%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW473+2 : 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 05:32:30 PM UTC 2026
% Result : Theorem 1.73s 1.79s
% Output : CNFRefutation 3.48s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_968)
% Comments :
%------------------------------------------------------------------------------
fof(fact_560_finite__subset__induct,axiom,
! [X13,X5,X7] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X7),X5))
=> ( hBOOL(hAPP_f1935102916l_bool(X13,bot_bo1649642514l_bool))
=> ( ! [X76,X77] :
( ( is_fun_pname_bool(X76)
& is_fun1661590463l_bool(X77) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X77))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X76),X5))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X76),X77))
=> ( hBOOL(hAPP_f1935102916l_bool(X13,X77))
=> hBOOL(hAPP_f1935102916l_bool(X13,insert1325755072e_bool(X76,X77))) ) ) ) ) )
=> hBOOL(hAPP_f1935102916l_bool(X13,X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_finite__subset__induct) ).
fof(fact_561_finite__subset__induct,axiom,
! [X13,X5,X7] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X7),X5))
=> ( hBOOL(hAPP_f621171935l_bool(X13,bot_bo1389914601l_bool))
=> ( ! [X76,X77] :
( ( is_fun_a_bool(X76)
& is_fun949378684l_bool(X77) )
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X77))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X76),X5))
=> ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X76),X77))
=> ( hBOOL(hAPP_f621171935l_bool(X13,X77))
=> hBOOL(hAPP_f621171935l_bool(X13,insert_fun_a_bool(X76,X77))) ) ) ) ) )
=> hBOOL(hAPP_f621171935l_bool(X13,X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_561_finite__subset__induct) ).
fof(fact_557_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))
=> ( ! [X76,X77] :
( ( is_pname(X76)
& is_fun_pname_bool(X77) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X77))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X76),X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X76),X77))
=> ( hBOOL(hAPP_f1664156314l_bool(X13,X77))
=> hBOOL(hAPP_f1664156314l_bool(X13,insert_pname(X76,X77))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X13,X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_finite__subset__induct) ).
fof(fact_558_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))
=> ( ! [X76,X77] :
( ( is_a(X76)
& is_fun_a_bool(X77) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X77))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X76),X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X76),X77))
=> ( hBOOL(hAPP_fun_a_bool_bool(X13,X77))
=> hBOOL(hAPP_fun_a_bool_bool(X13,insert_a(X76,X77))) ) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X13,X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_finite__subset__induct) ).
fof(fact_559_finite__subset__induct,axiom,
! [X13,X5,X7] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X7),X5))
=> ( hBOOL(hAPP_f1637334154l_bool(X13,bot_bo1701429464l_bool))
=> ( ! [X76,X77] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X77))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X76),X5))
=> ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X76),X77))
=> ( hBOOL(hAPP_f1637334154l_bool(X13,X77))
=> hBOOL(hAPP_f1637334154l_bool(X13,insert_fun_nat_bool(X76,X77))) ) ) ) )
=> hBOOL(hAPP_f1637334154l_bool(X13,X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_finite__subset__induct) ).
fof(fact_233_insert__compr,axiom,
! [X8,X10] : insert_fun_nat_bool(X8,X10) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X8)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_insert__compr) ).
fof(fact_292_Collect__def,axiom,
! [X13] : collect_fun_nat_bool(X13) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_Collect__def) ).
fof(fact_556_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))
=> ( ! [X76,X77] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X77))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X76),X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X76),X77))
=> ( hBOOL(hAPP_f54304608l_bool(X13,X77))
=> hBOOL(hAPP_f54304608l_bool(X13,insert_nat(X76,X77))) ) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X13,X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_finite__subset__induct) ).
fof(fact_236_insert__compr,axiom,
! [X8,X10] : 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_236_insert__compr) ).
fof(fact_295_Collect__def,axiom,
! [X13] : collect_nat(X13) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_Collect__def) ).
fof(fact_564_finite__induct,axiom,
! [X13,X7] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> ( hBOOL(hAPP_f1935102916l_bool(X13,bot_bo1649642514l_bool))
=> ( ! [X30,X77] :
( ( is_fun_pname_bool(X30)
& is_fun1661590463l_bool(X77) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X77))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X30),X77))
=> ( hBOOL(hAPP_f1935102916l_bool(X13,X77))
=> hBOOL(hAPP_f1935102916l_bool(X13,insert1325755072e_bool(X30,X77))) ) ) ) )
=> hBOOL(hAPP_f1935102916l_bool(X13,X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_finite__induct) ).
fof(fact_565_finite__induct,axiom,
! [X13,X7] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> ( hBOOL(hAPP_f621171935l_bool(X13,bot_bo1389914601l_bool))
=> ( ! [X30,X77] :
( ( is_fun_a_bool(X30)
& is_fun949378684l_bool(X77) )
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X77))
=> ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X30),X77))
=> ( hBOOL(hAPP_f621171935l_bool(X13,X77))
=> hBOOL(hAPP_f621171935l_bool(X13,insert_fun_a_bool(X30,X77))) ) ) ) )
=> hBOOL(hAPP_f621171935l_bool(X13,X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_finite__induct) ).
fof(fact_196_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X30),X5))
& ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X5)),hAPP_n215258509l_bool(cOMBC_385542954t_bool(cOMBB_1250273980t_bool(fequal_nat,X9)),hAPP_f22106695ol_nat(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_pigeonhole__infinite) ).
fof(fact_190_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X30),X5))
& ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X5)),hAPP_p130839763l_bool(cOMBC_615407716e_bool(cOMBB_141086128t_bool(fequal_pname,X9)),hAPP_f1291551745_pname(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_pigeonhole__infinite) ).
fof(fact_200_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_200_pigeonhole__infinite) ).
fof(fact_201_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_201_pigeonhole__infinite) ).
fof(fact_202_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_202_pigeonhole__infinite) ).
fof(fact_193_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(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_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(fequal_nat,X9)),hAPP_nat_nat(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_pigeonhole__infinite) ).
fof(fact_187_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(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_p1499970991t_bool(cOMBC_nat_pname_bool(cOMBB_1212655066ol_nat(fequal_pname,X9)),hAPP_nat_pname(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_pigeonhole__infinite) ).
fof(fact_199_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(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_a_fun_nat_bool(cOMBC_nat_a_bool(cOMBB_1885489796ol_nat(fequal_a,X9)),hAPP_nat_a(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_pigeonhole__infinite) ).
fof(fact_563_finite__induct,axiom,
! [X13,X7] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> ( hBOOL(hAPP_f1637334154l_bool(X13,bot_bo1701429464l_bool))
=> ( ! [X30,X77] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X77))
=> ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X30),X77))
=> ( hBOOL(hAPP_f1637334154l_bool(X13,X77))
=> hBOOL(hAPP_f1637334154l_bool(X13,insert_fun_nat_bool(X30,X77))) ) ) )
=> hBOOL(hAPP_f1637334154l_bool(X13,X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_finite__induct) ).
fof(fact_326_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),insert_pname(X11,X10)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_subset__insert) ).
fof(fact_327_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),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_327_subset__insert) ).
fof(fact_223_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),insert_pname(X31,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_insertCI) ).
fof(fact_224_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),insert_a(X31,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_insertCI) ).
fof(fact_325_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),insert_nat(X11,X10)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_subset__insert) ).
fof(fact_258_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))
=> ( insert_pname(X11,X5) = insert_pname(X11,X10)
<=> X5 = X10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_insert__ident) ).
fof(fact_259_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))
=> ( insert_a(X11,X5) = insert_a(X11,X10)
<=> X5 = X10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_insert__ident) ).
fof(fact_222_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),insert_nat(X31,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_insertCI) ).
fof(fact_62_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,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,insert_fun_a_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_card__insert__if) ).
fof(fact_61_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,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,insert1325755072e_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_card__insert__if) ).
fof(fact_65_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,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,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_65_card__insert__if) ).
fof(fact_64_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,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,insert_pname(X11,X5)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_card__insert__if) ).
fof(fact_68_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,insert_fun_a_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_card__insert__disjoint) ).
fof(fact_67_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,insert1325755072e_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_card__insert__disjoint) ).
fof(fact_71_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,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_71_card__insert__disjoint) ).
fof(fact_70_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,insert_pname(X11,X5)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_card__insert__disjoint) ).
fof(fact_257_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))
=> ( insert_nat(X11,X5) = insert_nat(X11,X10)
<=> X5 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_insert__ident) ).
fof(fact_474_Collect__conv__if,axiom,
! [X13,X8] :
( ( hBOOL(hAPP_f1664156314l_bool(X13,X8))
=> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X8)),X13)) = insert1325755072e_bool(X8,bot_bo1649642514l_bool) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(X13,X8))
=> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X8)),X13)) = bot_bo1649642514l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_Collect__conv__if) ).
fof(fact_475_Collect__conv__if,axiom,
! [X13,X8] :
( ( hBOOL(hAPP_fun_a_bool_bool(X13,X8))
=> collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X8)),X13)) = insert_fun_a_bool(X8,bot_bo1389914601l_bool) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(X13,X8))
=> collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X8)),X13)) = bot_bo1389914601l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_Collect__conv__if) ).
fof(fact_471_Collect__conv__if,axiom,
! [X13,X8] :
( ( hBOOL(hAPP_pname_bool(X13,X8))
=> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X8)),X13)) = insert_pname(X8,bot_bo844097828e_bool) )
& ( ~ hBOOL(hAPP_pname_bool(X13,X8))
=> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X8)),X13)) = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_Collect__conv__if) ).
fof(fact_472_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)) = 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_472_Collect__conv__if) ).
fof(fact_480_Collect__conv__if2,axiom,
! [X13,X8] :
( ( hBOOL(hAPP_f1664156314l_bool(X13,X8))
=> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,X8)),X13)) = insert1325755072e_bool(X8,bot_bo1649642514l_bool) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(X13,X8))
=> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,X8)),X13)) = bot_bo1649642514l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_Collect__conv__if2) ).
fof(fact_481_Collect__conv__if2,axiom,
! [X13,X8] :
( ( hBOOL(hAPP_fun_a_bool_bool(X13,X8))
=> collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,X8)),X13)) = insert_fun_a_bool(X8,bot_bo1389914601l_bool) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(X13,X8))
=> collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,X8)),X13)) = bot_bo1389914601l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_Collect__conv__if2) ).
fof(fact_477_Collect__conv__if2,axiom,
! [X13,X8] :
( ( hBOOL(hAPP_pname_bool(X13,X8))
=> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,X8)),X13)) = insert_pname(X8,bot_bo844097828e_bool) )
& ( ~ hBOOL(hAPP_pname_bool(X13,X8))
=> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,X8)),X13)) = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_Collect__conv__if2) ).
fof(fact_478_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)) = 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_478_Collect__conv__if2) ).
fof(fact_63_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,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,insert_nat(X11,X5)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_card__insert__if) ).
fof(fact_60_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,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,insert_fun_nat_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_card__insert__if) ).
fof(fact_69_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,insert_nat(X11,X5)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_card__insert__disjoint) ).
fof(fact_66_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,insert_fun_nat_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_card__insert__disjoint) ).
fof(fact_470_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)) = 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_470_Collect__conv__if) ).
fof(fact_473_Collect__conv__if,axiom,
! [X13,X8] :
( ( hBOOL(hAPP_f54304608l_bool(X13,X8))
=> collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X8)),X13)) = insert_fun_nat_bool(X8,bot_bo1701429464l_bool) )
& ( ~ hBOOL(hAPP_f54304608l_bool(X13,X8))
=> collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X8)),X13)) = bot_bo1701429464l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_Collect__conv__if) ).
fof(fact_476_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)) = 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_476_Collect__conv__if2) ).
fof(fact_479_Collect__conv__if2,axiom,
! [X13,X8] :
( ( hBOOL(hAPP_f54304608l_bool(X13,X8))
=> collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,X8)),X13)) = insert_fun_nat_bool(X8,bot_bo1701429464l_bool) )
& ( ~ hBOOL(hAPP_f54304608l_bool(X13,X8))
=> collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,X8)),X13)) = bot_bo1701429464l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_Collect__conv__if2) ).
fof(fact_408_empty__Collect__eq,axiom,
! [X13] :
( bot_bo1701429464l_bool = collect_fun_nat_bool(X13)
<=> ! [X30] : ~ hBOOL(hAPP_f54304608l_bool(X13,X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_empty__Collect__eq) ).
fof(fact_412_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_412_empty__Collect__eq) ).
fof(fact_399_Collect__empty__eq,axiom,
! [X13] :
( collect_fun_nat_bool(X13) = bot_bo1701429464l_bool
<=> ! [X30] : ~ hBOOL(hAPP_f54304608l_bool(X13,X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_Collect__empty__eq) ).
fof(fact_403_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_403_Collect__empty__eq) ).
fof(fact_562_assms_I2_J,axiom,
! [X78,X4] :
( hBOOL(hAPP_fun_a_bool_bool(p(insert_a(hAPP_pname_a(mgt_call,X78),X4)),insert_a(mgt(the_com(body(X78))),bot_bot_fun_a_bool)))
=> hBOOL(hAPP_fun_a_bool_bool(p(X4),insert_a(hAPP_pname_a(mgt_call,X78),bot_bot_fun_a_bool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_assms_I2_J) ).
fof(fact_238_insert__compr,axiom,
! [X8,X10] : 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_238_insert__compr) ).
fof(fact_234_insert__compr,axiom,
! [X8,X10] : insert1325755072e_bool(X8,X10) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X8)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_insert__compr) ).
fof(fact_235_insert__compr,axiom,
! [X8,X10] : insert_fun_a_bool(X8,X10) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X8)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_insert__compr) ).
fof(fact_237_insert__compr,axiom,
! [X8,X10] : 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_237_insert__compr) ).
fof(fact_452_doubleton__eq__iff,axiom,
! [X8,X31,X32,X47] :
( ( is_pname(X8)
& is_pname(X31)
& is_pname(X32)
& is_pname(X47) )
=> ( insert_pname(X8,insert_pname(X31,bot_bo844097828e_bool)) = insert_pname(X32,insert_pname(X47,bot_bo844097828e_bool))
<=> ( ( X8 = X32
& X31 = X47 )
| ( X8 = X47
& X31 = X32 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_doubleton__eq__iff) ).
fof(fact_454_doubleton__eq__iff,axiom,
! [X8,X31,X32,X47] :
( ( is_a(X8)
& is_a(X31)
& is_a(X32)
& is_a(X47) )
=> ( insert_a(X8,insert_a(X31,bot_bot_fun_a_bool)) = insert_a(X32,insert_a(X47,bot_bot_fun_a_bool))
<=> ( ( X8 = X32
& X31 = X47 )
| ( X8 = X47
& X31 = X32 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_doubleton__eq__iff) ).
fof(fact_373_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),insert_a(hAPP_pname_a(mgt_call,X30),bot_bot_fun_a_bool))) ) )
=> hBOOL(hAPP_fun_a_bool_bool(p(X4),insert_a(mgt(X32),bot_bot_fun_a_bool))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_assms_I3_J) ).
fof(conj_6,conjecture,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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_197_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X9,X5)))
=> ? [X30] :
( is_fun_pname_bool(X30)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X30),X5))
& ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X5)),hAPP_n850744903l_bool(cOMBC_1666426608t_bool(cOMBB_1896684278e_bool(fequal_nat,X9)),hAPP_f921600141ol_nat(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_pigeonhole__infinite) ).
fof(fact_191_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X9,X5)))
=> ? [X30] :
( is_fun_pname_bool(X30)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X30),X5))
& ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X5)),hAPP_p338031245l_bool(cOMBC_1004116266e_bool(cOMBB_598082538e_bool(fequal_pname,X9)),hAPP_f1297739591_pname(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_pigeonhole__infinite) ).
fof(fact_198_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X9,X5)))
=> ? [X30] :
( is_fun_a_bool(X30)
& hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X30),X5))
& ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X5)),hAPP_n1414589940l_bool(cOMBC_619334683t_bool(cOMBB_164527437a_bool(fequal_nat,X9)),hAPP_fun_a_bool_nat(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_pigeonhole__infinite) ).
fof(fact_192_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X9,X5)))
=> ? [X30] :
( is_fun_a_bool(X30)
& hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X30),X5))
& ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X5)),hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(cOMBB_1693087065a_bool(fequal_pname,X9)),hAPP_f1128469712_pname(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_pigeonhole__infinite) ).
fof(fact_203_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(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_f654413245e_bool(cOMBC_267053842l_bool(cOMBB_928955006_pname(fequal_fun_nat_bool,X9)),hAPP_p1499970991t_bool(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_pigeonhole__infinite) ).
fof(fact_204_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(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_f759274231e_bool(cOMBC_1058051404l_bool(cOMBB_408569982_pname(fequal533582459e_bool,X9)),hAPP_p61793385e_bool(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_pigeonhole__infinite) ).
fof(fact_205_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(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_f1794073134e_bool(cOMBC_445755039l_bool(cOMBB_392435466_pname(fequal_fun_a_bool,X9)),hAPP_p1534023578a_bool(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_pigeonhole__infinite) ).
fof(fact_195_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(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_n1025906991e_bool(cOMBC_pname_nat_bool(cOMBB_523834888_pname(fequal_nat,X9)),hAPP_pname_nat(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_pigeonhole__infinite) ).
fof(fact_189_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(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_p61793385e_bool(cOMBC_1149511130e_bool(cOMBB_542850580_pname(fequal_pname,X9)),hAPP_pname_pname(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_pigeonhole__infinite) ).
fof(fact_210_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_210_pigeonhole__infinite) ).
fof(fact_207_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(X9,X5)))
=> ? [X30] :
( is_a(X30)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
& ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5)),hAPP_f1549043526a_bool(cOMBC_777206479l_bool(cOMBB_743407885bool_a(fequal_fun_nat_bool,X9)),hAPP_a_fun_nat_bool(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_pigeonhole__infinite) ).
fof(fact_208_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(X9,X5)))
=> ? [X30] :
( is_a(X30)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
& ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5)),hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(cOMBB_1137537805bool_a(fequal533582459e_bool,X9)),hAPP_a93125764e_bool(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_pigeonhole__infinite) ).
fof(fact_209_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(X9,X5)))
=> ? [X30] :
( is_a(X30)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
& ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(cOMBB_472261505bool_a(fequal_fun_a_bool,X9)),hAPP_a_fun_a_bool(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_pigeonhole__infinite) ).
fof(fact_194_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X9,X5)))
=> ? [X30] :
( is_a(X30)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
& ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5)),hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(cOMBB_1321347587bool_a(fequal_nat,X9)),hAPP_a_nat(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_pigeonhole__infinite) ).
fof(fact_188_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X9,X5)))
=> ? [X30] :
( is_a(X30)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
& ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5)),hAPP_p1534023578a_bool(cOMBC_a_pname_bool(cOMBB_610033911bool_a(fequal_pname,X9)),hAPP_a_pname(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_pigeonhole__infinite) ).
fof(fact_206_pigeonhole__infinite,axiom,
! [X9,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X9,X5)))
=> ? [X30] :
( is_a(X30)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
& ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5)),hAPP_a_fun_a_bool(cOMBC_a_a_bool(cOMBB_a_fun_a_bool_a(fequal_a,X9)),hAPP_a_a(X9,X30)))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_pigeonhole__infinite) ).
fof(fact_248_insert__commute,axiom,
! [X11,X36,X5] : insert_pname(X11,insert_pname(X36,X5)) = insert_pname(X36,insert_pname(X11,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_insert__commute) ).
fof(fact_250_insert__commute,axiom,
! [X11,X36,X5] : insert_a(X11,insert_a(X36,X5)) = insert_a(X36,insert_a(X11,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_insert__commute) ).
fof(fact_323_insert__subset,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_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_323_insert__subset) ).
fof(fact_324_insert__subset,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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_324_insert__subset) ).
fof(fact_331_insert__mono,axiom,
! [X8,X37,X40] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X37),X40))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X8,X37)),insert_pname(X8,X40))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_insert__mono) ).
fof(fact_333_insert__mono,axiom,
! [X8,X37,X40] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X37),X40))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X8,X37)),insert_a(X8,X40))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_insert__mono) ).
fof(fact_245_insert__absorb2,axiom,
! [X11,X5] : insert_pname(X11,insert_pname(X11,X5)) = insert_pname(X11,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_insert__absorb2) ).
fof(fact_247_insert__absorb2,axiom,
! [X11,X5] : insert_a(X11,insert_a(X11,X5)) = insert_a(X11,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_insert__absorb2) ).
fof(fact_56_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,insert_fun_a_bool(X11,X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_card__insert__le) ).
fof(fact_55_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,insert1325755072e_bool(X11,X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_card__insert__le) ).
fof(fact_59_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,insert_a(X11,X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_card__insert__le) ).
fof(fact_57_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,insert_pname(X11,X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_card__insert__le) ).
fof(fact_453_doubleton__eq__iff,axiom,
! [X8,X31,X32,X47] :
( insert_nat(X8,insert_nat(X31,bot_bot_fun_nat_bool)) = insert_nat(X32,insert_nat(X47,bot_bot_fun_nat_bool))
<=> ( ( X8 = X32
& X31 = X47 )
| ( X8 = X47
& X31 = X32 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_doubleton__eq__iff) ).
fof(fact_495_subset__singletonD,axiom,
! [X5,X11] :
( is_fun_pname_bool(X5)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),insert_pname(X11,bot_bo844097828e_bool)))
=> ( X5 = bot_bo844097828e_bool
| X5 = insert_pname(X11,bot_bo844097828e_bool) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_subset__singletonD) ).
fof(fact_496_subset__singletonD,axiom,
! [X5,X11] :
( is_fun_a_bool(X5)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),insert_a(X11,bot_bot_fun_a_bool)))
=> ( X5 = bot_bot_fun_a_bool
| X5 = insert_a(X11,bot_bot_fun_a_bool) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_subset__singletonD) ).
fof(fact_252_insert__iff,axiom,
! [X8,X31,X5] :
( ( is_pname(X8)
& is_pname(X31) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),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_252_insert__iff) ).
fof(fact_226_insertE,axiom,
! [X8,X31,X5] :
( ( is_pname(X8)
& is_pname(X31) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),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_226_insertE) ).
fof(fact_253_insert__iff,axiom,
! [X8,X31,X5] :
( ( is_a(X8)
& is_a(X31) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),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_253_insert__iff) ).
fof(fact_227_insertE,axiom,
! [X8,X31,X5] :
( ( is_a(X8)
& is_a(X31) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),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_227_insertE) ).
fof(fact_322_insert__subset,axiom,
! [X11,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_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_322_insert__subset) ).
fof(fact_332_insert__mono,axiom,
! [X8,X37,X40] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X37),X40))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X8,X37)),insert_nat(X8,X40))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_insert__mono) ).
fof(fact_456_singleton__iff,axiom,
! [X31,X8] :
( ( is_pname(X31)
& is_pname(X8) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),insert_pname(X8,bot_bo844097828e_bool)))
<=> X31 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_singleton__iff) ).
fof(fact_450_singletonE,axiom,
! [X31,X8] :
( ( is_pname(X31)
& is_pname(X8) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),insert_pname(X8,bot_bo844097828e_bool)))
=> X31 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_singletonE) ).
fof(fact_457_singleton__iff,axiom,
! [X31,X8] :
( ( is_a(X31)
& is_a(X8) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),insert_a(X8,bot_bot_fun_a_bool)))
<=> X31 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_singleton__iff) ).
fof(fact_451_singletonE,axiom,
! [X31,X8] :
( ( is_a(X31)
& is_a(X8) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),insert_a(X8,bot_bot_fun_a_bool)))
=> X31 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_singletonE) ).
fof(fact_254_insert__code,axiom,
! [X36,X5,X11] :
( ( is_pname(X36)
& is_pname(X11) )
=> ( hBOOL(hAPP_pname_bool(insert_pname(X36,X5),X11))
<=> ( X36 = X11
| hBOOL(hAPP_pname_bool(X5,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_insert__code) ).
fof(fact_256_insert__code,axiom,
! [X36,X5,X11] :
( ( is_a(X36)
& is_a(X11) )
=> ( hBOOL(hAPP_a_bool(insert_a(X36,X5),X11))
<=> ( X36 = X11
| hBOOL(hAPP_a_bool(X5,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_insert__code) ).
fof(fact_98_finite__insert,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X8,X5)))
<=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_finite__insert) ).
fof(fact_99_finite__insert,axiom,
! [X8,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X8,X5)))
<=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_finite__insert) ).
fof(fact_100_finite__insert,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X8,X5)))
<=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_finite__insert) ).
fof(fact_102_finite__insert,axiom,
! [X8,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X8,X5)))
<=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_finite__insert) ).
fof(fact_249_insert__commute,axiom,
! [X11,X36,X5] : insert_nat(X11,insert_nat(X36,X5)) = insert_nat(X36,insert_nat(X11,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_insert__commute) ).
fof(fact_58_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,insert_nat(X11,X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_card__insert__le) ).
fof(fact_54_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,insert_fun_nat_bool(X11,X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_card__insert__le) ).
fof(fact_328_subset__insertI2,axiom,
! [X31,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),insert_pname(X31,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_subset__insertI2) ).
fof(fact_261_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),insert_pname(X31,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_insertI2) ).
fof(fact_330_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),insert_a(X31,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_subset__insertI2) ).
fof(fact_262_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),insert_a(X31,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_insertI2) ).
fof(fact_319_subset__insertI,axiom,
! [X10,X8] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),insert_pname(X8,X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_subset__insertI) ).
fof(fact_231_insertI1,axiom,
! [X8,X10] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),insert_pname(X8,X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_insertI1) ).
fof(fact_321_subset__insertI,axiom,
! [X10,X8] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),insert_a(X8,X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_subset__insertI) ).
fof(fact_232_insertI1,axiom,
! [X8,X10] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),insert_a(X8,X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_insertI1) ).
fof(fact_24_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X8,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_finite_OinsertI) ).
fof(fact_25_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X8,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_finite_OinsertI) ).
fof(fact_26_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X8,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_finite_OinsertI) ).
fof(fact_28_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X8,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_finite_OinsertI) ).
fof(fact_337_image__insert,axiom,
! [X9,X8,X10] : image_pname_a(X9,insert_pname(X8,X10)) = insert_a(hAPP_pname_a(X9,X8),image_pname_a(X9,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_image__insert) ).
fof(fact_334_image__insert,axiom,
! [X9,X8,X10] : image_a_pname(X9,insert_a(X8,X10)) = insert_pname(hAPP_a_pname(X9,X8),image_a_pname(X9,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_image__insert) ).
fof(fact_494_subset__singletonD,axiom,
! [X5,X11] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),insert_nat(X11,bot_bot_fun_nat_bool)))
=> ( X5 = bot_bot_fun_nat_bool
| X5 = insert_nat(X11,bot_bot_fun_nat_bool) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_subset__singletonD) ).
fof(fact_251_insert__iff,axiom,
! [X8,X31,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),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_251_insert__iff) ).
fof(fact_225_insertE,axiom,
! [X8,X31,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),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_225_insertE) ).
fof(fact_455_singleton__iff,axiom,
! [X31,X8] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),insert_nat(X8,bot_bot_fun_nat_bool)))
<=> X31 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_singleton__iff) ).
fof(fact_449_singletonE,axiom,
! [X31,X8] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),insert_nat(X8,bot_bot_fun_nat_bool)))
=> X31 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_singletonE) ).
fof(fact_255_insert__code,axiom,
! [X36,X5,X11] :
( hBOOL(hAPP_nat_bool(insert_nat(X36,X5),X11))
<=> ( X36 = X11
| hBOOL(hAPP_nat_bool(X5,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_insert__code) ).
fof(fact_97_finite__insert,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X8,X5)))
<=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_finite__insert) ).
fof(fact_101_finite__insert,axiom,
! [X8,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X8,X5)))
<=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_finite__insert) ).
fof(fact_336_image__insert,axiom,
! [X9,X8,X10] : image_nat_a(X9,insert_nat(X8,X10)) = insert_a(hAPP_nat_a(X9,X8),image_nat_a(X9,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_image__insert) ).
fof(fact_446_singleton__inject,axiom,
! [X8,X31] :
( ( is_pname(X8)
& is_pname(X31) )
=> ( insert_pname(X8,bot_bo844097828e_bool) = insert_pname(X31,bot_bo844097828e_bool)
=> X8 = X31 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_singleton__inject) ).
