnf(i_0_5794,plain,
( ~ hBOOL(hAPP_int_bool(X1,X2))
| bot_bot_fun_int_bool != X1 ),
inference(rename_variables,[],[i_0_4856]) ).
cnf(i_0_5795,plain,
hAPP_n1699378549t_bool(fequal_nat,X1) != bot_bot_fun_nat_bool,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5428,i_0_5431,i_0_5712,i_0_5732,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550,i_0_4552,i_0_4589,i_0_4677,i_0_4765,i_0_4766,i_0_4855,i_0_4856,i_0_4857]) ).
cnf(i_0_5796,plain,
( ~ hBOOL(hAPP_nat_bool(X1,X2))
| X1 != bot_bot_fun_nat_bool ),
inference(rename_variables,[],[i_0_4857]) ).
cnf(i_0_5797,plain,
hAPP_i1948725293t_bool(fequal_int,X1) != bot_bot_fun_int_bool,
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5428,i_0_5431,i_0_5712,i_0_5732,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550,i_0_4552,i_0_4589,i_0_4677,i_0_4765,i_0_4766,i_0_4855,i_0_4856,i_0_4857,i_0_4858]) ).
cnf(i_0_5798,plain,
( ~ hBOOL(hAPP_int_bool(X1,X2))
| X1 != bot_bot_fun_int_bool ),
inference(rename_variables,[],[i_0_4858]) ).
cnf(i_0_5799,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X1),X2)),X1)),X2)),
inference(scs_inference,[],[i_0_3177,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5428,i_0_5431,i_0_5712,i_0_5732,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550,i_0_4552,i_0_4589,i_0_4677,i_0_4765,i_0_4766,i_0_4855,i_0_4856,i_0_4857,i_0_4858,i_0_5355]) ).
cnf(i_0_5800,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X1)),
inference(rename_variables,[],[i_0_5428]) ).
cnf(i_0_5801,plain,
( ~ hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X2),X3)),X2)))
| hBOOL(hAPP_nat_bool(X1,X3)) ),
inference(rename_variables,[],[i_0_5355]) ).
cnf(i_0_5802,plain,
hAPP_bool_bool(hAPP_f1748468828l_bool(X1,X2),hAPP_f54304608l_bool(X3,X2)) = hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X1,X3),X2),
inference(scs_inference,[],[i_0_3177,i_0_4625,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5428,i_0_5431,i_0_5712,i_0_5732,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550,i_0_4552,i_0_4589,i_0_4677,i_0_4765,i_0_4766,i_0_4855,i_0_4856,i_0_4857,i_0_4858,i_0_5355,i_0_5104]) ).
cnf(i_0_5803,plain,
X1 != hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(X1,X2))),
inference(scs_inference,[],[i_0_3177,i_0_4625,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5428,i_0_5431,i_0_5712,i_0_5732,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550,i_0_4552,i_0_4589,i_0_4677,i_0_4765,i_0_4766,i_0_4855,i_0_4856,i_0_4857,i_0_4858,i_0_5355,i_0_5104,i_0_5108]) ).
cnf(i_0_5804,plain,
hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X1) != hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u)),
inference(scs_inference,[],[i_0_3177,i_0_4625,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5418,i_0_5428,i_0_5431,i_0_5712,i_0_5732,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550,i_0_4552,i_0_4589,i_0_4677,i_0_4765,i_0_4766,i_0_4855,i_0_4856,i_0_4857,i_0_4858,i_0_5355,i_0_5104,i_0_5108,i_0_5336]) ).