fof(fact_448_singleton__inject,axiom,
! [X8,X31] :
( ( is_a(X8)
& is_a(X31) )
=> ( insert_a(X8,bot_bot_fun_a_bool) = insert_a(X31,bot_bot_fun_a_bool)
=> X8 = X31 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_singleton__inject) ).
fof(fact_335_image__insert,axiom,
! [X9,X8,X10] : image_a_nat(X9,insert_a(X8,X10)) = insert_nat(hAPP_a_nat(X9,X8),image_a_nat(X9,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_image__insert) ).
fof(fact_566_finite__less__ub,axiom,
! [X79,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)),X79)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_finite__less__ub) ).
fof(fact_246_insert__absorb2,axiom,
! [X11,X5] : insert_nat(X11,insert_nat(X11,X5)) = insert_nat(X11,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_insert__absorb2) ).
fof(fact_260_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),insert_nat(X31,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_insertI2) ).
fof(fact_329_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),insert_nat(X31,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_subset__insertI2) ).
fof(fact_241_insert__Collect,axiom,
! [X8,X13] : insert1325755072e_bool(X8,collec1974731493e_bool(X13)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X8))),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_insert__Collect) ).
fof(fact_242_insert__Collect,axiom,
! [X8,X13] : insert_fun_a_bool(X8,collect_fun_a_bool(X13)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X8))),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_insert__Collect) ).
fof(fact_239_insert__Collect,axiom,
! [X8,X13] : insert_pname(X8,collect_pname(X13)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X8))),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_insert__Collect) ).
fof(fact_244_insert__Collect,axiom,
! [X8,X13] : 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_244_insert__Collect) ).
fof(fact_338_insert__image,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> insert_pname(hAPP_pname_pname(X9,X11),image_pname_pname(X9,X5)) = image_pname_pname(X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_insert__image) ).
fof(fact_340_insert__image,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> insert_pname(hAPP_a_pname(X9,X11),image_a_pname(X9,X5)) = image_a_pname(X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_insert__image) ).
fof(fact_342_insert__image,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> insert_a(hAPP_nat_a(X9,X11),image_nat_a(X9,X5)) = image_nat_a(X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_insert__image) ).
fof(fact_343_insert__image,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> 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_343_insert__image) ).
fof(fact_353_imageE,axiom,
! [X31,X9,X5] :
( is_a(X31)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),image_nat_a(X9,X5)))
=> ~ ! [X30] :
( X31 = hAPP_nat_a(X9,X30)
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_imageE) ).
fof(fact_352_imageE,axiom,
! [X31,X9,X5] :
( is_pname(X31)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),image_nat_pname(X9,X5)))
=> ~ ! [X30] :
( X31 = hAPP_nat_pname(X9,X30)
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_imageE) ).
fof(fact_356_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_356_imageE) ).
fof(fact_354_imageE,axiom,
! [X31,X9,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),image_pname_nat(X9,X5)))
=> ~ ! [X30] :
( is_pname(X30)
=> ( X31 = hAPP_pname_nat(X9,X30)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_imageE) ).
fof(fact_355_imageE,axiom,
! [X31,X9,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),image_a_nat(X9,X5)))
=> ~ ! [X30] :
( is_a(X30)
=> ( X31 = hAPP_a_nat(X9,X30)
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_imageE) ).
fof(fact_230_insertI1,axiom,
! [X8,X10] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),insert_nat(X8,X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_insertI1) ).
fof(fact_320_subset__insertI,axiom,
! [X10,X8] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),insert_nat(X8,X10))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_subset__insertI) ).
fof(fact_23_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X8,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_finite_OinsertI) ).
fof(fact_27_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X8,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_finite_OinsertI) ).
fof(gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [X1,X2] :
( ( is_fun_pname_bool(X1)
& is_fun1661590463l_bool(X2) )
=> is_fun1661590463l_bool(insert1325755072e_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1,X2] :
( ( is_fun_a_bool(X1)
& is_fun949378684l_bool(X2) )
=> is_fun949378684l_bool(insert_fun_a_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(gsy_c_Set_Oinsert_000tc__Com__Opname,axiom,
! [X1,X2] :
( ( is_pname(X1)
& is_fun_pname_bool(X2) )
=> is_fun_pname_bool(insert_pname(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__Com__Opname) ).
fof(gsy_c_Set_Oinsert_000t__a,hypothesis,
! [X1,X2] :
( ( is_a(X1)
& is_fun_a_bool(X2) )
=> is_fun_a_bool(insert_a(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000t__a) ).
fof(fact_594_add__leE,axiom,
! [X15,X22,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_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_594_add__leE) ).
fof(fact_339_insert__image,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> insert_nat(hAPP_pname_nat(X9,X11),image_pname_nat(X9,X5)) = image_pname_nat(X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_insert__image) ).
fof(fact_341_insert__image,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> insert_nat(hAPP_a_nat(X9,X11),image_a_nat(X9,X5)) = image_a_nat(X9,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_insert__image) ).
fof(fact_458_insert__not__empty,axiom,
! [X8,X5] : insert_pname(X8,X5) != bot_bo844097828e_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_insert__not__empty) ).
fof(fact_460_insert__not__empty,axiom,
! [X8,X5] : insert_a(X8,X5) != bot_bot_fun_a_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_insert__not__empty) ).
fof(fact_461_empty__not__insert,axiom,
! [X8,X5] : bot_bo844097828e_bool != insert_pname(X8,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_empty__not__insert) ).
fof(fact_463_empty__not__insert,axiom,
! [X8,X5] : bot_bot_fun_a_bool != insert_a(X8,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_empty__not__insert) ).
fof(fact_447_singleton__inject,axiom,
! [X8,X31] :
( insert_nat(X8,bot_bot_fun_nat_bool) = insert_nat(X31,bot_bot_fun_nat_bool)
=> X8 = X31 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_singleton__inject) ).
fof(fact_497_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) = insert_a(X32,bot_bot_fun_a_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_image__constant) ).
fof(fact_264_insert__absorb,axiom,
! [X8,X5] :
( is_fun_pname_bool(X5)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5))
=> insert_pname(X8,X5) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_insert__absorb) ).
fof(fact_265_insert__absorb,axiom,
! [X8,X5] :
( is_fun_a_bool(X5)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),X5))
=> insert_a(X8,X5) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_insert__absorb) ).
fof(fact_120_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_120_not__less__eq__eq) ).
fof(fact_625_not__add__less1,axiom,
! [X23,X24] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X23),X24)),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_not__add__less1) ).
fof(fact_624_not__add__less2,axiom,
! [X24,X23] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X24),X23)),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_not__add__less2) ).
fof(fact_243_insert__Collect,axiom,
! [X8,X13] : 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_243_insert__Collect) ).
fof(fact_240_insert__Collect,axiom,
! [X8,X13] : insert_fun_nat_bool(X8,collect_fun_nat_bool(X13)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X8))),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_insert__Collect) ).
fof(fact_636_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_636_not__less__eq) ).
fof(fact_654_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_654_finite__M__bounded__by__nat) ).
fof(fact_486_singleton__conv,axiom,
! [X8] : collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X8)) = insert1325755072e_bool(X8,bot_bo1649642514l_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_singleton__conv) ).
fof(fact_487_singleton__conv,axiom,
! [X8] : collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X8)) = insert_fun_a_bool(X8,bot_bo1389914601l_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_singleton__conv) ).
fof(fact_483_singleton__conv,axiom,
! [X8] : collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X8)) = insert_pname(X8,bot_bo844097828e_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_singleton__conv) ).
fof(fact_484_singleton__conv,axiom,
! [X8] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X8)) = insert_a(X8,bot_bot_fun_a_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_singleton__conv) ).
fof(fact_92_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_92_finite__Collect__disjI) ).
fof(fact_96_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_96_finite__Collect__disjI) ).
fof(fact_498_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) = insert_a(X32,bot_bot_fun_a_bool) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_image__constant__conv) ).
fof(fact_492_singleton__conv2,axiom,
! [X8] : collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X8)) = insert1325755072e_bool(X8,bot_bo1649642514l_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_singleton__conv2) ).
fof(fact_493_singleton__conv2,axiom,
! [X8] : collect_fun_a_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X8)) = insert_fun_a_bool(X8,bot_bo1389914601l_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_singleton__conv2) ).
fof(fact_489_singleton__conv2,axiom,
! [X8] : collect_pname(hAPP_p61793385e_bool(fequal_pname,X8)) = insert_pname(X8,bot_bo844097828e_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_singleton__conv2) ).
fof(fact_490_singleton__conv2,axiom,
! [X8] : collect_a(hAPP_a_fun_a_bool(fequal_a,X8)) = insert_a(X8,bot_bot_fun_a_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_singleton__conv2) ).
fof(fact_116_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_116_le__SucE) ).
fof(fact_633_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_633_not__less__less__Suc__eq) ).
fof(fact_632_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_632_less__antisym) ).
fof(fact_628_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_628_less__SucE) ).
fof(fact_121_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_121_Suc__n__not__le__n) ).
fof(fact_263_insert__absorb,axiom,
! [X8,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5))
=> insert_nat(X8,X5) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_insert__absorb) ).
fof(fact_73_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_73_finite__Collect__conjI) ).
fof(fact_77_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_77_finite__Collect__conjI) ).
fof(fact_459_insert__not__empty,axiom,
! [X8,X5] : insert_nat(X8,X5) != bot_bot_fun_nat_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_insert__not__empty) ).
fof(fact_462_empty__not__insert,axiom,
! [X8,X5] : bot_bot_fun_nat_bool != insert_nat(X8,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_empty__not__insert) ).
fof(fact_647_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_647_linorder__neqE__nat) ).
fof(fact_499_linorder__le__cases,axiom,
! [X48,X49] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X48),X49))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X49),X48)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_linorder__le__cases) ).
fof(fact_482_singleton__conv,axiom,
! [X8] : collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X8)) = insert_nat(X8,bot_bot_fun_nat_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_singleton__conv) ).
fof(fact_485_singleton__conv,axiom,
! [X8] : collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X8)) = insert_fun_nat_bool(X8,bot_bo1701429464l_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_singleton__conv) ).
fof(fact_488_singleton__conv2,axiom,
! [X8] : collect_nat(hAPP_n1699378549t_bool(fequal_nat,X8)) = insert_nat(X8,bot_bot_fun_nat_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_singleton__conv2) ).
fof(fact_491_singleton__conv2,axiom,
! [X8] : collect_fun_nat_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X8)) = insert_fun_nat_bool(X8,bot_bo1701429464l_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_singleton__conv2) ).
fof(fact_417_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_417_all__not__in__conv) ).
fof(fact_418_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_418_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_666_add__diff__inverse,axiom,
! [X15,X14] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> hAPP_nat_nat(plus_plus_nat(X14),hAPP_nat_nat(minus_minus_nat(X15),X14)) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_add__diff__inverse) ).
fof(fact_6_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_6_finite__Collect__subsets) ).
fof(help_fimplies_3_1_U,axiom,
! [X92,X93] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X92),X93))
| ~ hBOOL(X92)
| hBOOL(X93) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
fof(help_fdisj_3_1_U,axiom,
! [X92,X93] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X92),X93))
| hBOOL(X92)
| hBOOL(X93) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
fof(help_fconj_2_1_U,axiom,
! [X92,X93] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X92),X93))
| hBOOL(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
fof(help_fconj_3_1_U,axiom,
! [X92,X93] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X92),X93))
| hBOOL(X93) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
fof(fact_416_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_416_all__not__in__conv) ).
fof(fact_395_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_395_equals0D) ).
fof(fact_396_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_396_equals0D) ).
fof(fact_397_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_397_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__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(fact_648_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_648_less__irrefl__nat) ).
fof(fact_645_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_645_less__not__refl) ).
fof(fact_404_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_404_empty__iff) ).
fof(fact_383_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_383_emptyE) ).
fof(fact_405_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_405_empty__iff) ).
fof(fact_384_emptyE,axiom,
! [X8] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),bot_bo844097828e_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_emptyE) ).
fof(fact_406_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_406_empty__iff) ).
fof(fact_385_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_385_emptyE) ).
fof(fact_678_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_678_less__zeroE) ).
fof(fact_614_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_614_finite__Collect__less__nat) ).
fof(fact_79_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_79_finite__Collect__le__nat) ).
fof(help_fconj_1_1_U,axiom,
! [X93,X92] :
( ~ hBOOL(X92)
| ~ hBOOL(X93)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X92),X93)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
fof(help_fimplies_2_1_U,axiom,
! [X92,X93] :
( ~ hBOOL(X93)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X92),X93)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
fof(help_fdisj_1_1_U,axiom,
! [X93,X92] :
( ~ hBOOL(X92)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X92),X93)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
fof(help_fdisj_2_1_U,axiom,
! [X92,X93] :
( ~ hBOOL(X93)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X92),X93)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
fof(fact_300_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_300_equalityE) ).
fof(fact_299_equalityE,axiom,
! [X5,X10] :
( X5 = X10
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_equalityE) ).
fof(fact_301_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_301_equalityE) ).
fof(fact_400_Collect__empty__eq,axiom,
! [X13] :
( collec1974731493e_bool(X13) = bot_bo1649642514l_bool
<=> ! [X30] :
( is_fun_pname_bool(X30)
=> ~ hBOOL(hAPP_f1664156314l_bool(X13,X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_Collect__empty__eq) ).
fof(fact_401_Collect__empty__eq,axiom,
! [X13] :
( collect_fun_a_bool(X13) = bot_bo1389914601l_bool
<=> ! [X30] :
( is_fun_a_bool(X30)
=> ~ hBOOL(hAPP_fun_a_bool_bool(X13,X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_Collect__empty__eq) ).
fof(fact_398_Collect__empty__eq,axiom,
! [X13] :
( collect_pname(X13) = bot_bo844097828e_bool
<=> ! [X30] :
( is_pname(X30)
=> ~ hBOOL(hAPP_pname_bool(X13,X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_Collect__empty__eq) ).
fof(fact_402_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_402_Collect__empty__eq) ).
fof(fact_409_empty__Collect__eq,axiom,
! [X13] :
( bot_bo1649642514l_bool = collec1974731493e_bool(X13)
<=> ! [X30] :
( is_fun_pname_bool(X30)
=> ~ hBOOL(hAPP_f1664156314l_bool(X13,X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_empty__Collect__eq) ).
fof(fact_410_empty__Collect__eq,axiom,
! [X13] :
( bot_bo1389914601l_bool = collect_fun_a_bool(X13)
<=> ! [X30] :
( is_fun_a_bool(X30)
=> ~ hBOOL(hAPP_fun_a_bool_bool(X13,X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_empty__Collect__eq) ).
fof(fact_407_empty__Collect__eq,axiom,
! [X13] :
( bot_bo844097828e_bool = collect_pname(X13)
<=> ! [X30] :
( is_pname(X30)
=> ~ hBOOL(hAPP_pname_bool(X13,X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_empty__Collect__eq) ).
fof(fact_411_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_411_empty__Collect__eq) ).
fof(fact_80_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_80_card__Collect__le__nat) ).
fof(help_fNot_1_1_U,axiom,
! [X92] :
( ~ hBOOL(hAPP_bool_bool(fNot,X92))
| ~ hBOOL(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
fof(fact_653_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_653_card__Collect__less__nat) ).
fof(fact_184_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_184_lift__Suc__mono__le) ).
fof(fact_183_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_183_lift__Suc__mono__le) ).
fof(fact_185_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_185_lift__Suc__mono__le) ).
fof(fact_186_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_186_lift__Suc__mono__le) ).
fof(fact_182_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_182_lift__Suc__mono__le) ).
fof(fact_671_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(plus_plus_nat(hAPP_nat_nat(X9,X25)),X16)),hAPP_nat_nat(X9,hAPP_nat_nat(plus_plus_nat(X25),X16)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_mono__nat__linear__lb) ).
fof(fact_675_less__mono__imp__le__mono,axiom,
! [X33,X82,X9] :
( ! [X88,X89] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X88),X89))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X9,X88)),hAPP_nat_nat(X9,X89))) )
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X33),X82))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X9,X33)),hAPP_nat_nat(X9,X82))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_less__mono__imp__le__mono) ).
fof(fact_360_image__subsetI,axiom,
! [X9,X10,X5] :
( ! [X30] :
( is_pname(X30)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(X9,X30)),X10)) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(X9,X5)),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_image__subsetI) ).
fof(fact_362_image__subsetI,axiom,
! [X9,X10,X5] :
( ! [X30] :
( is_a(X30)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(X9,X30)),X10)) ) )
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(X9,X5)),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_image__subsetI) ).
fof(fact_364_image__subsetI,axiom,
! [X9,X10,X5] :
( ! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(X9,X30)),X10)) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_nat_pname(X9,X5)),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_image__subsetI) ).
fof(fact_361_image__subsetI,axiom,
! [X9,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,hAPP_pname_pname(X9,X30)),X10)) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(X9,X5)),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_image__subsetI) ).
fof(fact_363_image__subsetI,axiom,
! [X9,X10,X5] :
( ! [X30] :
( is_a(X30)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_a_pname(X9,X30)),X10)) ) )
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(X9,X5)),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_image__subsetI) ).
fof(fact_365_image__subsetI,axiom,
! [X9,X10,X5] :
( ! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(X9,X30)),X10)) )
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(X9,X5)),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_image__subsetI) ).
fof(fact_366_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_366_image__subsetI) ).
fof(fact_375_le__fun__def,axiom,
! [X9,X44] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),X44))
<=> ! [X30] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X9,X30)),hAPP_nat_bool(X44,X30))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_le__fun__def) ).
fof(fact_374_le__fun__def,axiom,
! [X9,X44] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),X44))
<=> ! [X30] :
( is_pname(X30)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(X9,X30)),hAPP_pname_bool(X44,X30))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_le__fun__def) ).
fof(fact_376_le__fun__def,axiom,
! [X9,X44] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),X44))
<=> ! [X30] :
( is_a(X30)
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X9,X30)),hAPP_a_bool(X44,X30))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_le__fun__def) ).
fof(fact_669_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(minus_minus_nat(X25),X16)),hAPP_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_669_less__diff__iff) ).
fof(fact_124_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(minus_minus_nat(X25),X16)),hAPP_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_124_le__diff__iff) ).
fof(fact_163_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_163_finite__subset__image) ).
fof(fact_155_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_155_finite__subset__image) ).
fof(fact_164_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_164_finite__subset__image) ).
fof(fact_156_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_156_finite__subset__image) ).
fof(fact_165_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_165_finite__subset__image) ).
fof(fact_157_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_157_finite__subset__image) ).
fof(fact_179_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_179_finite__subset__image) ).
fof(fact_178_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_178_finite__subset__image) ).
fof(fact_177_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_177_finite__subset__image) ).
fof(fact_175_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_175_finite__subset__image) ).
fof(fact_181_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_181_finite__subset__image) ).
fof(fact_173_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_173_finite__subset__image) ).
fof(fact_172_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_172_finite__subset__image) ).
fof(fact_171_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_171_finite__subset__image) ).
fof(fact_162_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_162_finite__subset__image) ).
fof(fact_161_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_161_finite__subset__image) ).
fof(fact_160_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_160_finite__subset__image) ).
fof(fact_158_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_158_finite__subset__image) ).
fof(fact_167_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_167_finite__subset__image) ).
fof(fact_168_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_168_finite__subset__image) ).
fof(fact_169_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_169_finite__subset__image) ).
fof(fact_180_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_nat_nat(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_nat(X9,X27) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_finite__subset__image) ).
fof(fact_176_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_176_finite__subset__image) ).
fof(fact_174_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_174_finite__subset__image) ).
fof(fact_170_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_170_finite__subset__image) ).
fof(fact_166_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_166_finite__subset__image) ).
fof(fact_159_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_159_finite__subset__image) ).
fof(fact_344_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_nat_a(X9,X5)))
<=> ? [X41] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X41),X5))
& X10 = image_nat_a(X9,X41) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_subset__image__iff) ).
fof(fact_347_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)))
<=> ? [X41] :
( is_fun_pname_bool(X41)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X41),X5))
& X10 = image_pname_a(X9,X41) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_subset__image__iff) ).
fof(fact_302_image__iff,axiom,
! [X38,X9,X5] :
( is_a(X38)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X38),image_pname_a(X9,X5)))
<=> ? [X30] :
( is_pname(X30)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
& X38 = hAPP_pname_a(X9,X30) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_image__iff) ).
fof(fact_345_subset__image__iff,axiom,
! [X10,X9,X5] :
( is_fun_pname_bool(X10)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),image_a_pname(X9,X5)))
<=> ? [X41] :
( is_fun_a_bool(X41)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X41),X5))
& X10 = image_a_pname(X9,X41) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_subset__image__iff) ).
fof(fact_346_subset__image__iff,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),image_a_nat(X9,X5)))
<=> ? [X41] :
( is_fun_a_bool(X41)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X41),X5))
& X10 = image_a_nat(X9,X41) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_subset__image__iff) ).
fof(fact_672_inc__induct,axiom,
! [X13,X33,X82] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X33),X82))
=> ( hBOOL(hAPP_nat_bool(X13,X82))
=> ( ! [X88] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X88),X82))
=> ( hBOOL(hAPP_nat_bool(X13,hAPP_nat_nat(suc,X88)))
=> hBOOL(hAPP_nat_bool(X13,X88)) ) )
=> hBOOL(hAPP_nat_bool(X13,X33)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_inc__induct) ).
fof(fact_228_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(minus_minus_nat(X16),X33))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_zero__induct__lemma) ).
fof(fact_600_le__diff__conv2,axiom,
! [X33,X16,X82] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X16),X82))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X33),hAPP_nat_nat(minus_minus_nat(X82),X16)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X33),X16)),X82)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_le__diff__conv2) ).
fof(fact_603_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(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X14),X15)),X22))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_le__add__diff) ).
fof(fact_623_nat__add__left__cancel__less,axiom,
! [X16,X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X16),X25)),hAPP_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_623_nat__add__left__cancel__less) ).
fof(fact_587_nat__add__left__cancel__le,axiom,
! [X16,X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X16),X25)),hAPP_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_587_nat__add__left__cancel__le) ).
fof(fact_93_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_93_finite__Collect__disjI) ).
fof(fact_94_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_94_finite__Collect__disjI) ).
fof(fact_95_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_95_finite__Collect__disjI) ).
fof(fact_91_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_91_finite__Collect__disjI) ).
fof(fact_619_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(plus_plus_nat(X23),X22)),hAPP_nat_nat(plus_plus_nat(X24),X26))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_add__less__mono) ).
fof(fact_668_diff__less__mono,axiom,
! [X85,X86,X87] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X86),X87))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X85),X86))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X86),X85)),hAPP_nat_nat(minus_minus_nat(X87),X85))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_diff__less__mono) ).
fof(fact_642_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(minus_minus_nat(X26),X14)),hAPP_nat_nat(minus_minus_nat(X26),X15))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_diff__less__mono2) ).
fof(fact_591_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(plus_plus_nat(X23),X22)),hAPP_nat_nat(plus_plus_nat(X24),X26))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_591_add__le__mono) ).
fof(fact_49_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_49_card__seteq) ).
fof(fact_50_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_50_card__seteq) ).
fof(fact_51_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_51_card__seteq) ).
fof(fact_52_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_52_card__seteq) ).
fof(fact_667_less__diff__conv,axiom,
! [X33,X82,X16] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X33),hAPP_nat_nat(minus_minus_nat(X82),X16)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X33),X16)),X82)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_less__diff__conv) ).
fof(fact_604_le__diff__conv,axiom,
! [X82,X16,X33] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X82),X16)),X33))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X82),hAPP_nat_nat(plus_plus_nat(X33),X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_le__diff__conv) ).
fof(fact_48_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_48_card__seteq) ).
fof(fact_53_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_53_card__seteq) ).
fof(fact_34_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_34_card__image__le) ).
fof(fact_38_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_38_card__image__le) ).
fof(fact_37_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_37_card__image__le) ).
fof(fact_36_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_36_card__image__le) ).
fof(fact_35_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_35_card__image__le) ).
fof(fact_31_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_31_card__image__le) ).
fof(fact_32_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_32_card__image__le) ).
fof(fact_33_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_33_card__image__le) ).
fof(fact_41_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_41_card__image__le) ).
fof(fact_30_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_30_card__image__le) ).
fof(fact_40_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_40_card__image__le) ).
fof(fact_29_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_29_card__image__le) ).
fof(fact_39_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_39_card__image__le) ).
fof(fact_608_diff__Suc__diff__eq2,axiom,
! [X15,X22,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X24),X22))),X15) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X24)),hAPP_nat_nat(plus_plus_nat(X22),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_diff__Suc__diff__eq2) ).
fof(fact_617_add__lessD1,axiom,
! [X23,X24,X22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_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_617_add__lessD1) ).
fof(fact_593_add__leD1,axiom,
! [X15,X22,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_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_593_add__leD1) ).
fof(fact_592_add__leD2,axiom,
! [X15,X22,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_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_592_add__leD2) ).
fof(fact_570_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_570_less__eq__nat_Osimps_I2_J) ).
fof(fact_620_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(plus_plus_nat(X23),X22)),hAPP_nat_nat(plus_plus_nat(X24),X22))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_add__less__mono1) ).
fof(fact_590_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(plus_plus_nat(X23),X22)),hAPP_nat_nat(plus_plus_nat(X24),X22))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_add__le__mono1) ).
fof(fact_128_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(minus_minus_nat(X15),X26)),hAPP_nat_nat(minus_minus_nat(X14),X26))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_diff__le__mono) ).
fof(fact_129_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(minus_minus_nat(X26),X14)),hAPP_nat_nat(minus_minus_nat(X26),X15))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_diff__le__mono2) ).
fof(fact_634_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_634_Suc__less__eq) ).
fof(fact_626_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_626_Suc__less__SucD) ).
fof(fact_118_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_118_Suc__le__mono) ).
fof(fact_629_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_629_less__trans__Suc) ).
fof(fact_122_Suc__diff__diff,axiom,
! [X15,X14,X22] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X15)),X14)),hAPP_nat_nat(suc,X22)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X15),X14)),X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Suc__diff__diff) ).
fof(fact_125_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(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X15),X22)),hAPP_nat_nat(minus_minus_nat(X14),X22)) = hAPP_nat_nat(minus_minus_nat(X15),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Nat_Odiff__diff__eq) ).
fof(fact_676_Suc__lessE,axiom,
! [X23,X22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X23)),X22))
=> ~ ! [X89] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X89))
=> X22 != hAPP_nat_nat(suc,X89) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_Suc__lessE) ).
fof(fact_74_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_74_finite__Collect__conjI) ).
fof(fact_75_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_75_finite__Collect__conjI) ).
fof(fact_76_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_76_finite__Collect__conjI) ).
fof(fact_72_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_72_finite__Collect__conjI) ).
fof(fact_47_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_47_card__mono) ).
fof(fact_44_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_44_card__mono) ).
fof(fact_43_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_43_card__mono) ).
fof(fact_42_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_42_card__mono) ).
fof(fact_46_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_46_card__mono) ).
fof(fact_45_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_45_card__mono) ).
fof(fact_357_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_357_subsetI) ).
fof(fact_358_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_358_subsetI) ).
fof(fact_359_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_359_subsetI) ).
fof(fact_609_diff__Suc__diff__eq1,axiom,
! [X15,X22,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
=> hAPP_nat_nat(minus_minus_nat(X15),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X24),X22))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X15),X22)),hAPP_nat_nat(suc,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_diff__Suc__diff__eq1) ).
fof(fact_303_imageI,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(X9,X11)),image_pname_nat(X9,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_imageI) ).
fof(fact_304_imageI,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(X9,X11)),image_a_nat(X9,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_imageI) ).
fof(fact_349_image__mono,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(X9,X5)),image_a_nat(X9,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_image__mono) ).
fof(fact_348_image__mono,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(X9,X5)),image_a_pname(X9,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_image__mono) ).
fof(fact_305_imageI,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(X9,X11)),image_nat_pname(X9,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_imageI) ).
fof(fact_350_image__mono,axiom,
! [X9,X5,X10] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(X9,X5)),image_nat_a(X9,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_image__mono) ).
fof(fact_351_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_351_image__mono) ).
fof(fact_306_imageI,axiom,
! [X9,X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(X9,X11)),image_nat_a(X9,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_imageI) ).