cnf(i_0_5805,plain,
$false,
inference(scs_inference,[],[i_0_3177,i_0_4625,i_0_5400,i_0_5527,i_0_5677,i_0_5680,i_0_5707,i_0_5735,i_0_5418,i_0_5428,i_0_5431,i_0_5712,i_0_5732,i_0_5386,i_0_5546,i_0_5549,i_0_5552,i_0_5617,i_0_5725,i_0_5375,i_0_5555,i_0_5383,i_0_4902,i_0_4564,i_0_5587,i_0_5620,i_0_4780,i_0_4782,i_0_5490,i_0_4784,i_0_4786,i_0_5498,i_0_5584,i_0_5623,i_0_4788,i_0_4591,i_0_4804,i_0_4810,i_0_4559,i_0_5495,i_0_5581,i_0_5634,i_0_4811,i_0_3678,i_0_4613,i_0_4595,i_0_4597,i_0_4599,i_0_5691,i_0_4601,i_0_4604,i_0_4816,i_0_4247,i_0_5611,i_0_5614,i_0_5637,i_0_4118,i_0_5667,i_0_5670,i_0_5704,i_0_4240,i_0_4241,i_0_5593,i_0_4242,i_0_4243,i_0_5599,i_0_4245,i_0_5463,i_0_4246,i_0_3434,i_0_5661,i_0_5664,i_0_5698,i_0_5758,i_0_3435,i_0_5701,i_0_3679,i_0_5608,i_0_3372,i_0_4622,i_0_4623,i_0_4624,i_0_4758,i_0_4759,i_0_3675,i_0_3748,i_0_3749,i_0_3775,i_0_3776,i_0_3777,i_0_3778,i_0_3962,i_0_4012,i_0_4017,i_0_4018,i_0_4020,i_0_4049,i_0_4138,i_0_4139,i_0_4158,i_0_4159,i_0_4220,i_0_4224,i_0_4228,i_0_4229,i_0_4330,i_0_4334,i_0_4335,i_0_4364,i_0_4365,i_0_4369,i_0_4370,i_0_4383,i_0_4384,i_0_4410,i_0_4411,i_0_4414,i_0_4486,i_0_4487,i_0_4488,i_0_4489,i_0_4490,i_0_4491,i_0_4574,i_0_4582,i_0_4867,i_0_4893,i_0_4895,i_0_4896,i_0_5348,i_0_5349,i_0_5382,i_0_3244,i_0_3245,i_0_3339,i_0_3341,i_0_3366,i_0_3367,i_0_3368,i_0_3369,i_0_3373,i_0_3374,i_0_3377,i_0_3378,i_0_3387,i_0_3530,i_0_3620,i_0_3666,i_0_3673,i_0_3674,i_0_3691,i_0_3708,i_0_3843,i_0_3844,i_0_3846,i_0_3849,i_0_3852,i_0_3854,i_0_3871,i_0_3874,i_0_3875,i_0_3890,i_0_3892,i_0_3894,i_0_3896,i_0_3928,i_0_3933,i_0_3934,i_0_3935,i_0_3936,i_0_4007,i_0_4113,i_0_4147,i_0_4148,i_0_4166,i_0_4190,i_0_4192,i_0_4194,i_0_4196,i_0_4259,i_0_4291,i_0_4295,i_0_4311,i_0_4325,i_0_4326,i_0_4333,i_0_4377,i_0_4386,i_0_4403,i_0_4404,i_0_4409,i_0_4424,i_0_4427,i_0_4434,i_0_4435,i_0_4436,i_0_4437,i_0_4453,i_0_4471,i_0_4476,i_0_4495,i_0_4496,i_0_4501,i_0_4502,i_0_4503,i_0_4510,i_0_4511,i_0_4512,i_0_4548,i_0_4549,i_0_4550,i_0_4552,i_0_4589,i_0_4677,i_0_4765,i_0_4766,i_0_4855,i_0_4856,i_0_4857,i_0_4858,i_0_5355,i_0_5104,i_0_5108,i_0_5336,i_0_3419]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW473+3 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n026.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 06:56:23 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 3.53/2.85 % Version : CSE_E---1.7
% 3.53/2.85 % Problem : theBenchmark.p
% 3.53/2.85 % SZS status Theorem for theBenchmark.p
% 3.53/2.85 % SZS output start CNFRefutation
% See solution above
% 7.01/6.35 % Total time : 2.495s
%------------------------------------------------------------------------------