fof(fact_307_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_307_imageI) ).
fof(fact_381_le__funE,axiom,
! [X11,X9,X44] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),X44))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X9,X11)),hAPP_nat_bool(X44,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_le__funE) ).
fof(fact_378_le__funD,axiom,
! [X11,X9,X44] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X9),X44))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X9,X11)),hAPP_nat_bool(X44,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_le__funD) ).
fof(fact_380_le__funE,axiom,
! [X11,X9,X44] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),X44))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(X9,X11)),hAPP_pname_bool(X44,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_le__funE) ).
fof(fact_377_le__funD,axiom,
! [X11,X9,X44] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X9),X44))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(X9,X11)),hAPP_pname_bool(X44,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_le__funD) ).
fof(fact_382_le__funE,axiom,
! [X11,X9,X44] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),X44))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X9,X11)),hAPP_a_bool(X44,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_le__funE) ).
fof(fact_379_le__funD,axiom,
! [X11,X9,X44] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X9),X44))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X9,X11)),hAPP_a_bool(X44,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_le__funD) ).
fof(fact_643_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(minus_minus_nat(X24),X14)),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_less__imp__diff__less) ).
fof(fact_627_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_627_Suc__lessD) ).
fof(fact_664_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_664_Suc__le__lessD) ).
fof(fact_660_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_660_Suc__le__eq) ).
fof(fact_658_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_658_less__eq__Suc__le) ).
fof(fact_115_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_115_Suc__leD) ).
fof(fact_613_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_613_Suc__mono) ).
fof(fact_281_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_281_set__rev__mp) ).
fof(fact_284_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_284_set__mp) ).
fof(fact_278_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_278_in__mono) ).
fof(fact_219_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_219_subsetD) ).
fof(fact_511_order__trans,axiom,
! [X38,X11,X36] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X36))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X36),X38))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X38)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_order__trans) ).
fof(fact_297_subset__trans,axiom,
! [X37,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),X37))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X37)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_subset__trans) ).
fof(fact_501_xt1_I6_J,axiom,
! [X38,X36,X11] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X36),X11))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X38),X36))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X38),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_xt1_I6_J) ).
fof(fact_512_order__trans,axiom,
! [X38,X11,X36] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X36))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X36),X38))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X38)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_order__trans) ).
fof(fact_296_subset__trans,axiom,
! [X37,X5,X10] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X37))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X37)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_subset__trans) ).
fof(fact_502_xt1_I6_J,axiom,
! [X38,X36,X11] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X36),X11))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X38),X36))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X38),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_xt1_I6_J) ).
fof(fact_282_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_282_set__rev__mp) ).
fof(fact_285_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_285_set__mp) ).
fof(fact_279_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_279_in__mono) ).
fof(fact_220_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_220_subsetD) ).
fof(fact_514_order__trans,axiom,
! [X38,X11,X36] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X36))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X36),X38))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X38)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_order__trans) ).
fof(fact_298_subset__trans,axiom,
! [X37,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),X37))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X37)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_subset__trans) ).
fof(fact_504_xt1_I6_J,axiom,
! [X38,X36,X11] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X36),X11))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X38),X36))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X38),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_xt1_I6_J) ).
fof(fact_283_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_283_set__rev__mp) ).
fof(fact_286_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_286_set__mp) ).
fof(fact_280_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_280_in__mono) ).
fof(fact_221_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_221_subsetD) ).
fof(fact_513_order__trans,axiom,
! [X55,X56,X57] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X56),X57))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X57),X55))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X56),X55)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_order__trans) ).
fof(fact_86_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_86_le__trans) ).
fof(fact_503_xt1_I6_J,axiom,
! [X50,X51,X52] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X51),X52))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X50),X51))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X50),X52)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_xt1_I6_J) ).
fof(fact_510_order__trans,axiom,
! [X38,X11,X36] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X11),X36))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X36),X38))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X11),X38)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_order__trans) ).
fof(fact_500_xt1_I6_J,axiom,
! [X38,X36,X11] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X36),X11))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X38),X36))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X38),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_xt1_I6_J) ).
fof(fact_663_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_663_le__less__Suc__eq) ).
fof(fact_596_add__diff__assoc2,axiom,
! [X23,X22,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
=> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X24),X22)),X23) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X24),X23)),X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_add__diff__assoc2) ).
fof(fact_595_diff__add__assoc2,axiom,
! [X23,X22,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X24),X23)),X22) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X24),X22)),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_diff__add__assoc2) ).
fof(fact_652_finite__nat__set__iff__bounded,axiom,
! [X43] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X43))
<=> ? [X35] :
! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X43))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X35)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_finite__nat__set__iff__bounded) ).
fof(fact_372_finite__nat__set__iff__bounded__le,axiom,
! [X43] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X43))
<=> ? [X35] :
! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X43))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X35)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_finite__nat__set__iff__bounded__le) ).
fof(fact_674_bounded__nat__set__is__finite,axiom,
! [X17,X43] :
( ! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X43))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X30),X17)) )
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_bounded__nat__set__is__finite) ).
fof(fact_126_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(minus_minus_nat(X25),X16) = hAPP_nat_nat(minus_minus_nat(X17),X16)
<=> X25 = X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_eq__diff__iff) ).
fof(fact_229_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_229_Suc__le__D) ).
fof(fact_630_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_630_Suc__lessI) ).
fof(fact_662_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_662_Suc__leI) ).
fof(fact_119_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_119_le__Suc__eq) ).
fof(fact_597_diff__add__assoc,axiom,
! [X23,X22,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X23),X24)),X22) = hAPP_nat_nat(plus_plus_nat(X23),hAPP_nat_nat(minus_minus_nat(X24),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_diff__add__assoc) ).
fof(fact_601_add__diff__assoc,axiom,
! [X23,X22,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
=> hAPP_nat_nat(plus_plus_nat(X23),hAPP_nat_nat(minus_minus_nat(X24),X22)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X23),X24)),X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_add__diff__assoc) ).
fof(fact_605_diff__diff__right,axiom,
! [X23,X22,X24] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X22),X24))
=> hAPP_nat_nat(minus_minus_nat(X23),hAPP_nat_nat(minus_minus_nat(X24),X22)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X23),X22)),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_diff__diff__right) ).
fof(fact_665_diff__less__Suc,axiom,
! [X15,X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X15),X14)),hAPP_nat_nat(suc,X15))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_diff__less__Suc) ).
fof(fact_655_less__add__Suc1,axiom,
! [X23,X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X23),X15)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_less__add__Suc1) ).
fof(fact_656_less__add__Suc2,axiom,
! [X23,X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X15),X23)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_less__add__Suc2) ).
fof(fact_622_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(plus_plus_nat(X24),X15))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_trans__less__add1) ).
fof(fact_615_termination__basic__simps_I1_J,axiom,
! [X80,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(plus_plus_nat(X19),X80))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_termination__basic__simps_I1_J) ).
fof(fact_621_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(plus_plus_nat(X15),X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_trans__less__add2) ).
fof(fact_616_termination__basic__simps_I2_J,axiom,
! [X19,X18,X80] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X18),X80))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X18),hAPP_nat_nat(plus_plus_nat(X19),X80))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_termination__basic__simps_I2_J) ).
fof(fact_610_termination__basic__simps_I3_J,axiom,
! [X80,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(plus_plus_nat(X19),X80))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_termination__basic__simps_I3_J) ).
fof(fact_588_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(plus_plus_nat(X24),X15))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_trans__le__add1) ).
fof(fact_611_termination__basic__simps_I4_J,axiom,
! [X19,X18,X80] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X18),X80))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X18),hAPP_nat_nat(plus_plus_nat(X19),X80))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_termination__basic__simps_I4_J) ).
fof(fact_589_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(plus_plus_nat(X15),X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_trans__le__add2) ).
fof(fact_141_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_141_finite__surj) ).
fof(fact_135_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_135_finite__surj) ).
fof(fact_142_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_142_finite__surj) ).
fof(fact_136_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_136_finite__surj) ).
fof(fact_143_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_143_finite__surj) ).
fof(fact_137_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_137_finite__surj) ).
fof(fact_151_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_151_finite__surj) ).
fof(fact_152_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_152_finite__surj) ).
fof(fact_153_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_153_finite__surj) ).
fof(fact_145_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),image_nat_nat(X9,X5)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_finite__surj) ).
fof(fact_139_finite__surj,axiom,
! [X10,X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),image_pname_nat(X9,X5)))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_finite__surj) ).
fof(fact_150_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_150_finite__surj) ).
fof(fact_147_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_147_finite__surj) ).
fof(fact_148_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_148_finite__surj) ).
fof(fact_149_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_149_finite__surj) ).
fof(fact_144_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_144_finite__surj) ).
fof(fact_138_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_138_finite__surj) ).
fof(fact_146_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_146_finite__surj) ).
fof(fact_132_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_132_finite__surj) ).
fof(fact_133_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_133_finite__surj) ).
fof(fact_134_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_134_finite__surj) ).
fof(fact_140_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_140_finite__surj) ).
fof(fact_154_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_154_finite__surj) ).
fof(fact_131_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_131_finite__surj) ).
fof(fact_211_image__eqI,axiom,
! [X5,X31,X9,X11] :
( X31 = hAPP_pname_nat(X9,X11)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),image_pname_nat(X9,X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_image__eqI) ).
fof(fact_212_image__eqI,axiom,
! [X5,X31,X9,X11] :
( X31 = hAPP_a_nat(X9,X11)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),image_a_nat(X9,X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_image__eqI) ).
fof(fact_308_rev__image__eqI,axiom,
! [X31,X9,X11,X5] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X11),X5))
=> ( X31 = hAPP_pname_nat(X9,X11)
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),image_pname_nat(X9,X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_rev__image__eqI) ).
fof(fact_309_rev__image__eqI,axiom,
! [X31,X9,X11,X5] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X11),X5))
=> ( X31 = hAPP_a_nat(X9,X11)
=> hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),image_a_nat(X9,X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_rev__image__eqI) ).
fof(fact_213_image__eqI,axiom,
! [X5,X31,X9,X11] :
( X31 = hAPP_nat_pname(X9,X11)
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),image_nat_pname(X9,X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_image__eqI) ).
fof(fact_310_rev__image__eqI,axiom,
! [X31,X9,X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( X31 = hAPP_nat_pname(X9,X11)
=> hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),image_nat_pname(X9,X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_rev__image__eqI) ).
fof(fact_214_image__eqI,axiom,
! [X5,X31,X9,X11] :
( X31 = hAPP_nat_a(X9,X11)
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),image_nat_a(X9,X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_image__eqI) ).
fof(fact_215_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_215_image__eqI) ).
fof(fact_311_rev__image__eqI,axiom,
! [X31,X9,X11,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X11),X5))
=> ( X31 = hAPP_nat_a(X9,X11)
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),image_nat_a(X9,X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_rev__image__eqI) ).
fof(fact_312_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_312_rev__image__eqI) ).
fof(fact_635_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_635_less__Suc__eq) ).
fof(fact_659_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_659_less__Suc__eq__le) ).
fof(fact_677_lessE,axiom,
! [X23,X22] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X22))
=> ( X22 != hAPP_nat_nat(suc,X23)
=> ~ ! [X89] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X23),X89))
=> X22 != hAPP_nat_nat(suc,X89) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_lessE) ).
fof(fact_618_less__add__eq__less,axiom,
! [X15,X14,X22,X26] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X22),X26))
=> ( hAPP_nat_nat(plus_plus_nat(X15),X26) = hAPP_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_618_less__add__eq__less) ).
fof(fact_552_order__eq__iff,axiom,
! [X11,X36] :
( ( is_fun_pname_bool(X11)
& is_fun_pname_bool(X36) )
=> ( X11 = X36
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X36))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X36),X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_order__eq__iff) ).
fof(fact_542_order__antisym__conv,axiom,
! [X36,X11] :
( ( is_fun_pname_bool(X36)
& is_fun_pname_bool(X11) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X36),X11))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X36))
<=> X11 = X36 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_order__antisym__conv) ).
fof(fact_517_order__antisym,axiom,
! [X11,X36] :
( ( is_fun_pname_bool(X11)
& is_fun_pname_bool(X36) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X36))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X36),X11))
=> X11 = X36 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_order__antisym) ).
fof(fact_507_xt1_I5_J,axiom,
! [X36,X11] :
( ( is_fun_pname_bool(X36)
& is_fun_pname_bool(X11) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X36),X11))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X36))
=> X11 = X36 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_xt1_I5_J) ).
fof(fact_269_set__eq__subset,axiom,
! [X5,X10] :
( ( is_fun_pname_bool(X5)
& is_fun_pname_bool(X10) )
=> ( X5 = X10
<=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_set__eq__subset) ).
fof(fact_216_equalityI,axiom,
! [X5,X10] :
( ( is_fun_pname_bool(X5)
& is_fun_pname_bool(X10) )
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5))
=> X5 = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_equalityI) ).
fof(fact_554_order__eq__iff,axiom,
! [X11,X36] :
( ( is_fun_a_bool(X11)
& is_fun_a_bool(X36) )
=> ( X11 = X36
<=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X36))
& hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X36),X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_order__eq__iff) ).
fof(fact_544_order__antisym__conv,axiom,
! [X36,X11] :
( ( is_fun_a_bool(X36)
& is_fun_a_bool(X11) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X36),X11))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X36))
<=> X11 = X36 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_order__antisym__conv) ).
fof(fact_519_order__antisym,axiom,
! [X11,X36] :
( ( is_fun_a_bool(X11)
& is_fun_a_bool(X36) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X36))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X36),X11))
=> X11 = X36 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_order__antisym) ).
fof(fact_509_xt1_I5_J,axiom,
! [X36,X11] :
( ( is_fun_a_bool(X36)
& is_fun_a_bool(X11) )
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X36),X11))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X36))
=> X11 = X36 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_xt1_I5_J) ).
fof(fact_271_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_271_set__eq__subset) ).
fof(fact_218_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_218_equalityI) ).
fof(fact_550_order__eq__iff,axiom,
! [X36,X11] :
( ( hBOOL(X11)
<=> hBOOL(X36) )
<=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X11),X36))
& hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X36),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_order__eq__iff) ).
fof(fact_540_order__antisym__conv,axiom,
! [X36,X11] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X36),X11))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X11),X36))
<=> ( hBOOL(X11)
<=> hBOOL(X36) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_order__antisym__conv) ).
fof(fact_515_order__antisym,axiom,
! [X11,X36] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X11),X36))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X36),X11))
=> ( hBOOL(X11)
<=> hBOOL(X36) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_order__antisym) ).
fof(fact_505_xt1_I5_J,axiom,
! [X36,X11] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X36),X11))
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X11),X36))
=> ( hBOOL(X11)
<=> hBOOL(X36) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_xt1_I5_J) ).
fof(fact_551_order__eq__iff,axiom,
! [X11,X36] :
( X11 = X36
<=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X36))
& hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X36),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_order__eq__iff) ).
fof(fact_541_order__antisym__conv,axiom,
! [X36,X11] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X36),X11))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X36))
<=> X11 = X36 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_order__antisym__conv) ).
fof(fact_516_order__antisym,axiom,
! [X11,X36] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X36))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X36),X11))
=> X11 = X36 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_order__antisym) ).
fof(fact_506_xt1_I5_J,axiom,
! [X36,X11] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X36),X11))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X36))
=> X11 = X36 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_xt1_I5_J) ).
fof(fact_270_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_270_set__eq__subset) ).
fof(fact_217_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_217_equalityI) ).
fof(fact_553_order__eq__iff,axiom,
! [X11,X36] :
( X11 = X36
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),X36))
& hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X36),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_order__eq__iff) ).
fof(fact_543_order__antisym__conv,axiom,
! [X36,X11] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X36),X11))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X11),X36))
<=> X11 = X36 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_order__antisym__conv) ).
fof(fact_518_order__antisym,axiom,
! [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),X58))
=> X58 = X59 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_order__antisym) ).
fof(fact_508_xt1_I5_J,axiom,
! [X53,X54] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X53),X54))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X54),X53))
=> X54 = X53 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_xt1_I5_J) ).
fof(fact_85_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_85_le__antisym) ).
fof(fact_631_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_631_less__SucI) ).
fof(fact_661_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_661_le__imp__less__Suc) ).
fof(fact_117_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_117_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_651_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_651_nat__less__cases) ).
fof(fact_78_Suc__diff__le,axiom,
! [X14,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15))
=> hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X15)),X14) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X15),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Suc__diff__le) ).
fof(fact_130_diff__le__self,axiom,
! [X15,X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X15),X14)),X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_diff__le__self) ).
fof(fact_673_less__imp__Suc__add,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> ? [X81] : X14 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X15),X81)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_less__imp__Suc__add) ).
fof(fact_657_less__iff__Suc__add,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X25),X17))
<=> ? [X81] : X17 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X25),X81)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_less__iff__Suc__add) ).
fof(fact_599_le__add__diff__inverse2,axiom,
! [X14,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15))
=> hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X15),X14)),X14) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_le__add__diff__inverse2) ).
fof(fact_1_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_1_finite__Collect__subsets) ).
fof(fact_2_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_2_finite__Collect__subsets) ).
fof(fact_3_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_3_finite__Collect__subsets) ).
fof(fact_5_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_5_finite__Collect__subsets) ).
fof(fact_4_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_4_finite__Collect__subsets) ).
fof(fact_535_ord__eq__le__trans,axiom,
! [X32,X31,X8] :
( ( hBOOL(X8)
<=> hBOOL(X31) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X31),X32))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X8),X32)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_ord__eq__le__trans) ).
fof(fact_520_xt1_I4_J,axiom,
! [X32,X31,X8] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X31),X8))
=> ( ( hBOOL(X31)
<=> hBOOL(X32) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X32),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_xt1_I4_J) ).
fof(fact_530_xt1_I3_J,axiom,
! [X32,X31,X8] :
( ( hBOOL(X8)
<=> hBOOL(X31) )
=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X32),X31))
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X32),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_xt1_I3_J) ).
fof(fact_525_ord__le__eq__trans,axiom,
! [X32,X8,X31] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X8),X31))
=> ( ( hBOOL(X31)
<=> hBOOL(X32) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X8),X32)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_ord__le__eq__trans) ).
fof(fact_641_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_641_nat__less__le) ).
fof(fact_640_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_640_le__eq__less__or__eq) ).
fof(fact_638_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_638_le__neq__implies__less) ).
fof(fact_644_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_644_termination__basic__simps_I5_J) ).
fof(fact_639_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_639_less__imp__le__nat) ).
fof(fact_637_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_637_less__or__eq__imp__le) ).
fof(fact_90_diff__commute,axiom,
! [X23,X24,X22] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X23),X24)),X22) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X23),X22)),X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_diff__commute) ).
fof(fact_103_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_103_finite__subset) ).
fof(fact_109_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_109_rev__finite__subset) ).
fof(fact_104_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_104_finite__subset) ).
fof(fact_110_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_110_rev__finite__subset) ).
fof(fact_105_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_105_finite__subset) ).
fof(fact_111_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_111_rev__finite__subset) ).
fof(fact_108_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_108_finite__subset) ).
fof(fact_114_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_114_rev__finite__subset) ).
fof(fact_107_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_107_finite__subset) ).
fof(fact_113_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_113_rev__finite__subset) ).
fof(fact_106_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_106_finite__subset) ).
fof(fact_112_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_112_rev__finite__subset) ).
fof(fact_602_le__add__diff__inverse,axiom,
! [X14,X15] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X15))
=> hAPP_nat_nat(plus_plus_nat(X14),hAPP_nat_nat(minus_minus_nat(X15),X14)) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_le__add__diff__inverse) ).
fof(fact_127_diff__diff__cancel,axiom,
! [X23,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X23),X14))
=> hAPP_nat_nat(minus_minus_nat(X14),hAPP_nat_nat(minus_minus_nat(X14),X23)) = X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_diff__diff__cancel) ).
fof(fact_598_le__imp__diff__is__add,axiom,
! [X16,X33,X82] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X33),X82))
=> ( hAPP_nat_nat(minus_minus_nat(X82),X33) = X16
<=> X82 = hAPP_nat_nat(plus_plus_nat(X16),X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_le__imp__diff__is__add) ).
fof(fact_586_le__iff__add,axiom,
! [X25,X17] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X25),X17))
<=> ? [X81] : X17 = hAPP_nat_nat(plus_plus_nat(X25),X81) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_le__iff__add) ).
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_567_assms_I4_J,axiom,
! [X78] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X78),u))
=> hBOOL(wt(the_com(body(X78)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_assms_I4_J) ).
fof(fact_646_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_646_nat__neq__iff) ).
fof(fact_582_diff__cancel,axiom,
! [X22,X15,X14] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X22),X15)),hAPP_nat_nat(plus_plus_nat(X22),X14)) = hAPP_nat_nat(minus_minus_nat(X15),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_diff__cancel) ).
fof(fact_583_diff__cancel2,axiom,
! [X15,X22,X14] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X15),X22)),hAPP_nat_nat(plus_plus_nat(X14),X22)) = hAPP_nat_nat(minus_minus_nat(X15),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_diff__cancel2) ).
fof(fact_576_nat__add__assoc,axiom,
! [X15,X14,X22] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X15),X14)),X22) = hAPP_nat_nat(plus_plus_nat(X15),hAPP_nat_nat(plus_plus_nat(X14),X22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_nat__add__assoc) ).
fof(fact_581_diff__diff__left,axiom,
! [X23,X24,X22] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X23),X24)),X22) = hAPP_nat_nat(minus_minus_nat(X23),hAPP_nat_nat(plus_plus_nat(X24),X22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_diff__diff__left) ).
fof(fact_555_linorder__linear,axiom,
! [X74,X75] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X74),X75))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X75),X74)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_linorder__linear) ).
fof(fact_88_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_88_nat__le__linear) ).
fof(fact_585_le__add1,axiom,
! [X14,X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),hAPP_nat_nat(plus_plus_nat(X14),X15))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_le__add1) ).
fof(fact_584_le__add2,axiom,
! [X14,X15] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),hAPP_nat_nat(plus_plus_nat(X15),X14))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_le__add2) ).
fof(fact_287_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_287_mem__def) ).
fof(fact_288_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_288_mem__def) ).
fof(fact_289_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_289_mem__def) ).
fof(fact_685_diff__is__0__eq,axiom,
! [X25,X17] :
( hAPP_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_685_diff__is__0__eq) ).
fof(fact_684_diff__is__0__eq_H,axiom,
! [X15,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14))
=> hAPP_nat_nat(minus_minus_nat(X15),X14) = zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_diff__is__0__eq_H) ).
fof(fact_414_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_414_ex__in__conv) ).
fof(fact_415_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_415_ex__in__conv) ).
fof(fact_568_diff__Suc__eq__diff__pred,axiom,
! [X15,X14] : hAPP_nat_nat(minus_minus_nat(X15),hAPP_nat_nat(suc,X14)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X15),one_one_nat)),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_diff__Suc__eq__diff__pred) ).
fof(fact_437_bot__unique,axiom,
! [X8] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X8),bot_bot_bool))
<=> ( hBOOL(X8)
<=> hBOOL(bot_bot_bool) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_bot__unique) ).
fof(fact_432_le__bot,axiom,
! [X8] :
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X8),bot_bot_bool))
=> ( hBOOL(X8)
<=> hBOOL(bot_bot_bool) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_le__bot) ).
fof(fact_465_subset__empty,axiom,
! [X5] :
( is_fun_pname_bool(X5)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),bot_bo844097828e_bool))
<=> X5 = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_subset__empty) ).
fof(fact_436_bot__unique,axiom,
! [X8] :
( is_fun_pname_bool(X8)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X8),bot_bo844097828e_bool))
<=> X8 = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_bot__unique) ).
fof(fact_431_le__bot,axiom,
! [X8] :
( is_fun_pname_bool(X8)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X8),bot_bo844097828e_bool))
=> X8 = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_le__bot) ).
fof(fact_466_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_466_subset__empty) ).
fof(fact_439_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_439_bot__unique) ).
fof(fact_434_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_434_le__bot) ).
fof(fact_650_less__not__refl3,axiom,
! [X83,X84] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X83),X84))
=> X83 != X84 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_less__not__refl3) ).
fof(fact_649_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_649_less__not__refl2) ).
fof(fact_11_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_11_finite__imageI) ).
fof(fact_7_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_7_finite__imageI) ).
fof(fact_12_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_12_finite__imageI) ).
fof(fact_8_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_8_finite__imageI) ).
fof(fact_13_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_13_finite__imageI) ).
fof(fact_9_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_9_finite__imageI) ).
fof(fact_21_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_21_finite__imageI) ).
fof(fact_20_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_20_finite__imageI) ).
fof(fact_19_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_19_finite__imageI) ).
fof(fact_18_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_18_finite__imageI) ).
fof(fact_15_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_15_finite__imageI) ).
fof(fact_16_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_16_finite__imageI) ).
fof(fact_17_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_17_finite__imageI) ).
fof(fact_14_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_14_finite__imageI) ).
fof(fact_10_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_10_finite__imageI) ).
fof(fact_22_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_22_finite__imageI) ).
fof(fact_413_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_413_ex__in__conv) ).
fof(fact_612_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_612_lessI) ).
fof(fact_577_nat__add__left__commute,axiom,
! [X18,X19,X80] : hAPP_nat_nat(plus_plus_nat(X18),hAPP_nat_nat(plus_plus_nat(X19),X80)) = hAPP_nat_nat(plus_plus_nat(X19),hAPP_nat_nat(plus_plus_nat(X18),X80)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_nat__add__left__commute) ).
fof(fact_572_add__Suc,axiom,
! [X15,X14] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,X15)),X14) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X15),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_add__Suc) ).
fof(fact_698_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_698_le__0__eq) ).
fof(fact_440_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_440_bot__unique) ).
fof(fact_435_le__bot,axiom,
! [X45] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X45),bot_bot_nat))
=> X45 = bot_bot_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_le__bot) ).
fof(fact_464_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_464_subset__empty) ).
fof(fact_438_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_438_bot__unique) ).
fof(fact_433_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_433_le__bot) ).
fof(fact_680_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_680_zero__less__Suc) ).
fof(fact_123_diff__Suc__Suc,axiom,
! [X15,X14] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X15)),hAPP_nat_nat(suc,X14)) = hAPP_nat_nat(minus_minus_nat(X15),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_diff__Suc__Suc) ).
fof(fact_573_add__Suc__shift,axiom,
! [X15,X14] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,X15)),X14) = hAPP_nat_nat(plus_plus_nat(X15),hAPP_nat_nat(suc,X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_add__Suc__shift) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
! [X92,X93,X94] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X92,X93),X94) = hAPP_bool_bool(hAPP_f1748468828l_bool(X92,X94),hAPP_f54304608l_bool(X93,X94)),
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__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O,axiom,
! [X92,X93,X94] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X92,X93),X94) = hAPP_bool_bool(hAPP_f1476298914l_bool(X92,X94),hAPP_f1664156314l_bool(X93,X94)),
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,
! [X92,X93,X94] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X92,X93),X94) = hAPP_bool_bool(hAPP_f198738859l_bool(X92,X94),hAPP_fun_a_bool_bool(X93,X94)),
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,
! [X92,X93,X94] : hAPP_nat_bool(cOMBS_nat_bool_bool(X92,X93),X94) = hAPP_bool_bool(hAPP_n1006566506l_bool(X92,X94),hAPP_nat_bool(X93,X94)),
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__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [X92,X93,X94] : hAPP_pname_bool(cOMBS_568398431l_bool(X92,X93),X94) = hAPP_bool_bool(hAPP_p393069232l_bool(X92,X94),hAPP_pname_bool(X93,X94)),
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,
! [X92,X93,X94] : hAPP_a_bool(cOMBS_a_bool_bool(X92,X93),X94) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X92,X94),hAPP_a_bool(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
fof(fact_580_diff__add__inverse,axiom,
! [X14,X15] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X14),X15)),X14) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_diff__add__inverse) ).
fof(fact_579_diff__add__inverse2,axiom,
! [X15,X14] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X15),X14)),X14) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_diff__add__inverse2) ).
fof(fact_571_add__Suc__right,axiom,
! [X15,X14] : hAPP_nat_nat(plus_plus_nat(X15),hAPP_nat_nat(suc,X14)) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X15),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_add__Suc__right) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H,axiom,
! [X92,X93,X94] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X92),X93),X94) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X92,X94),X93),
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__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom,
! [X92,X93,X94] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X92),X93),X94) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X92,X94),X93),
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,
! [X92,X93,X94] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X92),X93),X94) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X92,X94),X93),
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__Com__Opn,axiom,
! [X92,X93,X94] : hAPP_f54304608l_bool(hAPP_p130839763l_bool(cOMBC_615407716e_bool(X92),X93),X94) = hAPP_pname_bool(hAPP_f654413245e_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opn) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__021,axiom,
! [X92,X93,X94] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X92),X93),X94) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__021) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona,axiom,
! [X92,X93,X94] : hAPP_f54304608l_bool(hAPP_n215258509l_bool(cOMBC_385542954t_bool(X92),X93),X94) = hAPP_nat_bool(hAPP_f800510211t_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
! [X92,X93,X94] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X92),X93),X94) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X92,X94),X93),
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__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_024,axiom,
! [X92,X93,X94] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X92),X93),X94) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_024) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
! [X92,X93,X94] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X92),X93),X94) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X92,X94),X93),
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_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Nat__O,axiom,
! [X92,X93,X94] : hAPP_f1664156314l_bool(hAPP_n850744903l_bool(cOMBC_1666426608t_bool(X92),X93),X94) = hAPP_nat_bool(hAPP_f1066163005t_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Nat__O) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O,axiom,
! [X92,X93,X94] : hAPP_f1664156314l_bool(hAPP_p338031245l_bool(cOMBC_1004116266e_bool(X92),X93),X94) = hAPP_pname_bool(hAPP_f759274231e_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__,axiom,
! [X92,X93,X94] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X92),X93),X94) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO,axiom,
! [X92,X93,X94] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X92),X93),X94) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X92,X94),X93),
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__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat_000tc__,axiom,
! [X92,X93,X94] : hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(cOMBC_619334683t_bool(X92),X93),X94) = hAPP_nat_bool(hAPP_f282463732t_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat_000tc__) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname_000tc,axiom,
! [X92,X93,X94] : hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(X92),X93),X94) = hAPP_pname_bool(hAPP_f1794073134e_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname_000tc) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__,axiom,
! [X92,X93,X94] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(X92),X93),X94) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X92,X94),X93),
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,
! [X92,X93,X94] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(X92),X93),X94) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X92,X94),X93),
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_000t__a_000tc__HOL__Obool_U,axiom,
! [X92,X93,X94] : hAPP_nat_bool(hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(X92),X93),X94) = hAPP_a_bool(hAPP_nat_fun_a_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000t__a_000tc__HOL__Obool_U) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U,axiom,
! [X92,X93,X94] : hAPP_nat_bool(hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(X92),X93),X94) = hAPP_pname_bool(hAPP_n1025906991e_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [X92,X93,X94] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X92),X93),X94) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X92,X94),X93),
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__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
! [X92,X93,X94] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X92),X93),X94) = hAPP_nat_bool(hAPP_n1699378549t_bool(X92,X94),X93),
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__Com__Opname_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Oboo,axiom,
! [X92,X93,X94] : hAPP_pname_bool(hAPP_f654413245e_bool(cOMBC_267053842l_bool(X92),X93),X94) = hAPP_f54304608l_bool(hAPP_p130839763l_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Oboo) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom,
! [X92,X93,X94] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X92),X93),X94) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X92,X94),X93),
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__fun_It__a_Mtc__HOL__Obool_J_000tc,axiom,
! [X92,X93,X94] : hAPP_pname_bool(hAPP_f1794073134e_bool(cOMBC_445755039l_bool(X92),X93),X94) = hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
! [X92,X93,X94] : hAPP_pname_bool(hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(X92),X93),X94) = hAPP_nat_bool(hAPP_p1499970991t_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U,axiom,
! [X92,X93,X94] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X92),X93),X94) = hAPP_pname_bool(hAPP_p61793385e_bool(X92,X94),X93),
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,
! [X92,X93,X94] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X92),X93),X94) = hAPP_a_bool(hAPP_p1534023578a_bool(X92,X94),X93),
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_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__,axiom,
! [X92,X93,X94] : hAPP_a_bool(hAPP_f1549043526a_bool(cOMBC_777206479l_bool(X92),X93),X94) = hAPP_f54304608l_bool(hAPP_a1392362872l_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__) ).
fof(help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc,axiom,
! [X92,X93,X94] : hAPP_a_bool(hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(X92),X93),X94) = hAPP_f1664156314l_bool(hAPP_a217006258l_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc) ).
fof(help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo,axiom,
! [X92,X93,X94] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X92),X93),X94) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X92,X94),X93),
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_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
! [X92,X93,X94] : hAPP_a_bool(hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(X92),X93),X94) = hAPP_nat_bool(hAPP_a_fun_nat_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
fof(help_COMBC_1_1_COMBC_000t__a_000tc__Com__Opname_000tc__HOL__Obool_U,axiom,
! [X92,X93,X94] : hAPP_a_bool(hAPP_p1534023578a_bool(cOMBC_a_pname_bool(X92),X93),X94) = hAPP_pname_bool(hAPP_a93125764e_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__Com__Opname_000tc__HOL__Obool_U) ).
fof(help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U,axiom,
! [X92,X93,X94] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X92),X93),X94) = hAPP_a_bool(hAPP_a_fun_a_bool(X92,X94),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).
fof(fact_545_order__eq__refl,axiom,
! [X36,X11] :
( ( hBOOL(X11)
<=> hBOOL(X36) )
=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X11),X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_order__eq__refl) ).
fof(help_fimplies_1_1_U,axiom,
! [X93,X92] :
( hBOOL(X92)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X92),X93)) ),
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_016,axiom,
! [X92,X93,X94] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X92,X93),X94) = hAPP_b589554111l_bool(X92,hAPP_f1664156314l_bool(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_016) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_013,axiom,
! [X92,X93,X94] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X92,X93),X94) = hAPP_b589554111l_bool(X92,hAPP_f54304608l_bool(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_013) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010,axiom,
! [X92,X93,X94] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X92,X93),X94) = hAPP_b589554111l_bool(X92,hAPP_fun_a_bool_bool(X93,X94)),
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__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
! [X92,X93,X94] : hAPP_a1392362872l_bool(cOMBB_743407885bool_a(X92,X93),X94) = hAPP_f103356543l_bool(X92,hAPP_a_fun_nat_bool(X93,X94)),
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_007,axiom,
! [X92,X93,X94] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X92,X93),X94) = hAPP_b589554111l_bool(X92,hAPP_pname_bool(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_004,axiom,
! [X92,X93,X94] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X92,X93),X94) = hAPP_b589554111l_bool(X92,hAPP_nat_bool(X93,X94)),
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,axiom,
! [X92,X93,X94] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X92,X93),X94) = hAPP_b589554111l_bool(X92,hAPP_a_bool(X93,X94)),
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__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__009,axiom,
! [X92,X93,X94] : hAPP_f282463732t_bool(cOMBB_164527437a_bool(X92,X93),X94) = hAPP_n1699378549t_bool(X92,hAPP_fun_a_bool_nat(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__009) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__014,axiom,
! [X92,X93,X94] : hAPP_f1066163005t_bool(cOMBB_1896684278e_bool(X92,X93),X94) = hAPP_n1699378549t_bool(X92,hAPP_f921600141ol_nat(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__014) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [X92,X93,X94] : hAPP_a_fun_nat_bool(cOMBB_1321347587bool_a(X92,X93),X94) = hAPP_n1699378549t_bool(X92,hAPP_a_nat(X93,X94)),
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__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__022,axiom,
! [X92,X93,X94] : hAPP_p130839763l_bool(cOMBB_928955006_pname(X92,X93),X94) = hAPP_f103356543l_bool(X92,hAPP_p1499970991t_bool(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__022) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__005,axiom,
! [X92,X93,X94] : hAPP_p1499970991t_bool(cOMBB_523834888_pname(X92,X93),X94) = hAPP_n1699378549t_bool(X92,hAPP_pname_nat(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__005) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__012,axiom,
! [X92,X93,X94] : hAPP_f800510211t_bool(cOMBB_1250273980t_bool(X92,X93),X94) = hAPP_n1699378549t_bool(X92,hAPP_f22106695ol_nat(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__012) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__020,axiom,
! [X92,X93,X94] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(X92,X93),X94) = hAPP_f103356543l_bool(X92,hAPP_n1699378549t_bool(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__020) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__003,axiom,
! [X92,X93,X94] : hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(X92,X93),X94) = hAPP_n1699378549t_bool(X92,hAPP_nat_nat(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__003) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_015,axiom,
! [X92,X93,X94] : hAPP_f654413245e_bool(cOMBB_141086128t_bool(X92,X93),X94) = hAPP_p61793385e_bool(X92,hAPP_f1291551745_pname(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_015) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On,axiom,
! [X92,X93,X94] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(X92,X93),X94) = hAPP_bool_bool(X92,hAPP_f54304608l_bool(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_017,axiom,
! [X92,X93,X94] : hAPP_f759274231e_bool(cOMBB_598082538e_bool(X92,X93),X94) = hAPP_p61793385e_bool(X92,hAPP_f1297739591_pname(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_017) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op,axiom,
! [X92,X93,X94] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X92,X93),X94) = hAPP_bool_bool(X92,hAPP_f1664156314l_bool(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_011,axiom,
! [X92,X93,X94] : hAPP_f1794073134e_bool(cOMBB_1693087065a_bool(X92,X93),X94) = hAPP_p61793385e_bool(X92,hAPP_f1128469712_pname(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_011) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H,axiom,
! [X92,X93,X94] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X92,X93),X94) = hAPP_bool_bool(X92,hAPP_fun_a_bool_bool(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_023,axiom,
! [X92,X93,X94] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(X92,X93),X94) = hAPP_f434788991l_bool(X92,hAPP_n1025906991e_bool(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_023) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___018,axiom,
! [X92,X93,X94] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(X92,X93),X94) = hAPP_f1631501043l_bool(X92,hAPP_nat_fun_a_bool(X93,X94)),
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___018) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_006,axiom,
! [X92,X93,X94] : hAPP_n1025906991e_bool(cOMBB_1212655066ol_nat(X92,X93),X94) = hAPP_p61793385e_bool(X92,hAPP_nat_pname(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_006) ).
fof(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat,axiom,
! [X92,X93,X94] : hAPP_nat_fun_a_bool(cOMBB_1885489796ol_nat(X92,X93),X94) = hAPP_a_fun_a_bool(X92,hAPP_nat_a(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
! [X92,X93,X94] : hAPP_nat_bool(cOMBB_bool_bool_nat(X92,X93),X94) = hAPP_bool_bool(X92,hAPP_nat_bool(X93,X94)),
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_025,axiom,
! [X92,X93,X94] : hAPP_p338031245l_bool(cOMBB_408569982_pname(X92,X93),X94) = hAPP_f434788991l_bool(X92,hAPP_p61793385e_bool(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_025) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___019,axiom,
! [X92,X93,X94] : hAPP_p1824510254l_bool(cOMBB_392435466_pname(X92,X93),X94) = hAPP_f1631501043l_bool(X92,hAPP_p1534023578a_bool(X93,X94)),
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___019) ).
fof(help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_008,axiom,
! [X92,X93,X94] : hAPP_p61793385e_bool(cOMBB_542850580_pname(X92,X93),X94) = hAPP_p61793385e_bool(X92,hAPP_pname_pname(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_008) ).
fof(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna,axiom,
! [X92,X93,X94] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X92,X93),X94) = hAPP_a_fun_a_bool(X92,hAPP_pname_a(X93,X94)),
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,
! [X92,X93,X94] : hAPP_pname_bool(cOMBB_647938656_pname(X92,X93),X94) = hAPP_bool_bool(X92,hAPP_pname_bool(X93,X94)),
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_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
! [X92,X93,X94] : hAPP_a217006258l_bool(cOMBB_1137537805bool_a(X92,X93),X94) = hAPP_f434788991l_bool(X92,hAPP_a93125764e_bool(X93,X94)),
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,
! [X92,X93,X94] : hAPP_a85458249l_bool(cOMBB_472261505bool_a(X92,X93),X94) = hAPP_f1631501043l_bool(X92,hAPP_a_fun_a_bool(X93,X94)),
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_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom,
! [X92,X93,X94] : hAPP_a93125764e_bool(cOMBB_610033911bool_a(X92,X93),X94) = hAPP_p61793385e_bool(X92,hAPP_a_pname(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
fof(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a_U,axiom,
! [X92,X93,X94] : hAPP_a_fun_a_bool(cOMBB_a_fun_a_bool_a(X92,X93),X94) = hAPP_a_fun_a_bool(X92,hAPP_a_a(X93,X94)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a_U) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U,axiom,
! [X92,X93,X94] : hAPP_a_bool(cOMBB_bool_bool_a(X92,X93),X94) = hAPP_bool_bool(X92,hAPP_a_bool(X93,X94)),
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_546_order__eq__refl,axiom,
! [X11,X36] :
( X11 = X36
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_order__eq__refl) ).
fof(fact_273_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_273_equalityD1) ).
fof(fact_276_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_276_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(fact_547_order__eq__refl,axiom,
! [X11,X36] :
( X11 = X36
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_order__eq__refl) ).
fof(fact_272_equalityD1,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_equalityD1) ).
fof(fact_275_equalityD2,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_equalityD2) ).
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_549_order__eq__refl,axiom,
! [X11,X36] :
( X11 = X36
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_order__eq__refl) ).
fof(fact_274_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_274_equalityD1) ).
fof(fact_277_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_277_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_548_order__eq__refl,axiom,
! [X72,X73] :
( X72 = X73
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X72),X73)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_order__eq__refl) ).
fof(fact_87_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_87_eq__imp__le) ).
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_369_order__refl,axiom,
! [X11] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_order__refl) ).
fof(fact_267_subset__refl,axiom,
! [X5] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_subset__refl) ).
fof(fact_368_order__refl,axiom,
! [X11] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_order__refl) ).
fof(fact_266_subset__refl,axiom,
! [X5] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_subset__refl) ).
fof(fact_370_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_370_order__refl) ).
fof(fact_268_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_268_subset__refl) ).
fof(fact_371_order__refl,axiom,
! [X42] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X42),X42)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_order__refl) ).
fof(fact_89_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_89_le__refl) ).
fof(fact_367_order__refl,axiom,
! [X11] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X11),X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_order__refl) ).
fof(fact_681_add__is__1,axiom,
! [X25,X17] :
( hAPP_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_681_add__is__1) ).
fof(fact_682_one__is__add,axiom,
! [X25,X17] :
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_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_682_one__is__add) ).
fof(fact_443_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_443_bot__least) ).
fof(fact_393_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_393_empty__subsetI) ).
fof(fact_441_bot__least,axiom,
! [X8] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_bot__least) ).
fof(fact_392_empty__subsetI,axiom,
! [X5] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_empty__subsetI) ).
fof(fact_444_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_444_bot__least) ).
fof(fact_394_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_394_empty__subsetI) ).
fof(fact_699_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_699_less__eq__nat_Osimps_I1_J) ).
fof(fact_679_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_679_le0) ).
fof(fact_445_bot__least,axiom,
! [X46] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),X46)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_bot__least) ).
fof(fact_442_bot__least,axiom,
! [X8] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_bot__least) ).
fof(fact_687_diffs0__imp__equal,axiom,
! [X15,X14] :
( hAPP_nat_nat(minus_minus_nat(X15),X14) = zero_zero_nat
=> ( hAPP_nat_nat(minus_minus_nat(X14),X15) = zero_zero_nat
=> X15 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_diffs0__imp__equal) ).
fof(fact_574_nat__add__right__cancel,axiom,
! [X25,X16,X17] :
( hAPP_nat_nat(plus_plus_nat(X25),X16) = hAPP_nat_nat(plus_plus_nat(X17),X16)
<=> X25 = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_nat__add__right__cancel) ).
fof(fact_575_nat__add__left__cancel,axiom,
! [X16,X25,X17] :
( hAPP_nat_nat(plus_plus_nat(X16),X25) = hAPP_nat_nat(plus_plus_nat(X16),X17)
<=> X25 = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_nat__add__left__cancel) ).
fof(fact_569_diff__Suc__1,axiom,
! [X14] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X14)),one_one_nat) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_diff__Suc__1) ).
fof(fact_683_diff__add__0,axiom,
! [X14,X15] : hAPP_nat_nat(minus_minus_nat(X14),hAPP_nat_nat(plus_plus_nat(X14),X15)) = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_diff__add__0) ).
fof(fact_670_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_670_less__eq__Suc__le__raw) ).
fof(fact_429_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_429_bot__apply) ).
fof(fact_426_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_426_bot__fun__def) ).
fof(fact_428_bot__apply,axiom,
! [X11] :
( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X11))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_bot__apply) ).
fof(fact_425_bot__fun__def,axiom,
! [X30] :
( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X30))
<=> hBOOL(bot_bot_bool) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_bot__fun__def) ).
fof(fact_430_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_430_bot__apply) ).
fof(fact_427_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_427_bot__fun__def) ).
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_82_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_82_nat_Oinject) ).
fof(fact_81_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_81_Suc__inject) ).
fof(fact_578_nat__add__commute,axiom,
! [X15,X14] : hAPP_nat_nat(plus_plus_nat(X15),X14) = hAPP_nat_nat(plus_plus_nat(X14),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_nat__add__commute) ).
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__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_pname(hAPP_f1128469712_pname(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_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_000t__a_000tc__Com__Opname,axiom,
! [X1,X2] :
( is_a(X2)
=> is_pname(hAPP_a_pname(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__Com__Opname) ).
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,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_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_hAPP_000t__a_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__H,axiom,
! [X1,X2] :
( is_a(X2)
=> is_fun1661590463l_bool(hAPP_a217006258l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__H) ).
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_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun1661590463l_bool(cOMBB_307249310e_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_) ).
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_000tc__Com__Opname_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H,axiom,
! [X1,X2] :
( is_pname(X2)
=> is_fun949378684l_bool(hAPP_p1824510254l_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H) ).
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_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun949378684l_bool(cOMBB_2140588453a_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool) ).
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__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opname_Mtc__H,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_pname_bool(hAPP_f1794073134e_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opname_Mtc__H) ).
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_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__H,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun_a_bool(hAPP_f1051908748a_bool(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__H) ).
fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [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__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(help_fNot_2_1_U,axiom,
! [X92] :
( hBOOL(X92)
| hBOOL(hAPP_bool_bool(fNot,X92)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
fof(fact_467_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_467_image__is__empty) ).
fof(fact_469_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_469_empty__is__image) ).
fof(fact_606_Suc__eq__plus1,axiom,
! [X14] : hAPP_nat_nat(suc,X14) = hAPP_nat_nat(plus_plus_nat(X14),one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_Suc__eq__plus1) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom,
! [X1,X2] : is_pname(hAPP_f1291551745_pname(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Com__Opname,axiom,
! [X1,X2] : is_pname(hAPP_nat_pname(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Com__Opname) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000t__a,axiom,
! [X1,X2] : is_a(hAPP_nat_a(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000t__a) ).
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__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__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__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__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_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_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_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_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opna,axiom,
! [X1,X2] : is_fun_pname_bool(hAPP_f654413245e_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opna) ).
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_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__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_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL,axiom,
! [X1,X2] : is_fun_a_bool(hAPP_f1549043526a_bool(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL) ).
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_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__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(fact_607_Suc__eq__plus1__left,axiom,
! [X14] : hAPP_nat_nat(suc,X14) = hAPP_nat_nat(plus_plus_nat(one_one_nat),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_Suc__eq__plus1__left) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool,axiom,
! [X92,X93] :
( is_bool(X92)
=> hAPP_f54304608l_bool(cOMBK_1994329625t_bool(X92),X93) = X92 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo,axiom,
! [X92,X93] :
( is_bool(X92)
=> hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(X92),X93) = X92 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U,axiom,
! [X92,X93] :
( is_bool(X92)
=> hAPP_fun_a_bool_bool(cOMBK_324466864a_bool(X92),X93) = X92 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
! [X92,X93] :
( is_bool(X92)
=> hAPP_nat_bool(cOMBK_bool_nat(X92),X93) = X92 ),
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__Com__Opname_U,axiom,
! [X92,X93] :
( is_bool(X92)
=> hAPP_pname_bool(cOMBK_bool_pname(X92),X93) = X92 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) ).
fof(help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U,axiom,
! [X92,X93] :
( is_a(X92)
=> hAPP_pname_a(cOMBK_a_pname(X92),X93) = X92 ),
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,
! [X92,X93] :
( is_bool(X92)
=> hAPP_a_bool(cOMBK_bool_a(X92),X93) = X92 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U) ).
fof(fact_83_Suc__n__not__n,axiom,
! [X14] : hAPP_nat_nat(suc,X14) != X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Suc__n__not__n) ).
fof(fact_84_n__not__Suc__n,axiom,
! [X14] : X14 != hAPP_nat_nat(suc,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_n__not__Suc__n) ).
fof(fact_688_diff__self__eq__0,axiom,
! [X15] : hAPP_nat_nat(minus_minus_nat(X15),X15) = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_diff__self__eq__0) ).
fof(fact_694_Suc__not__Zero,axiom,
! [X15] : hAPP_nat_nat(suc,X15) != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_Suc__not__Zero) ).
fof(fact_693_nat_Osimps_I3_J,axiom,
! [X90] : hAPP_nat_nat(suc,X90) != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_nat_Osimps_I3_J) ).
fof(fact_691_Suc__neq__Zero,axiom,
! [X15] : hAPP_nat_nat(suc,X15) != zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_Suc__neq__Zero) ).
fof(fact_696_Zero__not__Suc,axiom,
! [X15] : zero_zero_nat != hAPP_nat_nat(suc,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_Zero__not__Suc) ).
fof(fact_695_nat_Osimps_I2_J,axiom,
! [X91] : zero_zero_nat != hAPP_nat_nat(suc,X91),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_nat_Osimps_I2_J) ).
fof(fact_692_Zero__neq__Suc,axiom,
! [X15] : zero_zero_nat != hAPP_nat_nat(suc,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_Zero__neq__Suc) ).
fof(fact_689_minus__nat_Odiff__0,axiom,
! [X15] : hAPP_nat_nat(minus_minus_nat(X15),zero_zero_nat) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_minus__nat_Odiff__0) ).
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_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [X1] :
( is_bool(X1)
=> is_fun1661590463l_bool(cOMBK_1857069011e_bool(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_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_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1] :
( is_bool(X1)
=> is_fun949378684l_bool(cOMBK_324466864a_bool(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_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_COMBK_000tc__HOL__Obool_000tc__Com__Opname,axiom,
! [X1] :
( is_bool(X1)
=> is_fun_pname_bool(cOMBK_bool_pname(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_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(fact_690_diff__0__eq__0,axiom,
! [X14] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X14) = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_diff__0__eq__0) ).
fof(fact_468_image__empty,axiom,
! [X9] : image_pname_a(X9,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_image__empty) ).
fof(fact_293_Collect__def,axiom,
! [X13] :
( is_fun1661590463l_bool(X13)
=> collec1974731493e_bool(X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_Collect__def) ).
fof(fact_294_Collect__def,axiom,
! [X13] :
( is_fun949378684l_bool(X13)
=> collect_fun_a_bool(X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_Collect__def) ).
fof(fact_291_Collect__def,axiom,
! [X13] :
( is_fun_pname_bool(X13)
=> collect_pname(X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_Collect__def) ).
fof(fact_290_Collect__def,axiom,
! [X13] :
( is_fun_a_bool(X13)
=> collect_a(X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_Collect__def) ).
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_fFalse_1_1_T,axiom,
! [X92] :
( is_bool(X92)
=> ( X92 = fTrue
| X92 = 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_420_empty__def,axiom,
bot_bo1701429464l_bool = collect_fun_nat_bool(cOMBK_1994329625t_bool(fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_empty__def) ).
fof(fact_424_empty__def,axiom,
bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_empty__def) ).
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(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(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_386_finite_OemptyI,axiom,
hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,bot_bo1701429464l_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_finite_OemptyI) ).
fof(fact_387_finite_OemptyI,axiom,
hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_finite_OemptyI) ).
fof(fact_388_finite_OemptyI,axiom,
hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,bot_bo1389914601l_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_finite_OemptyI) ).
fof(fact_391_finite_OemptyI,axiom,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_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_390_finite_OemptyI,axiom,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_finite_OemptyI) ).
fof(fact_389_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_389_finite_OemptyI) ).
fof(fact_686_One__nat__def,axiom,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_One__nat__def) ).
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_421_empty__def,axiom,
bot_bo1649642514l_bool = collec1974731493e_bool(cOMBK_1857069011e_bool(fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_empty__def) ).
fof(fact_422_empty__def,axiom,
bot_bo1389914601l_bool = collect_fun_a_bool(cOMBK_324466864a_bool(fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_empty__def) ).
fof(fact_419_empty__def,axiom,
bot_bo844097828e_bool = collect_pname(cOMBK_bool_pname(fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_empty__def) ).
fof(fact_423_empty__def,axiom,
bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_empty__def) ).
fof(gsy_v_pn,hypothesis,
is_pname(pn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_pn) ).
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_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__,axiom,
is_fun1661590463l_bool(bot_bo1649642514l_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__) ).
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_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc,axiom,
is_fun949378684l_bool(bot_bo1389914601l_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc) ).
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_697_bot__nat__def,axiom,
bot_bot_nat = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_bot__nat__def) ).
fof(i_0_895,plain,
! [X13,X5,X7] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X7),X5))
=> ( hBOOL(hAPP_f1935102916l_bool(X13,bot_bo1649642514l_bool))
=> ( ! [X76,X77] :
( ( is_fun_pname_bool(X76)
& is_fun1661590463l_bool(X77) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X77))
=> ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X76),X5))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X76),X77))
=> ( hBOOL(hAPP_f1935102916l_bool(X13,X77))
=> hBOOL(hAPP_f1935102916l_bool(X13,insert1325755072e_bool(X76,X77))) ) ) ) ) )
=> hBOOL(hAPP_f1935102916l_bool(X13,X7)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_560_finite__subset__induct]) ).
fof(i_0_896,plain,
! [X13,X5,X7] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X7),X5))
=> ( hBOOL(hAPP_f621171935l_bool(X13,bot_bo1389914601l_bool))
=> ( ! [X76,X77] :
( ( is_fun_a_bool(X76)
& is_fun949378684l_bool(X77) )
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X77))
=> ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X76),X5))
=> ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X76),X77))
=> ( hBOOL(hAPP_f621171935l_bool(X13,X77))
=> hBOOL(hAPP_f621171935l_bool(X13,insert_fun_a_bool(X76,X77))) ) ) ) ) )
=> hBOOL(hAPP_f621171935l_bool(X13,X7)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_561_finite__subset__induct]) ).
fof(i_0_897,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))
=> ( ! [X76,X77] :
( ( is_pname(X76)
& is_fun_pname_bool(X77) )
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X77))
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X76),X5))
=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X76),X77))
=> ( hBOOL(hAPP_f1664156314l_bool(X13,X77))
=> hBOOL(hAPP_f1664156314l_bool(X13,insert_pname(X76,X77))) ) ) ) ) )
=> hBOOL(hAPP_f1664156314l_bool(X13,X7)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_557_finite__subset__induct]) ).
fof(i_0_898,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))
=> ( ! [X76,X77] :
( ( is_a(X76)
& is_fun_a_bool(X77) )
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X77))
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X76),X5))
=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X76),X77))
=> ( hBOOL(hAPP_fun_a_bool_bool(X13,X77))
=> hBOOL(hAPP_fun_a_bool_bool(X13,insert_a(X76,X77))) ) ) ) ) )
=> hBOOL(hAPP_fun_a_bool_bool(X13,X7)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_558_finite__subset__induct]) ).
fof(i_0_899,plain,
! [X13,X5,X7] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X7),X5))
=> ( hBOOL(hAPP_f1637334154l_bool(X13,bot_bo1701429464l_bool))
=> ( ! [X76,X77] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X77))
=> ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X76),X5))
=> ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X76),X77))
=> ( hBOOL(hAPP_f1637334154l_bool(X13,X77))
=> hBOOL(hAPP_f1637334154l_bool(X13,insert_fun_nat_bool(X76,X77))) ) ) ) )
=> hBOOL(hAPP_f1637334154l_bool(X13,X7)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_559_finite__subset__induct]) ).
fof(i_0_900,plain,
! [X2951,X2952] : insert_fun_nat_bool(X2951,X2952) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X2951)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2952))),
inference(variable_rename,[status(thm)],[fact_233_insert__compr]) ).
fof(i_0_901,plain,
! [X3088] : collect_fun_nat_bool(X3088) = X3088,
inference(variable_rename,[status(thm)],[fact_292_Collect__def]) ).
fof(i_0_902,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))
=> ( ! [X76,X77] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X77))
=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X76),X5))
=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X76),X77))
=> ( hBOOL(hAPP_f54304608l_bool(X13,X77))
=> hBOOL(hAPP_f54304608l_bool(X13,insert_nat(X76,X77))) ) ) ) )
=> hBOOL(hAPP_f54304608l_bool(X13,X7)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_556_finite__subset__induct]) ).
fof(i_0_903,plain,
! [X2957,X2958] : insert_nat(X2957,X2958) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2957)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2958))),
inference(variable_rename,[status(thm)],[fact_236_insert__compr]) ).
fof(i_0_904,plain,
! [X3091] : collect_nat(X3091) = X3091,
inference(variable_rename,[status(thm)],[fact_295_Collect__def]) ).
fof(i_0_905,plain,
! [X13,X7] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> ( hBOOL(hAPP_f1935102916l_bool(X13,bot_bo1649642514l_bool))
=> ( ! [X30,X77] :
( ( is_fun_pname_bool(X30)
& is_fun1661590463l_bool(X77) )
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X77))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X30),X77))
=> ( hBOOL(hAPP_f1935102916l_bool(X13,X77))
=> hBOOL(hAPP_f1935102916l_bool(X13,insert1325755072e_bool(X30,X77))) ) ) ) )
=> hBOOL(hAPP_f1935102916l_bool(X13,X7)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_564_finite__induct]) ).
fof(i_0_906,plain,
! [X13,X7] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> ( hBOOL(hAPP_f621171935l_bool(X13,bot_bo1389914601l_bool))
=> ( ! [X30,X77] :
( ( is_fun_a_bool(X30)
& is_fun949378684l_bool(X77) )
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X77))
=> ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X30),X77))
=> ( hBOOL(hAPP_f621171935l_bool(X13,X77))
=> hBOOL(hAPP_f621171935l_bool(X13,insert_fun_a_bool(X30,X77))) ) ) ) )
=> hBOOL(hAPP_f621171935l_bool(X13,X7)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_565_finite__induct]) ).
fof(i_0_907,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X30),X5))
& ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X5)),hAPP_n215258509l_bool(cOMBC_385542954t_bool(cOMBB_1250273980t_bool(fequal_nat,X9)),hAPP_f22106695ol_nat(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_196_pigeonhole__infinite]) ).
fof(i_0_908,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X9,X5)))
=> ? [X30] :
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X30),X5))
& ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X5)),hAPP_p130839763l_bool(cOMBC_615407716e_bool(cOMBB_141086128t_bool(fequal_pname,X9)),hAPP_f1291551745_pname(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_190_pigeonhole__infinite]) ).
fof(i_0_909,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_200_pigeonhole__infinite]) ).
fof(i_0_910,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_201_pigeonhole__infinite]) ).
fof(i_0_911,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_202_pigeonhole__infinite]) ).
fof(i_0_912,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(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_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(fequal_nat,X9)),hAPP_nat_nat(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_193_pigeonhole__infinite]) ).
fof(i_0_913,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(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_p1499970991t_bool(cOMBC_nat_pname_bool(cOMBB_1212655066ol_nat(fequal_pname,X9)),hAPP_nat_pname(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_187_pigeonhole__infinite]) ).
fof(i_0_914,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(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_a_fun_nat_bool(cOMBC_nat_a_bool(cOMBB_1885489796ol_nat(fequal_a,X9)),hAPP_nat_a(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_199_pigeonhole__infinite]) ).
fof(i_0_915,plain,
! [X13,X7] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> ( hBOOL(hAPP_f1637334154l_bool(X13,bot_bo1701429464l_bool))
=> ( ! [X30,X77] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X77))
=> ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X30),X77))
=> ( hBOOL(hAPP_f1637334154l_bool(X13,X77))
=> hBOOL(hAPP_f1637334154l_bool(X13,insert_fun_nat_bool(X30,X77))) ) ) )
=> hBOOL(hAPP_f1637334154l_bool(X13,X7)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_563_finite__induct]) ).
fof(i_0_916,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),insert_pname(X11,X10)))
<=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_326_subset__insert]) ).
fof(i_0_917,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),insert_a(X11,X10)))
<=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_327_subset__insert]) ).
fof(i_0_918,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),insert_pname(X31,X10))) ),
inference(fof_simplification,[status(thm)],[fact_223_insertCI]) ).
fof(i_0_919,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),insert_a(X31,X10))) ),
inference(fof_simplification,[status(thm)],[fact_224_insertCI]) ).
fof(i_0_920,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),insert_nat(X11,X10)))
<=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ) ),
inference(fof_simplification,[status(thm)],[fact_325_subset__insert]) ).
fof(i_0_921,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))
=> ( insert_pname(X11,X5) = insert_pname(X11,X10)
<=> X5 = X10 ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_258_insert__ident]) ).
fof(i_0_922,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))
=> ( insert_a(X11,X5) = insert_a(X11,X10)
<=> X5 = X10 ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_259_insert__ident]) ).
fof(i_0_923,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),insert_nat(X31,X10))) ),
inference(fof_simplification,[status(thm)],[fact_222_insertCI]) ).
fof(i_0_924,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,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,insert_fun_a_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_62_card__insert__if]) ).
fof(i_0_925,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,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,insert1325755072e_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_61_card__insert__if]) ).
fof(i_0_926,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,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,insert_a(X11,X5)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_65_card__insert__if]) ).
fof(i_0_927,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,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,insert_pname(X11,X5)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_64_card__insert__if]) ).
fof(i_0_928,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,insert_fun_a_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_68_card__insert__disjoint]) ).
fof(i_0_929,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,insert1325755072e_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_67_card__insert__disjoint]) ).
fof(i_0_930,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,insert_a(X11,X5)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_71_card__insert__disjoint]) ).
fof(i_0_931,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,insert_pname(X11,X5)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_70_card__insert__disjoint]) ).
fof(i_0_932,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))
=> ( insert_nat(X11,X5) = insert_nat(X11,X10)
<=> X5 = X10 ) ) ),
inference(fof_simplification,[status(thm)],[fact_257_insert__ident]) ).
fof(i_0_933,plain,
! [X13,X8] :
( ( hBOOL(hAPP_f1664156314l_bool(X13,X8))
=> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X8)),X13)) = insert1325755072e_bool(X8,bot_bo1649642514l_bool) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(X13,X8))
=> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X8)),X13)) = bot_bo1649642514l_bool ) ),
inference(fof_simplification,[status(thm)],[fact_474_Collect__conv__if]) ).
fof(i_0_934,plain,
! [X13,X8] :
( ( hBOOL(hAPP_fun_a_bool_bool(X13,X8))
=> collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X8)),X13)) = insert_fun_a_bool(X8,bot_bo1389914601l_bool) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(X13,X8))
=> collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X8)),X13)) = bot_bo1389914601l_bool ) ),
inference(fof_simplification,[status(thm)],[fact_475_Collect__conv__if]) ).
fof(i_0_935,plain,
! [X13,X8] :
( ( hBOOL(hAPP_pname_bool(X13,X8))
=> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X8)),X13)) = insert_pname(X8,bot_bo844097828e_bool) )
& ( ~ hBOOL(hAPP_pname_bool(X13,X8))
=> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X8)),X13)) = bot_bo844097828e_bool ) ),
inference(fof_simplification,[status(thm)],[fact_471_Collect__conv__if]) ).
fof(i_0_936,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)) = 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_472_Collect__conv__if]) ).
fof(i_0_937,plain,
! [X13,X8] :
( ( hBOOL(hAPP_f1664156314l_bool(X13,X8))
=> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,X8)),X13)) = insert1325755072e_bool(X8,bot_bo1649642514l_bool) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(X13,X8))
=> collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,X8)),X13)) = bot_bo1649642514l_bool ) ),
inference(fof_simplification,[status(thm)],[fact_480_Collect__conv__if2]) ).
fof(i_0_938,plain,
! [X13,X8] :
( ( hBOOL(hAPP_fun_a_bool_bool(X13,X8))
=> collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,X8)),X13)) = insert_fun_a_bool(X8,bot_bo1389914601l_bool) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(X13,X8))
=> collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,X8)),X13)) = bot_bo1389914601l_bool ) ),
inference(fof_simplification,[status(thm)],[fact_481_Collect__conv__if2]) ).
fof(i_0_939,plain,
! [X13,X8] :
( ( hBOOL(hAPP_pname_bool(X13,X8))
=> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,X8)),X13)) = insert_pname(X8,bot_bo844097828e_bool) )
& ( ~ hBOOL(hAPP_pname_bool(X13,X8))
=> collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,X8)),X13)) = bot_bo844097828e_bool ) ),
inference(fof_simplification,[status(thm)],[fact_477_Collect__conv__if2]) ).
fof(i_0_940,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)) = 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_478_Collect__conv__if2]) ).
fof(i_0_941,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,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,insert_nat(X11,X5)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_63_card__insert__if]) ).
fof(i_0_942,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,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,insert_fun_nat_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_60_card__insert__if]) ).
fof(i_0_943,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,insert_nat(X11,X5)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_69_card__insert__disjoint]) ).
fof(i_0_944,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,insert_fun_nat_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_66_card__insert__disjoint]) ).
fof(i_0_945,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)) = 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_470_Collect__conv__if]) ).
fof(i_0_946,plain,
! [X13,X8] :
( ( hBOOL(hAPP_f54304608l_bool(X13,X8))
=> collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X8)),X13)) = insert_fun_nat_bool(X8,bot_bo1701429464l_bool) )
& ( ~ hBOOL(hAPP_f54304608l_bool(X13,X8))
=> collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X8)),X13)) = bot_bo1701429464l_bool ) ),
inference(fof_simplification,[status(thm)],[fact_473_Collect__conv__if]) ).
fof(i_0_947,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)) = 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_476_Collect__conv__if2]) ).
fof(i_0_948,plain,
! [X13,X8] :
( ( hBOOL(hAPP_f54304608l_bool(X13,X8))
=> collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,X8)),X13)) = insert_fun_nat_bool(X8,bot_bo1701429464l_bool) )
& ( ~ hBOOL(hAPP_f54304608l_bool(X13,X8))
=> collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,X8)),X13)) = bot_bo1701429464l_bool ) ),
inference(fof_simplification,[status(thm)],[fact_479_Collect__conv__if2]) ).
fof(i_0_949,plain,
! [X13] :
( bot_bo1701429464l_bool = collect_fun_nat_bool(X13)
<=> ! [X30] : ~ hBOOL(hAPP_f54304608l_bool(X13,X30)) ),
inference(fof_simplification,[status(thm)],[fact_408_empty__Collect__eq]) ).
fof(i_0_950,plain,
! [X13] :
( bot_bot_fun_nat_bool = collect_nat(X13)
<=> ! [X30] : ~ hBOOL(hAPP_nat_bool(X13,X30)) ),
inference(fof_simplification,[status(thm)],[fact_412_empty__Collect__eq]) ).
fof(i_0_951,plain,
! [X13] :
( collect_fun_nat_bool(X13) = bot_bo1701429464l_bool
<=> ! [X30] : ~ hBOOL(hAPP_f54304608l_bool(X13,X30)) ),
inference(fof_simplification,[status(thm)],[fact_399_Collect__empty__eq]) ).
fof(i_0_952,plain,
! [X13] :
( collect_nat(X13) = bot_bot_fun_nat_bool
<=> ! [X30] : ~ hBOOL(hAPP_nat_bool(X13,X30)) ),
inference(fof_simplification,[status(thm)],[fact_403_Collect__empty__eq]) ).
fof(i_0_953,plain,
! [X3756,X3757] :
( ~ hBOOL(hAPP_fun_a_bool_bool(p(insert_a(hAPP_pname_a(mgt_call,X3756),X3757)),insert_a(mgt(the_com(body(X3756))),bot_bot_fun_a_bool)))
| hBOOL(hAPP_fun_a_bool_bool(p(X3757),insert_a(hAPP_pname_a(mgt_call,X3756),bot_bot_fun_a_bool))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_562_assms_I2_J])]) ).
fof(i_0_954,plain,
! [X2961,X2962] : insert_a(X2961,X2962) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2961)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2962))),
inference(variable_rename,[status(thm)],[fact_238_insert__compr]) ).
fof(i_0_955,plain,
! [X3746,X3747,X3748] :
( ( is_fun_pname_bool(esk111_3(X3746,X3747,X3748))
| hBOOL(hAPP_f1935102916l_bool(X3746,X3748))
| ~ hBOOL(hAPP_f1935102916l_bool(X3746,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3748),X3747))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3748)) )
& ( is_fun1661590463l_bool(esk112_3(X3746,X3747,X3748))
| hBOOL(hAPP_f1935102916l_bool(X3746,X3748))
| ~ hBOOL(hAPP_f1935102916l_bool(X3746,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3748),X3747))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3748)) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk112_3(X3746,X3747,X3748)))
| hBOOL(hAPP_f1935102916l_bool(X3746,X3748))
| ~ hBOOL(hAPP_f1935102916l_bool(X3746,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3748),X3747))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3748)) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,esk111_3(X3746,X3747,X3748)),X3747))
| hBOOL(hAPP_f1935102916l_bool(X3746,X3748))
| ~ hBOOL(hAPP_f1935102916l_bool(X3746,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3748),X3747))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3748)) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,esk111_3(X3746,X3747,X3748)),esk112_3(X3746,X3747,X3748)))
| hBOOL(hAPP_f1935102916l_bool(X3746,X3748))
| ~ hBOOL(hAPP_f1935102916l_bool(X3746,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3748),X3747))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3748)) )
& ( hBOOL(hAPP_f1935102916l_bool(X3746,esk112_3(X3746,X3747,X3748)))
| hBOOL(hAPP_f1935102916l_bool(X3746,X3748))
| ~ hBOOL(hAPP_f1935102916l_bool(X3746,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3748),X3747))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3748)) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(X3746,insert1325755072e_bool(esk111_3(X3746,X3747,X3748),esk112_3(X3746,X3747,X3748))))
| hBOOL(hAPP_f1935102916l_bool(X3746,X3748))
| ~ hBOOL(hAPP_f1935102916l_bool(X3746,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3748),X3747))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3748)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_895])])])]) ).
fof(i_0_956,plain,
! [X2953,X2954] : insert1325755072e_bool(X2953,X2954) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X2953)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X2954))),
inference(variable_rename,[status(thm)],[fact_234_insert__compr]) ).
fof(i_0_957,plain,
! [X3751,X3752,X3753] :
( ( is_fun_a_bool(esk113_3(X3751,X3752,X3753))
| hBOOL(hAPP_f621171935l_bool(X3751,X3753))
| ~ hBOOL(hAPP_f621171935l_bool(X3751,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3753),X3752))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3753)) )
& ( is_fun949378684l_bool(esk114_3(X3751,X3752,X3753))
| hBOOL(hAPP_f621171935l_bool(X3751,X3753))
| ~ hBOOL(hAPP_f621171935l_bool(X3751,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3753),X3752))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3753)) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk114_3(X3751,X3752,X3753)))
| hBOOL(hAPP_f621171935l_bool(X3751,X3753))
| ~ hBOOL(hAPP_f621171935l_bool(X3751,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3753),X3752))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3753)) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,esk113_3(X3751,X3752,X3753)),X3752))
| hBOOL(hAPP_f621171935l_bool(X3751,X3753))
| ~ hBOOL(hAPP_f621171935l_bool(X3751,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3753),X3752))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3753)) )
& ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,esk113_3(X3751,X3752,X3753)),esk114_3(X3751,X3752,X3753)))
| hBOOL(hAPP_f621171935l_bool(X3751,X3753))
| ~ hBOOL(hAPP_f621171935l_bool(X3751,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3753),X3752))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3753)) )
& ( hBOOL(hAPP_f621171935l_bool(X3751,esk114_3(X3751,X3752,X3753)))
| hBOOL(hAPP_f621171935l_bool(X3751,X3753))
| ~ hBOOL(hAPP_f621171935l_bool(X3751,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3753),X3752))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3753)) )
& ( ~ hBOOL(hAPP_f621171935l_bool(X3751,insert_fun_a_bool(esk113_3(X3751,X3752,X3753),esk114_3(X3751,X3752,X3753))))
| hBOOL(hAPP_f621171935l_bool(X3751,X3753))
| ~ hBOOL(hAPP_f621171935l_bool(X3751,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3753),X3752))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3753)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_896])])])]) ).
fof(i_0_958,plain,
! [X2955,X2956] : insert_fun_a_bool(X2955,X2956) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X2955)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X2956))),
inference(variable_rename,[status(thm)],[fact_235_insert__compr]) ).
fof(i_0_959,plain,
! [X3731,X3732,X3733] :
( ( is_pname(esk105_3(X3731,X3732,X3733))
| hBOOL(hAPP_f1664156314l_bool(X3731,X3733))
| ~ hBOOL(hAPP_f1664156314l_bool(X3731,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3733),X3732))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3733)) )
& ( is_fun_pname_bool(esk106_3(X3731,X3732,X3733))
| hBOOL(hAPP_f1664156314l_bool(X3731,X3733))
| ~ hBOOL(hAPP_f1664156314l_bool(X3731,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3733),X3732))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3733)) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk106_3(X3731,X3732,X3733)))
| hBOOL(hAPP_f1664156314l_bool(X3731,X3733))
| ~ hBOOL(hAPP_f1664156314l_bool(X3731,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3733),X3732))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3733)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk105_3(X3731,X3732,X3733)),X3732))
| hBOOL(hAPP_f1664156314l_bool(X3731,X3733))
| ~ hBOOL(hAPP_f1664156314l_bool(X3731,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3733),X3732))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3733)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk105_3(X3731,X3732,X3733)),esk106_3(X3731,X3732,X3733)))
| hBOOL(hAPP_f1664156314l_bool(X3731,X3733))
| ~ hBOOL(hAPP_f1664156314l_bool(X3731,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3733),X3732))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3733)) )
& ( hBOOL(hAPP_f1664156314l_bool(X3731,esk106_3(X3731,X3732,X3733)))
| hBOOL(hAPP_f1664156314l_bool(X3731,X3733))
| ~ hBOOL(hAPP_f1664156314l_bool(X3731,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3733),X3732))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3733)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(X3731,insert_pname(esk105_3(X3731,X3732,X3733),esk106_3(X3731,X3732,X3733))))
| hBOOL(hAPP_f1664156314l_bool(X3731,X3733))
| ~ hBOOL(hAPP_f1664156314l_bool(X3731,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3733),X3732))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3733)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_897])])])]) ).
fof(i_0_960,plain,
! [X2959,X2960] : insert_pname(X2959,X2960) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2959)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2960))),
inference(variable_rename,[status(thm)],[fact_237_insert__compr]) ).
fof(i_0_961,plain,
! [X3736,X3737,X3738] :
( ( is_a(esk107_3(X3736,X3737,X3738))
| hBOOL(hAPP_fun_a_bool_bool(X3736,X3738))
| ~ hBOOL(hAPP_fun_a_bool_bool(X3736,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3738),X3737))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3738)) )
& ( is_fun_a_bool(esk108_3(X3736,X3737,X3738))
| hBOOL(hAPP_fun_a_bool_bool(X3736,X3738))
| ~ hBOOL(hAPP_fun_a_bool_bool(X3736,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3738),X3737))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3738)) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk108_3(X3736,X3737,X3738)))
| hBOOL(hAPP_fun_a_bool_bool(X3736,X3738))
| ~ hBOOL(hAPP_fun_a_bool_bool(X3736,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3738),X3737))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3738)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk107_3(X3736,X3737,X3738)),X3737))
| hBOOL(hAPP_fun_a_bool_bool(X3736,X3738))
| ~ hBOOL(hAPP_fun_a_bool_bool(X3736,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3738),X3737))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3738)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk107_3(X3736,X3737,X3738)),esk108_3(X3736,X3737,X3738)))
| hBOOL(hAPP_fun_a_bool_bool(X3736,X3738))
| ~ hBOOL(hAPP_fun_a_bool_bool(X3736,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3738),X3737))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3738)) )
& ( hBOOL(hAPP_fun_a_bool_bool(X3736,esk108_3(X3736,X3737,X3738)))
| hBOOL(hAPP_fun_a_bool_bool(X3736,X3738))
| ~ hBOOL(hAPP_fun_a_bool_bool(X3736,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3738),X3737))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3738)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(X3736,insert_a(esk107_3(X3736,X3737,X3738),esk108_3(X3736,X3737,X3738))))
| hBOOL(hAPP_fun_a_bool_bool(X3736,X3738))
| ~ hBOOL(hAPP_fun_a_bool_bool(X3736,bot_bot_fun_a_bool))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3738),X3737))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X3738)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_898])])])]) ).
fof(i_0_962,plain,
! [X3497,X3498,X3499,X3500] :
( ( X3497 = X3500
| X3497 = X3499
| insert_pname(X3497,insert_pname(X3498,bot_bo844097828e_bool)) != insert_pname(X3499,insert_pname(X3500,bot_bo844097828e_bool))
| ~ is_pname(X3497)
| ~ is_pname(X3498)
| ~ is_pname(X3499)
| ~ is_pname(X3500) )
& ( X3498 = X3499
| X3497 = X3499
| insert_pname(X3497,insert_pname(X3498,bot_bo844097828e_bool)) != insert_pname(X3499,insert_pname(X3500,bot_bo844097828e_bool))
| ~ is_pname(X3497)
| ~ is_pname(X3498)
| ~ is_pname(X3499)
| ~ is_pname(X3500) )
& ( X3497 = X3500
| X3498 = X3500
| insert_pname(X3497,insert_pname(X3498,bot_bo844097828e_bool)) != insert_pname(X3499,insert_pname(X3500,bot_bo844097828e_bool))
| ~ is_pname(X3497)
| ~ is_pname(X3498)
| ~ is_pname(X3499)
| ~ is_pname(X3500) )
& ( X3498 = X3499
| X3498 = X3500
| insert_pname(X3497,insert_pname(X3498,bot_bo844097828e_bool)) != insert_pname(X3499,insert_pname(X3500,bot_bo844097828e_bool))
| ~ is_pname(X3497)
| ~ is_pname(X3498)
| ~ is_pname(X3499)
| ~ is_pname(X3500) )
& ( X3497 != X3499
| X3498 != X3500
| insert_pname(X3497,insert_pname(X3498,bot_bo844097828e_bool)) = insert_pname(X3499,insert_pname(X3500,bot_bo844097828e_bool))
| ~ is_pname(X3497)
| ~ is_pname(X3498)
| ~ is_pname(X3499)
| ~ is_pname(X3500) )
& ( X3497 != X3500
| X3498 != X3499
| insert_pname(X3497,insert_pname(X3498,bot_bo844097828e_bool)) = insert_pname(X3499,insert_pname(X3500,bot_bo844097828e_bool))
| ~ is_pname(X3497)
| ~ is_pname(X3498)
| ~ is_pname(X3499)
| ~ is_pname(X3500) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_452_doubleton__eq__iff])])]) ).
fof(i_0_963,plain,
! [X3505,X3506,X3507,X3508] :
( ( X3505 = X3508
| X3505 = X3507
| insert_a(X3505,insert_a(X3506,bot_bot_fun_a_bool)) != insert_a(X3507,insert_a(X3508,bot_bot_fun_a_bool))
| ~ is_a(X3505)
| ~ is_a(X3506)
| ~ is_a(X3507)
| ~ is_a(X3508) )
& ( X3506 = X3507
| X3505 = X3507
| insert_a(X3505,insert_a(X3506,bot_bot_fun_a_bool)) != insert_a(X3507,insert_a(X3508,bot_bot_fun_a_bool))
| ~ is_a(X3505)
| ~ is_a(X3506)
| ~ is_a(X3507)
| ~ is_a(X3508) )
& ( X3505 = X3508
| X3506 = X3508
| insert_a(X3505,insert_a(X3506,bot_bot_fun_a_bool)) != insert_a(X3507,insert_a(X3508,bot_bot_fun_a_bool))
| ~ is_a(X3505)
| ~ is_a(X3506)
| ~ is_a(X3507)
| ~ is_a(X3508) )
& ( X3506 = X3507
| X3506 = X3508
| insert_a(X3505,insert_a(X3506,bot_bot_fun_a_bool)) != insert_a(X3507,insert_a(X3508,bot_bot_fun_a_bool))
| ~ is_a(X3505)
| ~ is_a(X3506)
| ~ is_a(X3507)
| ~ is_a(X3508) )
& ( X3505 != X3507
| X3506 != X3508
| insert_a(X3505,insert_a(X3506,bot_bot_fun_a_bool)) = insert_a(X3507,insert_a(X3508,bot_bot_fun_a_bool))
| ~ is_a(X3505)
| ~ is_a(X3506)
| ~ is_a(X3507)
| ~ is_a(X3508) )
& ( X3505 != X3508
| X3506 != X3507
| insert_a(X3505,insert_a(X3506,bot_bot_fun_a_bool)) = insert_a(X3507,insert_a(X3508,bot_bot_fun_a_bool))
| ~ is_a(X3505)
| ~ is_a(X3506)
| ~ is_a(X3507)
| ~ is_a(X3508) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_454_doubleton__eq__iff])])]) ).
fof(i_0_964,plain,
! [X3342,X3343] :
( ( is_pname(esk81_2(X3342,X3343))
| hBOOL(hAPP_fun_a_bool_bool(p(X3342),insert_a(mgt(X3343),bot_bot_fun_a_bool)))
| ~ hBOOL(wt(X3343)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk81_2(X3342,X3343)),u))
| hBOOL(hAPP_fun_a_bool_bool(p(X3342),insert_a(mgt(X3343),bot_bot_fun_a_bool)))
| ~ hBOOL(wt(X3343)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(p(X3342),insert_a(hAPP_pname_a(mgt_call,esk81_2(X3342,X3343)),bot_bot_fun_a_bool)))
| hBOOL(hAPP_fun_a_bool_bool(p(X3342),insert_a(mgt(X3343),bot_bot_fun_a_bool)))
| ~ hBOOL(wt(X3343)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_373_assms_I3_J])])])]) ).
fof(i_0_965,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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_966,plain,
! [X3741,X3742,X3743] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk110_3(X3741,X3742,X3743)))
| hBOOL(hAPP_f1637334154l_bool(X3741,X3743))
| ~ hBOOL(hAPP_f1637334154l_bool(X3741,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3743),X3742))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3743)) )
& ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,esk109_3(X3741,X3742,X3743)),X3742))
| hBOOL(hAPP_f1637334154l_bool(X3741,X3743))
| ~ hBOOL(hAPP_f1637334154l_bool(X3741,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3743),X3742))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3743)) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,esk109_3(X3741,X3742,X3743)),esk110_3(X3741,X3742,X3743)))
| hBOOL(hAPP_f1637334154l_bool(X3741,X3743))
| ~ hBOOL(hAPP_f1637334154l_bool(X3741,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3743),X3742))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3743)) )
& ( hBOOL(hAPP_f1637334154l_bool(X3741,esk110_3(X3741,X3742,X3743)))
| hBOOL(hAPP_f1637334154l_bool(X3741,X3743))
| ~ hBOOL(hAPP_f1637334154l_bool(X3741,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3743),X3742))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3743)) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(X3741,insert_fun_nat_bool(esk109_3(X3741,X3742,X3743),esk110_3(X3741,X3742,X3743))))
| hBOOL(hAPP_f1637334154l_bool(X3741,X3743))
| ~ hBOOL(hAPP_f1637334154l_bool(X3741,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3743),X3742))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3743)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_899])])])]) ).
cnf(i_0_967,plain,
insert_fun_nat_bool(X1,X2) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2))),
inference(split_conjunct,[status(thm)],[i_0_900]) ).
cnf(i_0_968,plain,
collect_fun_nat_bool(X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_901]) ).
fof(i_0_969,plain,
! [X3726,X3727,X3728] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk104_3(X3726,X3727,X3728)))
| hBOOL(hAPP_f54304608l_bool(X3726,X3728))
| ~ hBOOL(hAPP_f54304608l_bool(X3726,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3728),X3727))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3728)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk103_3(X3726,X3727,X3728)),X3727))
| hBOOL(hAPP_f54304608l_bool(X3726,X3728))
| ~ hBOOL(hAPP_f54304608l_bool(X3726,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3728),X3727))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3728)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk103_3(X3726,X3727,X3728)),esk104_3(X3726,X3727,X3728)))
| hBOOL(hAPP_f54304608l_bool(X3726,X3728))
| ~ hBOOL(hAPP_f54304608l_bool(X3726,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3728),X3727))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3728)) )
& ( hBOOL(hAPP_f54304608l_bool(X3726,esk104_3(X3726,X3727,X3728)))
| hBOOL(hAPP_f54304608l_bool(X3726,X3728))
| ~ hBOOL(hAPP_f54304608l_bool(X3726,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3728),X3727))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3728)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(X3726,insert_nat(esk103_3(X3726,X3727,X3728),esk104_3(X3726,X3727,X3728))))
| hBOOL(hAPP_f54304608l_bool(X3726,X3728))
| ~ hBOOL(hAPP_f54304608l_bool(X3726,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3728),X3727))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3728)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_902])])])]) ).
cnf(i_0_970,plain,
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_903]) ).
cnf(i_0_971,plain,
collect_nat(X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_904]) ).
fof(i_0_972,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X9,X5)))
=> ? [X30] :
( is_fun_pname_bool(X30)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X30),X5))
& ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X5)),hAPP_n850744903l_bool(cOMBC_1666426608t_bool(cOMBB_1896684278e_bool(fequal_nat,X9)),hAPP_f921600141ol_nat(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_197_pigeonhole__infinite]) ).
fof(i_0_973,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X9,X5)))
=> ? [X30] :
( is_fun_pname_bool(X30)
& hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X30),X5))
& ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X5)),hAPP_p338031245l_bool(cOMBC_1004116266e_bool(cOMBB_598082538e_bool(fequal_pname,X9)),hAPP_f1297739591_pname(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_191_pigeonhole__infinite]) ).
fof(i_0_974,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X9,X5)))
=> ? [X30] :
( is_fun_a_bool(X30)
& hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X30),X5))
& ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X5)),hAPP_n1414589940l_bool(cOMBC_619334683t_bool(cOMBB_164527437a_bool(fequal_nat,X9)),hAPP_fun_a_bool_nat(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_198_pigeonhole__infinite]) ).
fof(i_0_975,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X9,X5)))
=> ? [X30] :
( is_fun_a_bool(X30)
& hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X30),X5))
& ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X5)),hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(cOMBB_1693087065a_bool(fequal_pname,X9)),hAPP_f1128469712_pname(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_192_pigeonhole__infinite]) ).
fof(i_0_976,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(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_f654413245e_bool(cOMBC_267053842l_bool(cOMBB_928955006_pname(fequal_fun_nat_bool,X9)),hAPP_p1499970991t_bool(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_203_pigeonhole__infinite]) ).
fof(i_0_977,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(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_f759274231e_bool(cOMBC_1058051404l_bool(cOMBB_408569982_pname(fequal533582459e_bool,X9)),hAPP_p61793385e_bool(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_204_pigeonhole__infinite]) ).
fof(i_0_978,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(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_f1794073134e_bool(cOMBC_445755039l_bool(cOMBB_392435466_pname(fequal_fun_a_bool,X9)),hAPP_p1534023578a_bool(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_205_pigeonhole__infinite]) ).
fof(i_0_979,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(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_n1025906991e_bool(cOMBC_pname_nat_bool(cOMBB_523834888_pname(fequal_nat,X9)),hAPP_pname_nat(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_195_pigeonhole__infinite]) ).
fof(i_0_980,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(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_p61793385e_bool(cOMBC_1149511130e_bool(cOMBB_542850580_pname(fequal_pname,X9)),hAPP_pname_pname(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_189_pigeonhole__infinite]) ).
fof(i_0_981,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_210_pigeonhole__infinite]) ).
fof(i_0_982,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(X9,X5)))
=> ? [X30] :
( is_a(X30)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
& ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5)),hAPP_f1549043526a_bool(cOMBC_777206479l_bool(cOMBB_743407885bool_a(fequal_fun_nat_bool,X9)),hAPP_a_fun_nat_bool(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_207_pigeonhole__infinite]) ).
fof(i_0_983,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(X9,X5)))
=> ? [X30] :
( is_a(X30)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
& ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5)),hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(cOMBB_1137537805bool_a(fequal533582459e_bool,X9)),hAPP_a93125764e_bool(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_208_pigeonhole__infinite]) ).
fof(i_0_984,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(X9,X5)))
=> ? [X30] :
( is_a(X30)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
& ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(cOMBB_472261505bool_a(fequal_fun_a_bool,X9)),hAPP_a_fun_a_bool(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_209_pigeonhole__infinite]) ).
fof(i_0_985,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X9,X5)))
=> ? [X30] :
( is_a(X30)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
& ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5)),hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(cOMBB_1321347587bool_a(fequal_nat,X9)),hAPP_a_nat(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_194_pigeonhole__infinite]) ).
fof(i_0_986,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X9,X5)))
=> ? [X30] :
( is_a(X30)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
& ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5)),hAPP_p1534023578a_bool(cOMBC_a_pname_bool(cOMBB_610033911bool_a(fequal_pname,X9)),hAPP_a_pname(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_188_pigeonhole__infinite]) ).
fof(i_0_987,plain,
! [X9,X5] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X9,X5)))
=> ? [X30] :
( is_a(X30)
& hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5))
& ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X5)),hAPP_a_fun_a_bool(cOMBC_a_a_bool(cOMBB_a_fun_a_bool_a(fequal_a,X9)),hAPP_a_a(X9,X30)))))) ) ) ),
inference(fof_simplification,[status(thm)],[fact_206_pigeonhole__infinite]) ).
fof(i_0_988,plain,
! [X2981,X2982,X2983] : insert_pname(X2981,insert_pname(X2982,X2983)) = insert_pname(X2982,insert_pname(X2981,X2983)),
inference(variable_rename,[status(thm)],[fact_248_insert__commute]) ).
fof(i_0_989,plain,
! [X2987,X2988,X2989] : insert_a(X2987,insert_a(X2988,X2989)) = insert_a(X2988,insert_a(X2987,X2989)),
inference(variable_rename,[status(thm)],[fact_250_insert__commute]) ).
fof(i_0_990,plain,
! [X3762,X3763] :
( ( is_fun_pname_bool(esk117_2(X3762,X3763))
| hBOOL(hAPP_f1935102916l_bool(X3762,X3763))
| ~ hBOOL(hAPP_f1935102916l_bool(X3762,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3763)) )
& ( is_fun1661590463l_bool(esk118_2(X3762,X3763))
| hBOOL(hAPP_f1935102916l_bool(X3762,X3763))
| ~ hBOOL(hAPP_f1935102916l_bool(X3762,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3763)) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk118_2(X3762,X3763)))
| hBOOL(hAPP_f1935102916l_bool(X3762,X3763))
| ~ hBOOL(hAPP_f1935102916l_bool(X3762,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3763)) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,esk117_2(X3762,X3763)),esk118_2(X3762,X3763)))
| hBOOL(hAPP_f1935102916l_bool(X3762,X3763))
| ~ hBOOL(hAPP_f1935102916l_bool(X3762,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3763)) )
& ( hBOOL(hAPP_f1935102916l_bool(X3762,esk118_2(X3762,X3763)))
| hBOOL(hAPP_f1935102916l_bool(X3762,X3763))
| ~ hBOOL(hAPP_f1935102916l_bool(X3762,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3763)) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(X3762,insert1325755072e_bool(esk117_2(X3762,X3763),esk118_2(X3762,X3763))))
| hBOOL(hAPP_f1935102916l_bool(X3762,X3763))
| ~ hBOOL(hAPP_f1935102916l_bool(X3762,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3763)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_905])])])]) ).
fof(i_0_991,plain,
! [X3766,X3767] :
( ( is_fun_a_bool(esk119_2(X3766,X3767))
| hBOOL(hAPP_f621171935l_bool(X3766,X3767))
| ~ hBOOL(hAPP_f621171935l_bool(X3766,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3767)) )
& ( is_fun949378684l_bool(esk120_2(X3766,X3767))
| hBOOL(hAPP_f621171935l_bool(X3766,X3767))
| ~ hBOOL(hAPP_f621171935l_bool(X3766,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3767)) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk120_2(X3766,X3767)))
| hBOOL(hAPP_f621171935l_bool(X3766,X3767))
| ~ hBOOL(hAPP_f621171935l_bool(X3766,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3767)) )
& ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,esk119_2(X3766,X3767)),esk120_2(X3766,X3767)))
| hBOOL(hAPP_f621171935l_bool(X3766,X3767))
| ~ hBOOL(hAPP_f621171935l_bool(X3766,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3767)) )
& ( hBOOL(hAPP_f621171935l_bool(X3766,esk120_2(X3766,X3767)))
| hBOOL(hAPP_f621171935l_bool(X3766,X3767))
| ~ hBOOL(hAPP_f621171935l_bool(X3766,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3767)) )
& ( ~ hBOOL(hAPP_f621171935l_bool(X3766,insert_fun_a_bool(esk119_2(X3766,X3767),esk120_2(X3766,X3767))))
| hBOOL(hAPP_f621171935l_bool(X3766,X3767))
| ~ hBOOL(hAPP_f621171935l_bool(X3766,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3767)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_906])])])]) ).
fof(i_0_992,plain,
! [X3170,X3171,X3172] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3170),X3172))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X3170,X3171)),X3172)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3171),X3172))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X3170,X3171)),X3172)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3170),X3172))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3171),X3172))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X3170,X3171)),X3172)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_323_insert__subset])])]) ).
fof(i_0_993,plain,
! [X3173,X3174,X3175] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3173),X3175))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X3173,X3174)),X3175)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3174),X3175))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X3173,X3174)),X3175)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3173),X3175))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3174),X3175))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X3173,X3174)),X3175)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_324_insert__subset])])]) ).
fof(i_0_994,plain,
! [X3194,X3195,X3196] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3195),X3196))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X3194,X3195)),insert_pname(X3194,X3196))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_331_insert__mono])]) ).
fof(i_0_995,plain,
! [X3200,X3201,X3202] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3201),X3202))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X3200,X3201)),insert_a(X3200,X3202))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_333_insert__mono])]) ).
fof(i_0_996,plain,
! [X2975,X2976] : insert_pname(X2975,insert_pname(X2975,X2976)) = insert_pname(X2975,X2976),
inference(variable_rename,[status(thm)],[fact_245_insert__absorb2]) ).
fof(i_0_997,plain,
! [X2979,X2980] : insert_a(X2979,insert_a(X2979,X2980)) = insert_a(X2979,X2980),
inference(variable_rename,[status(thm)],[fact_247_insert__absorb2]) ).
fof(i_0_998,plain,
! [X2840,X2841] :
( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,esk42_2(X2840,X2841)),X2841))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X2840,X2841)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2841)) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2841)),hAPP_n215258509l_bool(cOMBC_385542954t_bool(cOMBB_1250273980t_bool(fequal_nat,X2840)),hAPP_f22106695ol_nat(X2840,esk42_2(X2840,X2841)))))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X2840,X2841)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2841)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_907])])])]) ).
fof(i_0_999,plain,
! [X2822,X2823] :
( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,esk36_2(X2822,X2823)),X2823))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X2822,X2823)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2823)) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2823)),hAPP_p130839763l_bool(cOMBC_615407716e_bool(cOMBB_141086128t_bool(fequal_pname,X2822)),hAPP_f1291551745_pname(X2822,esk36_2(X2822,X2823)))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X2822,X2823)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2823)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_908])])])]) ).
fof(i_0_1000,plain,
! [X2852,X2853] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk46_2(X2852,X2853)),X2853))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X2852,X2853)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2853)) )
& ( ~ 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),X2853)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,X2852)),hAPP_n1699378549t_bool(X2852,esk46_2(X2852,X2853)))))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X2852,X2853)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2853)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_909])])])]) ).
fof(i_0_1001,plain,
! [X2855,X2856] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk47_2(X2855,X2856)),X2856))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X2855,X2856)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2856)) )
& ( ~ 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),X2856)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,X2855)),hAPP_n1025906991e_bool(X2855,esk47_2(X2855,X2856)))))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X2855,X2856)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2856)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_910])])])]) ).
fof(i_0_1002,plain,
! [X2858,X2859] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk48_2(X2858,X2859)),X2859))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X2858,X2859)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2859)) )
& ( ~ 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),X2859)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,X2858)),hAPP_nat_fun_a_bool(X2858,esk48_2(X2858,X2859)))))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X2858,X2859)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2859)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_911])])])]) ).
fof(i_0_1003,plain,
! [X2831,X2832] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk39_2(X2831,X2832)),X2832))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(X2831,X2832)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2832)) )
& ( ~ 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),X2832)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(fequal_nat,X2831)),hAPP_nat_nat(X2831,esk39_2(X2831,X2832)))))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(X2831,X2832)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2832)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_912])])])]) ).
fof(i_0_1004,plain,
! [X2813,X2814] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk33_2(X2813,X2814)),X2814))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X2813,X2814)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2814)) )
& ( ~ 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),X2814)),hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(cOMBB_1212655066ol_nat(fequal_pname,X2813)),hAPP_nat_pname(X2813,esk33_2(X2813,X2814)))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X2813,X2814)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2814)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_913])])])]) ).
fof(i_0_1005,plain,
! [X2849,X2850] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk45_2(X2849,X2850)),X2850))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X2849,X2850)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2850)) )
& ( ~ 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),X2850)),hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(cOMBB_1885489796ol_nat(fequal_a,X2849)),hAPP_nat_a(X2849,esk45_2(X2849,X2850)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X2849,X2850)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2850)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_914])])])]) ).
fof(i_0_1006,plain,
! [X2461,X2462] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2462))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2462)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2461,X2462)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_56_card__insert__le])]) ).
fof(i_0_1007,plain,
! [X2459,X2460] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2460))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2460)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2459,X2460)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_55_card__insert__le])]) ).
fof(i_0_1008,plain,
! [X2467,X2468] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2468))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2468)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2467,X2468)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_59_card__insert__le])]) ).
fof(i_0_1009,plain,
! [X2463,X2464] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2464))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2464)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2463,X2464)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_57_card__insert__le])]) ).
fof(i_0_1010,plain,
! [X3501,X3502,X3503,X3504] :
( ( X3501 = X3504
| X3501 = X3503
| insert_nat(X3501,insert_nat(X3502,bot_bot_fun_nat_bool)) != insert_nat(X3503,insert_nat(X3504,bot_bot_fun_nat_bool)) )
& ( X3502 = X3503
| X3501 = X3503
| insert_nat(X3501,insert_nat(X3502,bot_bot_fun_nat_bool)) != insert_nat(X3503,insert_nat(X3504,bot_bot_fun_nat_bool)) )
& ( X3501 = X3504
| X3502 = X3504
| insert_nat(X3501,insert_nat(X3502,bot_bot_fun_nat_bool)) != insert_nat(X3503,insert_nat(X3504,bot_bot_fun_nat_bool)) )
& ( X3502 = X3503
| X3502 = X3504
| insert_nat(X3501,insert_nat(X3502,bot_bot_fun_nat_bool)) != insert_nat(X3503,insert_nat(X3504,bot_bot_fun_nat_bool)) )
& ( X3501 != X3503
| X3502 != X3504
| insert_nat(X3501,insert_nat(X3502,bot_bot_fun_nat_bool)) = insert_nat(X3503,insert_nat(X3504,bot_bot_fun_nat_bool)) )
& ( X3501 != X3504
| X3502 != X3503
| insert_nat(X3501,insert_nat(X3502,bot_bot_fun_nat_bool)) = insert_nat(X3503,insert_nat(X3504,bot_bot_fun_nat_bool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_453_doubleton__eq__iff])])]) ).
fof(i_0_1011,plain,
! [X3573,X3574] :
( ~ is_fun_pname_bool(X3573)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3573),insert_pname(X3574,bot_bo844097828e_bool)))
| X3573 = bot_bo844097828e_bool
| X3573 = insert_pname(X3574,bot_bo844097828e_bool) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_495_subset__singletonD])]) ).
fof(i_0_1012,plain,
! [X3575,X3576] :
( ~ is_fun_a_bool(X3575)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3575),insert_a(X3576,bot_bot_fun_a_bool)))
| X3575 = bot_bot_fun_a_bool
| X3575 = insert_a(X3576,bot_bot_fun_a_bool) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_496_subset__singletonD])]) ).
fof(i_0_1013,plain,
! [X3758,X3759] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk116_2(X3758,X3759)))
| hBOOL(hAPP_f1637334154l_bool(X3758,X3759))
| ~ hBOOL(hAPP_f1637334154l_bool(X3758,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3759)) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,esk115_2(X3758,X3759)),esk116_2(X3758,X3759)))
| hBOOL(hAPP_f1637334154l_bool(X3758,X3759))
| ~ hBOOL(hAPP_f1637334154l_bool(X3758,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3759)) )
& ( hBOOL(hAPP_f1637334154l_bool(X3758,esk116_2(X3758,X3759)))
| hBOOL(hAPP_f1637334154l_bool(X3758,X3759))
| ~ hBOOL(hAPP_f1637334154l_bool(X3758,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3759)) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(X3758,insert_fun_nat_bool(esk115_2(X3758,X3759),esk116_2(X3758,X3759))))
| hBOOL(hAPP_f1637334154l_bool(X3758,X3759))
| ~ hBOOL(hAPP_f1637334154l_bool(X3758,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3759)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_915])])])]) ).
fof(i_0_1014,plain,
! [X3179,X3180,X3181] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3181),insert_pname(X3180,X3179)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3181),X3179))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3180),X3181)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3181),X3179))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3181),insert_pname(X3180,X3179)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3180),X3181)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_916])])]) ).
fof(i_0_1015,plain,
! [X3182,X3183,X3184] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3184),insert_a(X3183,X3182)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3184),X3182))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3183),X3184)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3184),X3182))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3184),insert_a(X3183,X3182)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3183),X3184)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_917])])]) ).
fof(i_0_1016,plain,
! [X2993,X2994,X2995] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2993),insert_pname(X2994,X2995)))
| X2993 = X2994
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2993),X2995))
| ~ is_pname(X2993)
| ~ is_pname(X2994) )
& ( X2993 != X2994
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2993),insert_pname(X2994,X2995)))
| ~ is_pname(X2993)
| ~ is_pname(X2994) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2993),X2995))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2993),insert_pname(X2994,X2995)))
| ~ is_pname(X2993)
| ~ is_pname(X2994) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_252_insert__iff])])]) ).
fof(i_0_1017,plain,
! [X2932,X2933,X2934] :
( ~ is_pname(X2932)
| ~ is_pname(X2933)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2932),insert_pname(X2933,X2934)))
| X2932 = X2933
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2932),X2934)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_226_insertE])]) ).
fof(i_0_1018,plain,
! [X2996,X2997,X2998] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2996),insert_a(X2997,X2998)))
| X2996 = X2997
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2996),X2998))
| ~ is_a(X2996)
| ~ is_a(X2997) )
& ( X2996 != X2997
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2996),insert_a(X2997,X2998)))
| ~ is_a(X2996)
| ~ is_a(X2997) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2996),X2998))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2996),insert_a(X2997,X2998)))
| ~ is_a(X2996)
| ~ is_a(X2997) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_253_insert__iff])])]) ).
fof(i_0_1019,plain,
! [X2935,X2936,X2937] :
( ~ is_a(X2935)
| ~ is_a(X2936)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2935),insert_a(X2936,X2937)))
| X2935 = X2936
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2935),X2937)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_227_insertE])]) ).
fof(i_0_1020,plain,
! [X3167,X3168,X3169] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3167),X3169))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X3167,X3168)),X3169)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3168),X3169))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X3167,X3168)),X3169)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3167),X3169))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3168),X3169))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X3167,X3168)),X3169)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_322_insert__subset])])]) ).
fof(i_0_1021,plain,
! [X3197,X3198,X3199] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3198),X3199))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X3197,X3198)),insert_nat(X3197,X3199))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_332_insert__mono])]) ).
fof(i_0_1022,plain,
! [X3511,X3512] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3511),insert_pname(X3512,bot_bo844097828e_bool)))
| X3511 = X3512
| ~ is_pname(X3511)
| ~ is_pname(X3512) )
& ( X3511 != X3512
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3511),insert_pname(X3512,bot_bo844097828e_bool)))
| ~ is_pname(X3511)
| ~ is_pname(X3512) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_456_singleton__iff])])]) ).
fof(i_0_1023,plain,
! [X3493,X3494] :
( ~ is_pname(X3493)
| ~ is_pname(X3494)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3493),insert_pname(X3494,bot_bo844097828e_bool)))
| X3493 = X3494 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_450_singletonE])]) ).
fof(i_0_1024,plain,
! [X3513,X3514] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3513),insert_a(X3514,bot_bot_fun_a_bool)))
| X3513 = X3514
| ~ is_a(X3513)
| ~ is_a(X3514) )
& ( X3513 != X3514
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3513),insert_a(X3514,bot_bot_fun_a_bool)))
| ~ is_a(X3513)
| ~ is_a(X3514) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_457_singleton__iff])])]) ).
fof(i_0_1025,plain,
! [X3495,X3496] :
( ~ is_a(X3495)
| ~ is_a(X3496)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3495),insert_a(X3496,bot_bot_fun_a_bool)))
| X3495 = X3496 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_451_singletonE])]) ).
fof(i_0_1026,plain,
! [X2999,X3000,X3001] :
( ( ~ hBOOL(hAPP_pname_bool(insert_pname(X2999,X3000),X3001))
| X2999 = X3001
| hBOOL(hAPP_pname_bool(X3000,X3001))
| ~ is_pname(X2999)
| ~ is_pname(X3001) )
& ( X2999 != X3001
| hBOOL(hAPP_pname_bool(insert_pname(X2999,X3000),X3001))
| ~ is_pname(X2999)
| ~ is_pname(X3001) )
& ( ~ hBOOL(hAPP_pname_bool(X3000,X3001))
| hBOOL(hAPP_pname_bool(insert_pname(X2999,X3000),X3001))
| ~ is_pname(X2999)
| ~ is_pname(X3001) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_254_insert__code])])]) ).
fof(i_0_1027,plain,
! [X3005,X3006,X3007] :
( ( ~ hBOOL(hAPP_a_bool(insert_a(X3005,X3006),X3007))
| X3005 = X3007
| hBOOL(hAPP_a_bool(X3006,X3007))
| ~ is_a(X3005)
| ~ is_a(X3007) )
& ( X3005 != X3007
| hBOOL(hAPP_a_bool(insert_a(X3005,X3006),X3007))
| ~ is_a(X3005)
| ~ is_a(X3007) )
& ( ~ hBOOL(hAPP_a_bool(X3006,X3007))
| hBOOL(hAPP_a_bool(insert_a(X3005,X3006),X3007))
| ~ is_a(X3005)
| ~ is_a(X3007) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_256_insert__code])])]) ).
fof(i_0_1028,plain,
! [X2542,X2543] :
( ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X2542,X2543)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2543)) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2543))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X2542,X2543))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_98_finite__insert])]) ).
fof(i_0_1029,plain,
! [X2544,X2545] :
( ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X2544,X2545)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2545)) )
& ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2545))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X2544,X2545))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_99_finite__insert])]) ).
fof(i_0_1030,plain,
! [X2546,X2547] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X2546,X2547)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2547)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2547))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X2546,X2547))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_100_finite__insert])]) ).
fof(i_0_1031,plain,
! [X2550,X2551] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X2550,X2551)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2551)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2551))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X2550,X2551))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_102_finite__insert])]) ).
fof(i_0_1032,plain,
! [X2984,X2985,X2986] : insert_nat(X2984,insert_nat(X2985,X2986)) = insert_nat(X2985,insert_nat(X2984,X2986)),
inference(variable_rename,[status(thm)],[fact_249_insert__commute]) ).
fof(i_0_1033,plain,
! [X2465,X2466] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2466))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X2466)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2465,X2466)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_58_card__insert__le])]) ).
fof(i_0_1034,plain,
! [X2457,X2458] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2458))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X2458)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2457,X2458)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_54_card__insert__le])]) ).
fof(i_0_1035,plain,
! [X3185,X3186,X3187] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3186),X3187))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3186),insert_pname(X3185,X3187))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_328_subset__insertI2])]) ).
fof(i_0_1036,plain,
! [X3020,X3021,X3022] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3021),X3022))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3021),insert_pname(X3020,X3022))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_261_insertI2])]) ).
fof(i_0_1037,plain,
! [X2923,X2924,X2925] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2924),X2925))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2924),insert_pname(X2923,X2925))) )
& ( X2924 != X2923
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2924),insert_pname(X2923,X2925))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_918])])]) ).
fof(i_0_1038,plain,
! [X3191,X3192,X3193] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3192),X3193))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3192),insert_a(X3191,X3193))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_330_subset__insertI2])]) ).
fof(i_0_1039,plain,
! [X3023,X3024,X3025] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3024),X3025))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3024),insert_a(X3023,X3025))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_262_insertI2])]) ).
fof(i_0_1040,plain,
! [X2926,X2927,X2928] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2927),X2928))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2927),insert_a(X2926,X2928))) )
& ( X2927 != X2926
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2927),insert_a(X2926,X2928))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_919])])]) ).
fof(i_0_1041,plain,
! [X3161,X3162] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3161),insert_pname(X3162,X3161))),
inference(variable_rename,[status(thm)],[fact_319_subset__insertI]) ).
fof(i_0_1042,plain,
! [X2947,X2948] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2947),insert_pname(X2947,X2948))),
inference(variable_rename,[status(thm)],[fact_231_insertI1]) ).
fof(i_0_1043,plain,
! [X3165,X3166] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3165),insert_a(X3166,X3165))),
inference(variable_rename,[status(thm)],[fact_321_subset__insertI]) ).
fof(i_0_1044,plain,
! [X2949,X2950] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2949),insert_a(X2949,X2950))),
inference(variable_rename,[status(thm)],[fact_232_insertI1]) ).
fof(i_0_1045,plain,
! [X2397,X2398] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2398))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X2397,X2398))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_24_finite_OinsertI])]) ).
fof(i_0_1046,plain,
! [X2399,X2400] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2400))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X2399,X2400))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_25_finite_OinsertI])]) ).
fof(i_0_1047,plain,
! [X2401,X2402] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2402))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X2401,X2402))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_26_finite_OinsertI])]) ).
fof(i_0_1048,plain,
! [X2405,X2406] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2406))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X2405,X2406))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_28_finite_OinsertI])]) ).
fof(i_0_1049,plain,
! [X3212,X3213,X3214] : image_pname_a(X3212,insert_pname(X3213,X3214)) = insert_a(hAPP_pname_a(X3212,X3213),image_pname_a(X3212,X3214)),
inference(variable_rename,[status(thm)],[fact_337_image__insert]) ).
fof(i_0_1050,plain,
! [X3203,X3204,X3205] : image_a_pname(X3203,insert_a(X3204,X3205)) = insert_pname(hAPP_a_pname(X3203,X3204),image_a_pname(X3203,X3205)),
inference(variable_rename,[status(thm)],[fact_334_image__insert]) ).
fof(i_0_1051,plain,
! [X3176,X3177,X3178] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3178),insert_nat(X3177,X3176)))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3178),X3176))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3177),X3178)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3178),X3176))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3178),insert_nat(X3177,X3176)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3177),X3178)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_920])])]) ).
fof(i_0_1052,plain,
! [X3571,X3572] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3571),insert_nat(X3572,bot_bot_fun_nat_bool)))
| X3571 = bot_bot_fun_nat_bool
| X3571 = insert_nat(X3572,bot_bot_fun_nat_bool) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_494_subset__singletonD])]) ).
fof(i_0_1053,plain,
! [X2990,X2991,X2992] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2990),insert_nat(X2991,X2992)))
| X2990 = X2991
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2990),X2992)) )
& ( X2990 != X2991
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2990),insert_nat(X2991,X2992))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2990),X2992))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2990),insert_nat(X2991,X2992))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_251_insert__iff])])]) ).
fof(i_0_1054,plain,
! [X2929,X2930,X2931] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2929),insert_nat(X2930,X2931)))
| X2929 = X2930
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2929),X2931)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_225_insertE])]) ).
fof(i_0_1055,plain,
! [X3011,X3012,X3013] :
( ( insert_pname(X3012,X3013) != insert_pname(X3012,X3011)
| X3013 = X3011
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3012),X3011))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3012),X3013))
| ~ is_fun_pname_bool(X3011)
| ~ is_fun_pname_bool(X3013) )
& ( X3013 != X3011
| insert_pname(X3012,X3013) = insert_pname(X3012,X3011)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3012),X3011))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3012),X3013))
| ~ is_fun_pname_bool(X3011)
| ~ is_fun_pname_bool(X3013) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_921])])]) ).
fof(i_0_1056,plain,
! [X3014,X3015,X3016] :
( ( insert_a(X3015,X3016) != insert_a(X3015,X3014)
| X3016 = X3014
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3015),X3014))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3015),X3016))
| ~ is_fun_a_bool(X3014)
| ~ is_fun_a_bool(X3016) )
& ( X3016 != X3014
| insert_a(X3015,X3016) = insert_a(X3015,X3014)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3015),X3014))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3015),X3016))
| ~ is_fun_a_bool(X3014)
| ~ is_fun_a_bool(X3016) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_922])])]) ).
fof(i_0_1057,plain,
! [X3509,X3510] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3509),insert_nat(X3510,bot_bot_fun_nat_bool)))
| X3509 = X3510 )
& ( X3509 != X3510
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3509),insert_nat(X3510,bot_bot_fun_nat_bool))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_455_singleton__iff])]) ).
fof(i_0_1058,plain,
! [X3491,X3492] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3491),insert_nat(X3492,bot_bot_fun_nat_bool)))
| X3491 = X3492 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_449_singletonE])]) ).
fof(i_0_1059,plain,
! [X3002,X3003,X3004] :
( ( ~ hBOOL(hAPP_nat_bool(insert_nat(X3002,X3003),X3004))
| X3002 = X3004
| hBOOL(hAPP_nat_bool(X3003,X3004)) )
& ( X3002 != X3004
| hBOOL(hAPP_nat_bool(insert_nat(X3002,X3003),X3004)) )
& ( ~ hBOOL(hAPP_nat_bool(X3003,X3004))
| hBOOL(hAPP_nat_bool(insert_nat(X3002,X3003),X3004)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_255_insert__code])])]) ).
fof(i_0_1060,plain,
! [X2540,X2541] :
( ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X2540,X2541)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2541)) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2541))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X2540,X2541))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_97_finite__insert])]) ).
fof(i_0_1061,plain,
! [X2548,X2549] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X2548,X2549)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2549)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2549))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X2548,X2549))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_101_finite__insert])]) ).
fof(i_0_1062,plain,
! [X3209,X3210,X3211] : image_nat_a(X3209,insert_nat(X3210,X3211)) = insert_a(hAPP_nat_a(X3209,X3210),image_nat_a(X3209,X3211)),
inference(variable_rename,[status(thm)],[fact_336_image__insert]) ).
fof(i_0_1063,plain,
! [X3485,X3486] :
( ~ is_pname(X3485)
| ~ is_pname(X3486)
| insert_pname(X3485,bot_bo844097828e_bool) != insert_pname(X3486,bot_bo844097828e_bool)
| X3485 = X3486 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_446_singleton__inject])]) ).
fof(i_0_1064,plain,
! [X3489,X3490] :
( ~ is_a(X3489)
| ~ is_a(X3490)
| insert_a(X3489,bot_bot_fun_a_bool) != insert_a(X3490,bot_bot_fun_a_bool)
| X3489 = X3490 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_448_singleton__inject])]) ).
fof(i_0_1065,plain,
! [X3206,X3207,X3208] : image_a_nat(X3206,insert_a(X3207,X3208)) = insert_nat(hAPP_a_nat(X3206,X3207),image_a_nat(X3206,X3208)),
inference(variable_rename,[status(thm)],[fact_335_image__insert]) ).
fof(i_0_1066,plain,
! [X3770,X3771] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk121_2(X3770,X3771)),hAPP_nat_nat(X3771,esk121_2(X3770,X3771))))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,X3771)),X3770)))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_566_finite__less__ub])])]) ).
fof(i_0_1067,plain,
! [X2977,X2978] : insert_nat(X2977,insert_nat(X2977,X2978)) = insert_nat(X2977,X2978),
inference(variable_rename,[status(thm)],[fact_246_insert__absorb2]) ).
fof(i_0_1068,plain,
! [X3017,X3018,X3019] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3018),X3019))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3018),insert_nat(X3017,X3019))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_260_insertI2])]) ).
fof(i_0_1069,plain,
! [X2920,X2921,X2922] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2921),X2922))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2921),insert_nat(X2920,X2922))) )
& ( X2921 != X2920
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2921),insert_nat(X2920,X2922))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_923])])]) ).
fof(i_0_1070,plain,
! [X3188,X3189,X3190] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3189),X3190))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3189),insert_nat(X3188,X3190))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_329_subset__insertI2])]) ).
fof(i_0_1071,plain,
! [X2473,X2474] :
( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2473),X2474))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2473,X2474)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X2474)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2474)) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2473),X2474))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2473,X2474)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2474))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2474)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_924])])]) ).
fof(i_0_1072,plain,
! [X2471,X2472] :
( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2471),X2472))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2471,X2472)) = hAPP_f55526627ol_nat(finite1340463720e_bool,X2472)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2472)) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2471),X2472))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2471,X2472)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X2472))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2472)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_925])])]) ).
fof(i_0_1073,plain,
! [X2479,X2480] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2479),X2480))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2479,X2480)) = hAPP_fun_a_bool_nat(finite_card_a,X2480)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2480)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2479),X2480))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2479,X2480)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X2480))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2480)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_926])])]) ).
fof(i_0_1074,plain,
! [X2477,X2478] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2477),X2478))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2477,X2478)) = hAPP_f921600141ol_nat(finite_card_pname,X2478)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2478)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2477),X2478))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2477,X2478)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X2478))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2478)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_927])])]) ).
fof(i_0_1075,plain,
! [X2967,X2968] : insert1325755072e_bool(X2967,collec1974731493e_bool(X2968)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X2967))),X2968)),
inference(variable_rename,[status(thm)],[fact_241_insert__Collect]) ).
fof(i_0_1076,plain,
! [X2969,X2970] : insert_fun_a_bool(X2969,collect_fun_a_bool(X2970)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X2969))),X2970)),
inference(variable_rename,[status(thm)],[fact_242_insert__Collect]) ).
fof(i_0_1077,plain,
! [X2963,X2964] : insert_pname(X2963,collect_pname(X2964)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2963))),X2964)),
inference(variable_rename,[status(thm)],[fact_239_insert__Collect]) ).
fof(i_0_1078,plain,
! [X2973,X2974] : insert_a(X2973,collect_a(X2974)) = 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),X2973))),X2974)),
inference(variable_rename,[status(thm)],[fact_244_insert__Collect]) ).
fof(i_0_1079,plain,
! [X3215,X3216,X3217] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3216),X3217))
| insert_pname(hAPP_pname_pname(X3215,X3216),image_pname_pname(X3215,X3217)) = image_pname_pname(X3215,X3217) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_338_insert__image])]) ).
fof(i_0_1080,plain,
! [X3221,X3222,X3223] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3222),X3223))
| insert_pname(hAPP_a_pname(X3221,X3222),image_a_pname(X3221,X3223)) = image_a_pname(X3221,X3223) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_340_insert__image])]) ).
fof(i_0_1081,plain,
! [X3227,X3228,X3229] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3228),X3229))
| insert_a(hAPP_nat_a(X3227,X3228),image_nat_a(X3227,X3229)) = image_nat_a(X3227,X3229) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_342_insert__image])]) ).
fof(i_0_1082,plain,
! [X3230,X3231,X3232] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3231),X3232))
| insert_a(hAPP_pname_a(X3230,X3231),image_pname_a(X3230,X3232)) = image_pname_a(X3230,X3232) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_343_insert__image])]) ).
fof(i_0_1083,plain,
! [X31,X9,X5] :
( is_a(X31)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X31),image_nat_a(X9,X5)))
=> ~ ! [X30] :
( X31 = hAPP_nat_a(X9,X30)
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_353_imageE]) ).
fof(i_0_1084,plain,
! [X31,X9,X5] :
( is_pname(X31)
=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X31),image_nat_pname(X9,X5)))
=> ~ ! [X30] :
( X31 = hAPP_nat_pname(X9,X30)
=> ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_352_imageE]) ).
fof(i_0_1085,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_356_imageE]) ).
fof(i_0_1086,plain,
! [X31,X9,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),image_pname_nat(X9,X5)))
=> ~ ! [X30] :
( is_pname(X30)
=> ( X31 = hAPP_pname_nat(X9,X30)
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_354_imageE]) ).
fof(i_0_1087,plain,
! [X31,X9,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X31),image_a_nat(X9,X5)))
=> ~ ! [X30] :
( is_a(X30)
=> ( X31 = hAPP_a_nat(X9,X30)
=> ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X30),X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_355_imageE]) ).
fof(i_0_1088,plain,
! [X2485,X2486] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2486))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2485),X2486))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2485,X2486)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2486)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_928])]) ).
fof(i_0_1089,plain,
! [X2483,X2484] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2484))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2483),X2484))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2483,X2484)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X2484)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_929])]) ).
fof(i_0_1090,plain,
! [X2491,X2492] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2492))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2491),X2492))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X2491,X2492)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X2492)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_930])]) ).
fof(i_0_1091,plain,
! [X2489,X2490] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2490))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2489),X2490))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X2489,X2490)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X2490)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_931])]) ).
fof(i_0_1092,plain,
! [X2945,X2946] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2945),insert_nat(X2945,X2946))),
inference(variable_rename,[status(thm)],[fact_230_insertI1]) ).
fof(i_0_1093,plain,
! [X3163,X3164] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3163),insert_nat(X3164,X3163))),
inference(variable_rename,[status(thm)],[fact_320_subset__insertI]) ).
fof(i_0_1094,plain,
! [X2395,X2396] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2396))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X2395,X2396))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_23_finite_OinsertI])]) ).
fof(i_0_1095,plain,
! [X2403,X2404] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2404))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X2403,X2404))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_27_finite_OinsertI])]) ).
fof(i_0_1096,plain,
! [X3008,X3009,X3010] :
( ( insert_nat(X3009,X3010) != insert_nat(X3009,X3008)
| X3010 = X3008
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3009),X3008))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3009),X3010)) )
& ( X3010 != X3008
| insert_nat(X3009,X3010) = insert_nat(X3009,X3008)
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3009),X3008))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3009),X3010)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_932])])]) ).
fof(i_0_1097,plain,
! [X2262,X2263] :
( ~ is_fun_pname_bool(X2262)
| ~ is_fun1661590463l_bool(X2263)
| is_fun1661590463l_bool(insert1325755072e_bool(X2262,X2263)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J])]) ).
fof(i_0_1098,plain,
! [X2260,X2261] :
( ~ is_fun_a_bool(X2260)
| ~ is_fun949378684l_bool(X2261)
| is_fun949378684l_bool(insert_fun_a_bool(X2260,X2261)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J])]) ).
fof(i_0_1099,plain,
! [X2258,X2259] :
( ~ is_pname(X2258)
| ~ is_fun_pname_bool(X2259)
| is_fun_pname_bool(insert_pname(X2258,X2259)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oinsert_000tc__Com__Opname])]) ).
fof(i_0_1100,hypothesis,
! [X2256,X2257] :
( ~ is_a(X2256)
| ~ is_fun_a_bool(X2257)
| is_fun_a_bool(insert_a(X2256,X2257)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oinsert_000t__a])]) ).
fof(i_0_1101,plain,
! [X3543,X3544] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(X3543,X3544))
| collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X3544)),X3543)) = insert1325755072e_bool(X3544,bot_bo1649642514l_bool) )
& ( hBOOL(hAPP_f1664156314l_bool(X3543,X3544))
| collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X3544)),X3543)) = bot_bo1649642514l_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_933])]) ).
fof(i_0_1102,plain,
! [X3545,X3546] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(X3545,X3546))
| collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X3546)),X3545)) = insert_fun_a_bool(X3546,bot_bo1389914601l_bool) )
& ( hBOOL(hAPP_fun_a_bool_bool(X3545,X3546))
| collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X3546)),X3545)) = bot_bo1389914601l_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_934])]) ).
fof(i_0_1103,plain,
! [X3537,X3538] :
( ( ~ hBOOL(hAPP_pname_bool(X3537,X3538))
| collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3538)),X3537)) = insert_pname(X3538,bot_bo844097828e_bool) )
& ( hBOOL(hAPP_pname_bool(X3537,X3538))
| collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3538)),X3537)) = bot_bo844097828e_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_935])]) ).
fof(i_0_1104,plain,
! [X3539,X3540] :
( ( ~ hBOOL(hAPP_a_bool(X3539,X3540))
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3540)),X3539)) = insert_a(X3540,bot_bot_fun_a_bool) )
& ( hBOOL(hAPP_a_bool(X3539,X3540))
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3540)),X3539)) = bot_bot_fun_a_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_936])]) ).
fof(i_0_1105,plain,
! [X3555,X3556] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(X3555,X3556))
| collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,X3556)),X3555)) = insert1325755072e_bool(X3556,bot_bo1649642514l_bool) )
& ( hBOOL(hAPP_f1664156314l_bool(X3555,X3556))
| collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,X3556)),X3555)) = bot_bo1649642514l_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_937])]) ).
fof(i_0_1106,plain,
! [X3557,X3558] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(X3557,X3558))
| collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,X3558)),X3557)) = insert_fun_a_bool(X3558,bot_bo1389914601l_bool) )
& ( hBOOL(hAPP_fun_a_bool_bool(X3557,X3558))
| collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,X3558)),X3557)) = bot_bo1389914601l_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_938])]) ).
fof(i_0_1107,plain,
! [X3549,X3550] :
( ( ~ hBOOL(hAPP_pname_bool(X3549,X3550))
| collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,X3550)),X3549)) = insert_pname(X3550,bot_bo844097828e_bool) )
& ( hBOOL(hAPP_pname_bool(X3549,X3550))
| collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,X3550)),X3549)) = bot_bo844097828e_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_939])]) ).
fof(i_0_1108,plain,
! [X3551,X3552] :
( ( ~ hBOOL(hAPP_a_bool(X3551,X3552))
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X3552)),X3551)) = insert_a(X3552,bot_bot_fun_a_bool) )
& ( hBOOL(hAPP_a_bool(X3551,X3552))
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X3552)),X3551)) = bot_bot_fun_a_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_940])]) ).
fof(i_0_1109,plain,
! [X2475,X2476] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2475),X2476))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2475,X2476)) = hAPP_f22106695ol_nat(finite_card_nat,X2476)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2476)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2475),X2476))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2475,X2476)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X2476))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2476)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_941])])]) ).
fof(i_0_1110,plain,
! [X2469,X2470] :
( ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2469),X2470))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2469,X2470)) = hAPP_f696928925ol_nat(finite346522414t_bool,X2470)
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2470)) )
& ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2469),X2470))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2469,X2470)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X2470))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2470)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_942])])]) ).
fof(i_0_1111,plain,
! [X15,X22,X14] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_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_594_add__leE]) ).
fof(i_0_1112,plain,
! [X2487,X2488] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2488))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2487),X2488))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X2487,X2488)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X2488)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_943])]) ).
fof(i_0_1113,plain,
! [X2481,X2482] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2482))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2481),X2482))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2481,X2482)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X2482)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_944])]) ).
fof(i_0_1114,plain,
! [X3218,X3219,X3220] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3219),X3220))
| insert_nat(hAPP_pname_nat(X3218,X3219),image_pname_nat(X3218,X3220)) = image_pname_nat(X3218,X3220) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_339_insert__image])]) ).
fof(i_0_1115,plain,
! [X3224,X3225,X3226] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3225),X3226))
| insert_nat(hAPP_a_nat(X3224,X3225),image_a_nat(X3224,X3226)) = image_a_nat(X3224,X3226) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_341_insert__image])]) ).
fof(i_0_1116,plain,
! [X3515,X3516] : insert_pname(X3515,X3516) != bot_bo844097828e_bool,
inference(variable_rename,[status(thm)],[fact_458_insert__not__empty]) ).
fof(i_0_1117,plain,
! [X3519,X3520] : insert_a(X3519,X3520) != bot_bot_fun_a_bool,
inference(variable_rename,[status(thm)],[fact_460_insert__not__empty]) ).
fof(i_0_1118,plain,
! [X3521,X3522] : bot_bo844097828e_bool != insert_pname(X3521,X3522),
inference(variable_rename,[status(thm)],[fact_461_empty__not__insert]) ).
fof(i_0_1119,plain,
! [X3525,X3526] : bot_bot_fun_a_bool != insert_a(X3525,X3526),
inference(variable_rename,[status(thm)],[fact_463_empty__not__insert]) ).
fof(i_0_1120,plain,
! [X3487,X3488] :
( insert_nat(X3487,bot_bot_fun_nat_bool) != insert_nat(X3488,bot_bot_fun_nat_bool)
| X3487 = X3488 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_447_singleton__inject])]) ).
fof(i_0_1121,plain,
! [X3577,X3578,X3579] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3578),X3579))
| image_pname_a(cOMBK_a_pname(X3577),X3579) = insert_a(X3577,bot_bot_fun_a_bool) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_497_image__constant])]) ).
fof(i_0_1122,plain,
! [X3028,X3029] :
( ~ is_fun_pname_bool(X3029)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3028),X3029))
| insert_pname(X3028,X3029) = X3029 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_264_insert__absorb])]) ).
fof(i_0_1123,plain,
! [X3030,X3031] :
( ~ is_fun_a_bool(X3031)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3030),X3031))
| insert_a(X3030,X3031) = X3031 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_265_insert__absorb])]) ).
fof(i_0_1124,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_120_not__less__eq__eq]) ).
fof(i_0_1125,plain,
! [X23,X24] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X23),X24)),X23)),
inference(fof_simplification,[status(thm)],[fact_625_not__add__less1]) ).
fof(i_0_1126,plain,
! [X24,X23] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X24),X23)),X23)),
inference(fof_simplification,[status(thm)],[fact_624_not__add__less2]) ).
fof(i_0_1127,plain,
! [X2971,X2972] : insert_nat(X2971,collect_nat(X2972)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2971))),X2972)),
inference(variable_rename,[status(thm)],[fact_243_insert__Collect]) ).
fof(i_0_1128,plain,
! [X2965,X2966] : insert_fun_nat_bool(X2965,collect_fun_nat_bool(X2966)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X2965))),X2966)),
inference(variable_rename,[status(thm)],[fact_240_insert__Collect]) ).
fof(i_0_1129,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_636_not__less__eq]) ).
fof(i_0_1130,plain,
! [X3990,X3991] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X3990),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X3991))))),
inference(variable_rename,[status(thm)],[fact_654_finite__M__bounded__by__nat]) ).
fof(i_0_1131,plain,
! [X3563] : collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X3563)) = insert1325755072e_bool(X3563,bot_bo1649642514l_bool),
inference(variable_rename,[status(thm)],[fact_486_singleton__conv]) ).
fof(i_0_1132,plain,
! [X3564] : collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X3564)) = insert_fun_a_bool(X3564,bot_bo1389914601l_bool),
inference(variable_rename,[status(thm)],[fact_487_singleton__conv]) ).
fof(i_0_1133,plain,
! [X3560] : collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3560)) = insert_pname(X3560,bot_bo844097828e_bool),
inference(variable_rename,[status(thm)],[fact_483_singleton__conv]) ).
fof(i_0_1134,plain,
! [X3561] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3561)) = insert_a(X3561,bot_bot_fun_a_bool),
inference(variable_rename,[status(thm)],[fact_484_singleton__conv]) ).
fof(i_0_1135,plain,
! [X2530,X2531] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2530)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X2530),X2531)))) )
& ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2531)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X2530),X2531)))) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2530)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2531)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X2530),X2531)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_92_finite__Collect__disjI])])]) ).
fof(i_0_1136,plain,
! [X2538,X2539] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2538)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X2538),X2539)))) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2539)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X2538),X2539)))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2538)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2539)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X2538),X2539)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_96_finite__Collect__disjI])])]) ).
fof(i_0_1137,plain,
! [X3580,X3581] :
( ( X3581 != bot_bo844097828e_bool
| image_pname_a(cOMBK_a_pname(X3580),X3581) = bot_bot_fun_a_bool
| ~ is_fun_pname_bool(X3581) )
& ( X3581 = bot_bo844097828e_bool
| image_pname_a(cOMBK_a_pname(X3580),X3581) = insert_a(X3580,bot_bot_fun_a_bool)
| ~ is_fun_pname_bool(X3581) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_498_image__constant__conv])])]) ).
fof(i_0_1138,plain,
! [X3569] : collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X3569)) = insert1325755072e_bool(X3569,bot_bo1649642514l_bool),
inference(variable_rename,[status(thm)],[fact_492_singleton__conv2]) ).
fof(i_0_1139,plain,
! [X3570] : collect_fun_a_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X3570)) = insert_fun_a_bool(X3570,bot_bo1389914601l_bool),
inference(variable_rename,[status(thm)],[fact_493_singleton__conv2]) ).
fof(i_0_1140,plain,
! [X3566] : collect_pname(hAPP_p61793385e_bool(fequal_pname,X3566)) = insert_pname(X3566,bot_bo844097828e_bool),
inference(variable_rename,[status(thm)],[fact_489_singleton__conv2]) ).
fof(i_0_1141,plain,
! [X3567] : collect_a(hAPP_a_fun_a_bool(fequal_a,X3567)) = insert_a(X3567,bot_bot_fun_a_bool),
inference(variable_rename,[status(thm)],[fact_490_singleton__conv2]) ).
fof(i_0_1142,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_116_le__SucE]) ).
fof(i_0_1143,plain,
! [X3535,X3536] :
( ( ~ hBOOL(hAPP_nat_bool(X3535,X3536))
| collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3536)),X3535)) = insert_nat(X3536,bot_bot_fun_nat_bool) )
& ( hBOOL(hAPP_nat_bool(X3535,X3536))
| collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3536)),X3535)) = bot_bot_fun_nat_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_945])]) ).
fof(i_0_1144,plain,
! [X3541,X3542] :
( ( ~ hBOOL(hAPP_f54304608l_bool(X3541,X3542))
| collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X3542)),X3541)) = insert_fun_nat_bool(X3542,bot_bo1701429464l_bool) )
& ( hBOOL(hAPP_f54304608l_bool(X3541,X3542))
| collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X3542)),X3541)) = bot_bo1701429464l_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_946])]) ).
fof(i_0_1145,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_633_not__less__less__Suc__eq]) ).
fof(i_0_1146,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_632_less__antisym]) ).
fof(i_0_1147,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_628_less__SucE]) ).
fof(i_0_1148,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_121_Suc__n__not__le__n]) ).
fof(i_0_1149,plain,
! [X3547,X3548] :
( ( ~ hBOOL(hAPP_nat_bool(X3547,X3548))
| collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X3548)),X3547)) = insert_nat(X3548,bot_bot_fun_nat_bool) )
& ( hBOOL(hAPP_nat_bool(X3547,X3548))
| collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X3548)),X3547)) = bot_bot_fun_nat_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_947])]) ).
fof(i_0_1150,plain,
! [X3553,X3554] :
( ( ~ hBOOL(hAPP_f54304608l_bool(X3553,X3554))
| collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,X3554)),X3553)) = insert_fun_nat_bool(X3554,bot_bo1701429464l_bool) )
& ( hBOOL(hAPP_f54304608l_bool(X3553,X3554))
| collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,X3554)),X3553)) = bot_bo1701429464l_bool ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_948])]) ).
fof(i_0_1151,plain,
! [X3026,X3027] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3026),X3027))
| insert_nat(X3026,X3027) = X3027 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_263_insert__absorb])]) ).
fof(i_0_1152,plain,
! [X2495,X2496] :
( ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2496)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X2496),X2495)))) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X2495)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X2496),X2495)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_73_finite__Collect__conjI])])]) ).
fof(i_0_1153,plain,
! [X2503,X2504] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2504)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X2504),X2503)))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X2503)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X2504),X2503)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_77_finite__Collect__conjI])])]) ).
fof(i_0_1154,plain,
! [X3517,X3518] : insert_nat(X3517,X3518) != bot_bot_fun_nat_bool,
inference(variable_rename,[status(thm)],[fact_459_insert__not__empty]) ).
fof(i_0_1155,plain,
! [X3523,X3524] : bot_bot_fun_nat_bool != insert_nat(X3523,X3524),
inference(variable_rename,[status(thm)],[fact_462_empty__not__insert]) ).
fof(i_0_1156,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_647_linorder__neqE__nat]) ).
fof(i_0_1157,plain,
! [X48,X49] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X48),X49))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X49),X48)) ),
inference(fof_simplification,[status(thm)],[fact_499_linorder__le__cases]) ).
fof(i_0_1158,plain,
! [X3559] : collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3559)) = insert_nat(X3559,bot_bot_fun_nat_bool),
inference(variable_rename,[status(thm)],[fact_482_singleton__conv]) ).
fof(i_0_1159,plain,
! [X3562] : collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X3562)) = insert_fun_nat_bool(X3562,bot_bo1701429464l_bool),
inference(variable_rename,[status(thm)],[fact_485_singleton__conv]) ).
fof(i_0_1160,plain,
! [X3565] : collect_nat(hAPP_n1699378549t_bool(fequal_nat,X3565)) = insert_nat(X3565,bot_bot_fun_nat_bool),
inference(variable_rename,[status(thm)],[fact_488_singleton__conv2]) ).
fof(i_0_1161,plain,
! [X3568] : collect_fun_nat_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X3568)) = insert_fun_nat_bool(X3568,bot_bo1701429464l_bool),
inference(variable_rename,[status(thm)],[fact_491_singleton__conv2]) ).
fof(i_0_1162,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_417_all__not__in__conv]) ).
fof(i_0_1163,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_418_all__not__in__conv]) ).
fof(i_0_1164,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_1165,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_1166,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_1167,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_1168,plain,
! [X15,X14] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X15),X14))
=> hAPP_nat_nat(plus_plus_nat(X14),hAPP_nat_nat(minus_minus_nat(X15),X14)) = X15 ),
inference(fof_simplification,[status(thm)],[fact_666_add__diff__inverse]) ).
fof(i_0_1169,plain,
! [X2362] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2362))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X2362)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_6_finite__Collect__subsets])]) ).
fof(i_0_1170,plain,
! [X92,X93] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X92),X93))
| ~ hBOOL(X92)
| hBOOL(X93) ),
inference(fof_simplification,[status(thm)],[help_fimplies_3_1_U]) ).
fof(i_0_1171,plain,
! [X92,X93] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X92),X93))
| hBOOL(X92)
| hBOOL(X93) ),
inference(fof_simplification,[status(thm)],[help_fdisj_3_1_U]) ).
fof(i_0_1172,plain,
! [X92,X93] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X92),X93))
| hBOOL(X92) ),
inference(fof_simplification,[status(thm)],[help_fconj_2_1_U]) ).
fof(i_0_1173,plain,
! [X92,X93] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X92),X93))
| hBOOL(X93) ),
inference(fof_simplification,[status(thm)],[help_fconj_3_1_U]) ).
fof(i_0_1174,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_416_all__not__in__conv]) ).
fof(i_0_1175,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_395_equals0D]) ).
fof(i_0_1176,plain,
! [X8,X5] :
( X5 = bot_bo844097828e_bool
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),X5)) ),
inference(fof_simplification,[status(thm)],[fact_396_equals0D]) ).
fof(i_0_1177,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_397_equals0D]) ).
fof(i_0_1178,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_1179,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_1180,plain,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X14)),
inference(fof_simplification,[status(thm)],[fact_648_less__irrefl__nat]) ).
fof(i_0_1181,plain,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),X14)),
inference(fof_simplification,[status(thm)],[fact_645_less__not__refl]) ).
fof(i_0_1182,plain,
! [X32] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X32),bot_bot_fun_nat_bool)),
inference(fof_simplification,[status(thm)],[fact_404_empty__iff]) ).
fof(i_0_1183,plain,
! [X8] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),bot_bot_fun_nat_bool)),
inference(fof_simplification,[status(thm)],[fact_383_emptyE]) ).
fof(i_0_1184,plain,
! [X32] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X32),bot_bo844097828e_bool)),
inference(fof_simplification,[status(thm)],[fact_405_empty__iff]) ).
fof(i_0_1185,plain,
! [X8] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),bot_bo844097828e_bool)),
inference(fof_simplification,[status(thm)],[fact_384_emptyE]) ).
fof(i_0_1186,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_406_empty__iff]) ).
fof(i_0_1187,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_385_emptyE]) ).
fof(i_0_1188,plain,
! [X14] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X14),zero_zero_nat)),
inference(fof_simplification,[status(thm)],[fact_678_less__zeroE]) ).
fof(i_0_1189,plain,
! [X3895] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X3895)))),
inference(variable_rename,[status(thm)],[fact_614_finite__Collect__less__nat]) ).
fof(i_0_1190,plain,
! [X2507] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X2507)))),
inference(variable_rename,[status(thm)],[fact_79_finite__Collect__le__nat]) ).
fof(i_0_1191,plain,
! [X93,X92] :
( ~ hBOOL(X92)
| ~ hBOOL(X93)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X92),X93)) ),
inference(fof_simplification,[status(thm)],[help_fconj_1_1_U]) ).
fof(i_0_1192,plain,
! [X92,X93] :
( ~ hBOOL(X93)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X92),X93)) ),
inference(fof_simplification,[status(thm)],[help_fimplies_2_1_U]) ).
fof(i_0_1193,plain,
! [X93,X92] :
( ~ hBOOL(X92)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X92),X93)) ),
inference(fof_simplification,[status(thm)],[help_fdisj_1_1_U]) ).
fof(i_0_1194,plain,
! [X92,X93] :
( ~ hBOOL(X93)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X92),X93)) ),
inference(fof_simplification,[status(thm)],[help_fdisj_2_1_U]) ).
fof(i_0_1195,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_300_equalityE]) ).
fof(i_0_1196,plain,
! [X5,X10] :
( X5 = X10
=> ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10))
=> ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5)) ) ),
inference(fof_simplification,[status(thm)],[fact_299_equalityE]) ).
fof(i_0_1197,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_301_equalityE]) ).
fof(i_0_1198,plain,
! [X13] :
( collec1974731493e_bool(X13) = bot_bo1649642514l_bool
<=> ! [X30] :
( is_fun_pname_bool(X30)
=> ~ hBOOL(hAPP_f1664156314l_bool(X13,X30)) ) ),
inference(fof_simplification,[status(thm)],[fact_400_Collect__empty__eq]) ).
fof(i_0_1199,plain,
! [X13] :
( collect_fun_a_bool(X13) = bot_bo1389914601l_bool
<=> ! [X30] :
( is_fun_a_bool(X30)
=> ~ hBOOL(hAPP_fun_a_bool_bool(X13,X30)) ) ),
inference(fof_simplification,[status(thm)],[fact_401_Collect__empty__eq]) ).
fof(i_0_1200,plain,
! [X13] :
( collect_pname(X13) = bot_bo844097828e_bool
<=> ! [X30] :
( is_pname(X30)
=> ~ hBOOL(hAPP_pname_bool(X13,X30)) ) ),
inference(fof_simplification,[status(thm)],[fact_398_Collect__empty__eq]) ).
fof(i_0_1201,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_402_Collect__empty__eq]) ).
fof(i_0_1202,plain,
! [X13] :
( bot_bo1649642514l_bool = collec1974731493e_bool(X13)
<=> ! [X30] :
( is_fun_pname_bool(X30)
=> ~ hBOOL(hAPP_f1664156314l_bool(X13,X30)) ) ),
inference(fof_simplification,[status(thm)],[fact_409_empty__Collect__eq]) ).
fof(i_0_1203,plain,
! [X13] :
( bot_bo1389914601l_bool = collect_fun_a_bool(X13)
<=> ! [X30] :
( is_fun_a_bool(X30)
=> ~ hBOOL(hAPP_fun_a_bool_bool(X13,X30)) ) ),
inference(fof_simplification,[status(thm)],[fact_410_empty__Collect__eq]) ).
fof(i_0_1204,plain,
! [X13] :
( bot_bo844097828e_bool = collect_pname(X13)
<=> ! [X30] :
( is_pname(X30)
=> ~ hBOOL(hAPP_pname_bool(X13,X30)) ) ),
inference(fof_simplification,[status(thm)],[fact_407_empty__Collect__eq]) ).
fof(i_0_1205,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_411_empty__Collect__eq]) ).
fof(i_0_1206,plain,
! [X2508] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X2508))) = hAPP_nat_nat(suc,X2508),
inference(variable_rename,[status(thm)],[fact_80_card__Collect__le__nat]) ).
fof(i_0_1207,plain,
! [X92] :
( ~ hBOOL(hAPP_bool_bool(fNot,X92))
| ~ hBOOL(X92) ),
inference(fof_simplification,[status(thm)],[help_fNot_1_1_U]) ).
fof(i_0_1208,plain,
! [X3424,X3425,X3426] :
( ( bot_bo1701429464l_bool != collect_fun_nat_bool(X3424)
| ~ hBOOL(hAPP_f54304608l_bool(X3424,X3425)) )
& ( hBOOL(hAPP_f54304608l_bool(X3426,esk92_1(X3426)))
| bot_bo1701429464l_bool = collect_fun_nat_bool(X3426) ) ),
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_949])])])])]) ).
fof(i_0_1209,plain,
! [X3440,X3441,X3442] :
( ( bot_bot_fun_nat_bool != collect_nat(X3440)
| ~ hBOOL(hAPP_nat_bool(X3440,X3441)) )
& ( hBOOL(hAPP_nat_bool(X3442,esk96_1(X3442)))
| bot_bot_fun_nat_bool = collect_nat(X3442) ) ),
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_950])])])])]) ).
fof(i_0_1210,plain,
! [X3397,X3398,X3399] :
( ( collect_fun_nat_bool(X3397) != bot_bo1701429464l_bool
| ~ hBOOL(hAPP_f54304608l_bool(X3397,X3398)) )
& ( hBOOL(hAPP_f54304608l_bool(X3399,esk86_1(X3399)))
| collect_fun_nat_bool(X3399) = bot_bo1701429464l_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_951])])])])]) ).
fof(i_0_1211,plain,
! [X3413,X3414,X3415] :
( ( collect_nat(X3413) != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_nat_bool(X3413,X3414)) )
& ( hBOOL(hAPP_nat_bool(X3415,esk90_1(X3415)))
| collect_nat(X3415) = 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_952])])])])]) ).
fof(i_0_1212,plain,
! [X3989] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),X3989))) = X3989,
inference(variable_rename,[status(thm)],[fact_653_card__Collect__less__nat]) ).
cnf(i_0_1213,plain,
( hBOOL(hAPP_fun_a_bool_bool(p(X2),insert_a(hAPP_pname_a(mgt_call,X1),bot_bot_fun_a_bool)))
| ~ hBOOL(hAPP_fun_a_bool_bool(p(insert_a(hAPP_pname_a(mgt_call,X1),X2)),insert_a(mgt(the_com(body(X1))),bot_bot_fun_a_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_953]) ).
cnf(i_0_1214,plain,
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_954]) ).
cnf(i_0_1215,plain,
( hBOOL(hAPP_f1935102916l_bool(X1,X3))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,insert1325755072e_bool(esk111_3(X1,X2,X3),esk112_3(X1,X2,X3))))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_955]) ).
cnf(i_0_1216,plain,
insert1325755072e_bool(X1,X2) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X2))),
inference(split_conjunct,[status(thm)],[i_0_956]) ).
cnf(i_0_1217,plain,
( hBOOL(hAPP_f621171935l_bool(X1,X3))
| ~ hBOOL(hAPP_f621171935l_bool(X1,insert_fun_a_bool(esk113_3(X1,X2,X3),esk114_3(X1,X2,X3))))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_957]) ).
cnf(i_0_1218,plain,
insert_fun_a_bool(X1,X2) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X2))),
inference(split_conjunct,[status(thm)],[i_0_958]) ).
cnf(i_0_1219,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,insert_pname(esk105_3(X1,X2,X3),esk106_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_959]) ).
cnf(i_0_1220,plain,
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_960]) ).
cnf(i_0_1221,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,insert_a(esk107_3(X1,X2,X3),esk108_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_961]) ).
cnf(i_0_1222,plain,
( X1 = X2
| X1 = X3
| insert_pname(X1,insert_pname(X4,bot_bo844097828e_bool)) != insert_pname(X3,insert_pname(X2,bot_bo844097828e_bool))
| ~ is_pname(X1)
| ~ is_pname(X4)
| ~ is_pname(X3)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_962]) ).
cnf(i_0_1223,plain,
( X1 = X2
| X1 = X3
| insert_pname(X4,insert_pname(X1,bot_bo844097828e_bool)) != insert_pname(X2,insert_pname(X3,bot_bo844097828e_bool))
| ~ is_pname(X4)
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ is_pname(X3) ),
inference(split_conjunct,[status(thm)],[i_0_962]) ).
cnf(i_0_1224,plain,
( X1 = X2
| X1 = X3
| insert_a(X1,insert_a(X4,bot_bot_fun_a_bool)) != insert_a(X3,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_963]) ).
cnf(i_0_1225,plain,
( X1 = X2
| X1 = X3
| insert_a(X4,insert_a(X1,bot_bot_fun_a_bool)) != insert_a(X2,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_963]) ).
cnf(i_0_1226,plain,
( X1 = X2
| X3 = X2
| insert_pname(X1,insert_pname(X3,bot_bo844097828e_bool)) != insert_pname(X4,insert_pname(X2,bot_bo844097828e_bool))
| ~ is_pname(X1)
| ~ is_pname(X3)
| ~ is_pname(X4)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_962]) ).
cnf(i_0_1227,plain,
( X1 = X2
| X3 = X2
| insert_pname(X3,insert_pname(X1,bot_bo844097828e_bool)) != insert_pname(X2,insert_pname(X4,bot_bo844097828e_bool))
| ~ is_pname(X3)
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ is_pname(X4) ),
inference(split_conjunct,[status(thm)],[i_0_962]) ).
cnf(i_0_1228,plain,
( X1 = X2
| X3 = X2
| insert_a(X1,insert_a(X3,bot_bot_fun_a_bool)) != insert_a(X4,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_963]) ).
cnf(i_0_1229,plain,
( X1 = X2
| X3 = X2
| insert_a(X3,insert_a(X1,bot_bot_fun_a_bool)) != insert_a(X2,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_963]) ).
cnf(i_0_1230,plain,
( hBOOL(hAPP_fun_a_bool_bool(p(X1),insert_a(mgt(X2),bot_bot_fun_a_bool)))
| ~ hBOOL(hAPP_fun_a_bool_bool(p(X1),insert_a(hAPP_pname_a(mgt_call,esk81_2(X1,X2)),bot_bot_fun_a_bool)))
| ~ hBOOL(wt(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_964]) ).
cnf(i_0_1231,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
inference(split_conjunct,[status(thm)],[i_0_965]) ).
cnf(i_0_1232,plain,
( hBOOL(hAPP_f1637334154l_bool(X1,X3))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,insert_fun_nat_bool(esk109_3(X1,X2,X3),esk110_3(X1,X2,X3))))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_966]) ).
cnf(i_0_1233,plain,
insert_fun_nat_bool(X1,X2) = cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2)),
inference(rw,[status(thm)],[i_0_967,c_0_968]) ).
cnf(i_0_1234,plain,
( hBOOL(hAPP_f54304608l_bool(X1,X3))
| ~ hBOOL(hAPP_f54304608l_bool(X1,insert_nat(esk103_3(X1,X2,X3),esk104_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_969]) ).
cnf(i_0_1235,plain,
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_970,c_0_971]) ).
fof(i_0_1236,plain,
! [X2843,X2844] :
( ( is_fun_pname_bool(esk43_2(X2843,X2844))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X2843,X2844)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2844)) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,esk43_2(X2843,X2844)),X2844))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X2843,X2844)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2844)) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X2844)),hAPP_n850744903l_bool(cOMBC_1666426608t_bool(cOMBB_1896684278e_bool(fequal_nat,X2843)),hAPP_f921600141ol_nat(X2843,esk43_2(X2843,X2844)))))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X2843,X2844)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2844)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_972])])])]) ).
fof(i_0_1237,plain,
! [X2825,X2826] :
( ( is_fun_pname_bool(esk37_2(X2825,X2826))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X2825,X2826)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2826)) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,esk37_2(X2825,X2826)),X2826))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X2825,X2826)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2826)) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X2826)),hAPP_p338031245l_bool(cOMBC_1004116266e_bool(cOMBB_598082538e_bool(fequal_pname,X2825)),hAPP_f1297739591_pname(X2825,esk37_2(X2825,X2826)))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X2825,X2826)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2826)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_973])])])]) ).
fof(i_0_1238,plain,
! [X2846,X2847] :
( ( is_fun_a_bool(esk44_2(X2846,X2847))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X2846,X2847)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2847)) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,esk44_2(X2846,X2847)),X2847))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X2846,X2847)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2847)) )
& ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X2847)),hAPP_n1414589940l_bool(cOMBC_619334683t_bool(cOMBB_164527437a_bool(fequal_nat,X2846)),hAPP_fun_a_bool_nat(X2846,esk44_2(X2846,X2847)))))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X2846,X2847)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2847)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_974])])])]) ).
fof(i_0_1239,plain,
! [X2828,X2829] :
( ( is_fun_a_bool(esk38_2(X2828,X2829))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X2828,X2829)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2829)) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,esk38_2(X2828,X2829)),X2829))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X2828,X2829)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2829)) )
& ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X2829)),hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(cOMBB_1693087065a_bool(fequal_pname,X2828)),hAPP_f1128469712_pname(X2828,esk38_2(X2828,X2829)))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X2828,X2829)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2829)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_975])])])]) ).
fof(i_0_1240,plain,
! [X2861,X2862] :
( ( is_pname(esk49_2(X2861,X2862))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X2861,X2862)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2862)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk49_2(X2861,X2862)),X2862))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X2861,X2862)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2862)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2862)),hAPP_f654413245e_bool(cOMBC_267053842l_bool(cOMBB_928955006_pname(fequal_fun_nat_bool,X2861)),hAPP_p1499970991t_bool(X2861,esk49_2(X2861,X2862)))))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X2861,X2862)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2862)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_976])])])]) ).
fof(i_0_1241,plain,
! [X2864,X2865] :
( ( is_pname(esk50_2(X2864,X2865))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X2864,X2865)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2865)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk50_2(X2864,X2865)),X2865))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X2864,X2865)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2865)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2865)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(cOMBB_408569982_pname(fequal533582459e_bool,X2864)),hAPP_p61793385e_bool(X2864,esk50_2(X2864,X2865)))))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X2864,X2865)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2865)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_977])])])]) ).
fof(i_0_1242,plain,
! [X2867,X2868] :
( ( is_pname(esk51_2(X2867,X2868))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X2867,X2868)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2868)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk51_2(X2867,X2868)),X2868))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X2867,X2868)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2868)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2868)),hAPP_f1794073134e_bool(cOMBC_445755039l_bool(cOMBB_392435466_pname(fequal_fun_a_bool,X2867)),hAPP_p1534023578a_bool(X2867,esk51_2(X2867,X2868)))))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X2867,X2868)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2868)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_978])])])]) ).
fof(i_0_1243,plain,
! [X2837,X2838] :
( ( is_pname(esk41_2(X2837,X2838))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X2837,X2838)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2838)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk41_2(X2837,X2838)),X2838))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X2837,X2838)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2838)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2838)),hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(cOMBB_523834888_pname(fequal_nat,X2837)),hAPP_pname_nat(X2837,esk41_2(X2837,X2838)))))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X2837,X2838)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2838)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_979])])])]) ).
fof(i_0_1244,plain,
! [X2819,X2820] :
( ( is_pname(esk35_2(X2819,X2820))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X2819,X2820)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2820)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk35_2(X2819,X2820)),X2820))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X2819,X2820)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2820)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2820)),hAPP_p61793385e_bool(cOMBC_1149511130e_bool(cOMBB_542850580_pname(fequal_pname,X2819)),hAPP_pname_pname(X2819,esk35_2(X2819,X2820)))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X2819,X2820)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2820)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_980])])])]) ).
fof(i_0_1245,plain,
! [X2882,X2883] :
( ( is_pname(esk56_2(X2882,X2883))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2882,X2883)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2883)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk56_2(X2882,X2883)),X2883))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2882,X2883)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2883)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2883)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X2882)),hAPP_pname_a(X2882,esk56_2(X2882,X2883)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2882,X2883)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2883)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_981])])])]) ).
fof(i_0_1246,plain,
! [X2873,X2874] :
( ( is_a(esk53_2(X2873,X2874))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(X2873,X2874)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2874)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk53_2(X2873,X2874)),X2874))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(X2873,X2874)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2874)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2874)),hAPP_f1549043526a_bool(cOMBC_777206479l_bool(cOMBB_743407885bool_a(fequal_fun_nat_bool,X2873)),hAPP_a_fun_nat_bool(X2873,esk53_2(X2873,X2874)))))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(X2873,X2874)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2874)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_982])])])]) ).
fof(i_0_1247,plain,
! [X2876,X2877] :
( ( is_a(esk54_2(X2876,X2877))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(X2876,X2877)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2877)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk54_2(X2876,X2877)),X2877))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(X2876,X2877)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2877)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2877)),hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(cOMBB_1137537805bool_a(fequal533582459e_bool,X2876)),hAPP_a93125764e_bool(X2876,esk54_2(X2876,X2877)))))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(X2876,X2877)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2877)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_983])])])]) ).
fof(i_0_1248,plain,
! [X2879,X2880] :
( ( is_a(esk55_2(X2879,X2880))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(X2879,X2880)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2880)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk55_2(X2879,X2880)),X2880))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(X2879,X2880)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2880)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2880)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(cOMBB_472261505bool_a(fequal_fun_a_bool,X2879)),hAPP_a_fun_a_bool(X2879,esk55_2(X2879,X2880)))))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(X2879,X2880)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2880)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_984])])])]) ).
fof(i_0_1249,plain,
! [X2834,X2835] :
( ( is_a(esk40_2(X2834,X2835))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X2834,X2835)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2835)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk40_2(X2834,X2835)),X2835))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X2834,X2835)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2835)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2835)),hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(cOMBB_1321347587bool_a(fequal_nat,X2834)),hAPP_a_nat(X2834,esk40_2(X2834,X2835)))))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X2834,X2835)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2835)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_985])])])]) ).
fof(i_0_1250,plain,
! [X2816,X2817] :
( ( is_a(esk34_2(X2816,X2817))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X2816,X2817)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2817)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk34_2(X2816,X2817)),X2817))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X2816,X2817)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2817)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2817)),hAPP_p1534023578a_bool(cOMBC_a_pname_bool(cOMBB_610033911bool_a(fequal_pname,X2816)),hAPP_a_pname(X2816,esk34_2(X2816,X2817)))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X2816,X2817)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2817)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_986])])])]) ).
fof(i_0_1251,plain,
! [X2870,X2871] :
( ( is_a(esk52_2(X2870,X2871))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X2870,X2871)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2871)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk52_2(X2870,X2871)),X2871))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X2870,X2871)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2871)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2871)),hAPP_a_fun_a_bool(cOMBC_a_a_bool(cOMBB_a_fun_a_bool_a(fequal_a,X2870)),hAPP_a_a(X2870,esk52_2(X2870,X2871)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X2870,X2871)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2871)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_987])])])]) ).
cnf(i_0_1252,plain,
insert_pname(X1,insert_pname(X2,X3)) = insert_pname(X2,insert_pname(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_988]) ).
cnf(i_0_1253,plain,
insert_a(X1,insert_a(X2,X3)) = insert_a(X2,insert_a(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_989]) ).
cnf(i_0_1254,plain,
( insert_pname(X1,insert_pname(X3,bot_bo844097828e_bool)) = insert_pname(X4,insert_pname(X2,bot_bo844097828e_bool))
| X1 != X2
| X3 != X4
| ~ is_pname(X1)
| ~ is_pname(X3)
| ~ is_pname(X4)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_962]) ).
cnf(i_0_1255,plain,
( insert_a(X1,insert_a(X3,bot_bot_fun_a_bool)) = insert_a(X4,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_963]) ).
cnf(i_0_1256,plain,
( hBOOL(hAPP_f1935102916l_bool(X1,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,insert1325755072e_bool(esk117_2(X1,X2),esk118_2(X1,X2))))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_990]) ).
cnf(i_0_1257,plain,
( hBOOL(hAPP_f621171935l_bool(X1,X2))
| ~ hBOOL(hAPP_f621171935l_bool(X1,insert_fun_a_bool(esk119_2(X1,X2),esk120_2(X1,X2))))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_991]) ).
cnf(i_0_1258,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X3,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_992]) ).
cnf(i_0_1259,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_992]) ).
cnf(i_0_1260,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,insert_a(X3,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_993]) ).
cnf(i_0_1261,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,insert_a(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_993]) ).
fof(i_0_1262,plain,
! [X2801,X2802,X2803] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2803,esk30_3(X2801,X2802,X2803))),hAPP_n1699378549t_bool(X2803,hAPP_nat_nat(suc,esk30_3(X2801,X2802,X2803)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2801),X2802))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X2803,X2801)),hAPP_n1699378549t_bool(X2803,X2802))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_184_lift__Suc__mono__le])])]) ).
fof(i_0_1263,plain,
! [X2797,X2798,X2799] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2799,esk29_3(X2797,X2798,X2799))),hAPP_n1025906991e_bool(X2799,hAPP_nat_nat(suc,esk29_3(X2797,X2798,X2799)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2797),X2798))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X2799,X2797)),hAPP_n1025906991e_bool(X2799,X2798))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_183_lift__Suc__mono__le])])]) ).
fof(i_0_1264,plain,
! [X2805,X2806,X2807] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2807,esk31_3(X2805,X2806,X2807))),hAPP_nat_fun_a_bool(X2807,hAPP_nat_nat(suc,esk31_3(X2805,X2806,X2807)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2805),X2806))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X2807,X2805)),hAPP_nat_fun_a_bool(X2807,X2806))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_185_lift__Suc__mono__le])])]) ).
fof(i_0_1265,plain,
! [X2809,X2810,X2811] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X2811,esk32_3(X2809,X2810,X2811))),hAPP_nat_nat(X2811,hAPP_nat_nat(suc,esk32_3(X2809,X2810,X2811)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2809),X2810))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X2811,X2809)),hAPP_nat_nat(X2811,X2810))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_186_lift__Suc__mono__le])])]) ).
fof(i_0_1266,plain,
! [X2793,X2794,X2795] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X2795,esk28_3(X2793,X2794,X2795))),hAPP_nat_bool(X2795,hAPP_nat_nat(suc,esk28_3(X2793,X2794,X2795)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2793),X2794))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X2795,X2793)),hAPP_nat_bool(X2795,X2794))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_182_lift__Suc__mono__le])])]) ).
cnf(i_0_1267,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X3,X1)),insert_pname(X3,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_994]) ).
cnf(i_0_1268,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X3,X1)),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_995]) ).
fof(i_0_1269,plain,
! [X4030,X4031,X4032] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk126_3(X4030,X4031,X4032)),esk127_3(X4030,X4031,X4032)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X4032,X4030)),X4031)),hAPP_nat_nat(X4032,hAPP_nat_nat(plus_plus_nat(X4030),X4031)))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X4032,esk126_3(X4030,X4031,X4032))),hAPP_nat_nat(X4032,esk127_3(X4030,X4031,X4032))))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X4032,X4030)),X4031)),hAPP_nat_nat(X4032,hAPP_nat_nat(plus_plus_nat(X4030),X4031)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_671_mono__nat__linear__lb])])])]) ).
fof(i_0_1270,plain,
! [X4045,X4046,X4047] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk131_3(X4045,X4046,X4047)),esk132_3(X4045,X4046,X4047)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4045),X4046))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X4047,X4045)),hAPP_nat_nat(X4047,X4046))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X4047,esk131_3(X4045,X4046,X4047))),hAPP_nat_nat(X4047,esk132_3(X4045,X4046,X4047))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4045),X4046))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X4047,X4045)),hAPP_nat_nat(X4047,X4046))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_675_less__mono__imp__le__mono])])])]) ).
cnf(i_0_1271,plain,
insert_pname(X1,insert_pname(X1,X2)) = insert_pname(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_996]) ).
cnf(i_0_1272,plain,
insert_a(X1,insert_a(X1,X2)) = insert_a(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_997]) ).
cnf(i_0_1273,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)),hAPP_n215258509l_bool(cOMBC_385542954t_bool(cOMBB_1250273980t_bool(fequal_nat,X2)),hAPP_f22106695ol_nat(X2,esk42_2(X2,X1)))))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_998]) ).
cnf(i_0_1274,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)),hAPP_p130839763l_bool(cOMBC_615407716e_bool(cOMBB_141086128t_bool(fequal_pname,X2)),hAPP_f1291551745_pname(X2,esk36_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_999]) ).
cnf(i_0_1275,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,esk46_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1000]) ).
cnf(i_0_1276,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,esk47_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1001]) ).
cnf(i_0_1277,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,esk48_2(X2,X1)))))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1002]) ).
cnf(i_0_1278,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_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(fequal_nat,X2)),hAPP_nat_nat(X2,esk39_2(X2,X1)))))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1003]) ).
cnf(i_0_1279,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_p1499970991t_bool(cOMBC_nat_pname_bool(cOMBB_1212655066ol_nat(fequal_pname,X2)),hAPP_nat_pname(X2,esk33_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1004]) ).
cnf(i_0_1280,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_a_fun_nat_bool(cOMBC_nat_a_bool(cOMBB_1885489796ol_nat(fequal_a,X2)),hAPP_nat_a(X2,esk45_2(X2,X1)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1005]) ).
cnf(i_0_1281,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_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_992]) ).
cnf(i_0_1282,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_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_993]) ).
cnf(i_0_1283,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X2,X1))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1006]) ).
cnf(i_0_1284,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X2,X1))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1007]) ).
cnf(i_0_1285,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,insert_a(X2,X1))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1008]) ).
cnf(i_0_1286,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,insert_pname(X2,X1))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1009]) ).
cnf(i_0_1287,plain,
( X1 = X2
| X1 = X3
| insert_nat(X1,insert_nat(X4,bot_bot_fun_nat_bool)) != insert_nat(X3,insert_nat(X2,bot_bot_fun_nat_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1010]) ).
cnf(i_0_1288,plain,
( X1 = X2
| X1 = X3
| insert_nat(X4,insert_nat(X1,bot_bot_fun_nat_bool)) != insert_nat(X2,insert_nat(X3,bot_bot_fun_nat_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1010]) ).
cnf(i_0_1289,plain,
( X1 = X2
| X3 = X2
| insert_nat(X1,insert_nat(X3,bot_bot_fun_nat_bool)) != insert_nat(X4,insert_nat(X2,bot_bot_fun_nat_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1010]) ).
cnf(i_0_1290,plain,
( X1 = X2
| X3 = X2
| insert_nat(X3,insert_nat(X1,bot_bot_fun_nat_bool)) != insert_nat(X2,insert_nat(X4,bot_bot_fun_nat_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1010]) ).
cnf(i_0_1291,plain,
( X1 = bot_bo844097828e_bool
| X1 = insert_pname(X2,bot_bo844097828e_bool)
| ~ is_fun_pname_bool(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X2,bot_bo844097828e_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_1011]) ).
cnf(i_0_1292,plain,
( X1 = bot_bot_fun_a_bool
| X1 = 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),insert_a(X2,bot_bot_fun_a_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_1012]) ).
cnf(i_0_1293,plain,
( hBOOL(hAPP_f1637334154l_bool(X1,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,insert_fun_nat_bool(esk115_2(X1,X2),esk116_2(X1,X2))))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1013]) ).
cnf(i_0_1294,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),insert_pname(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1014]) ).
cnf(i_0_1295,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),insert_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1015]) ).
cnf(i_0_1296,plain,
( X1 = X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3)))
| ~ is_pname(X1)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1016]) ).
cnf(i_0_1297,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),insert_pname(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1017]) ).
cnf(i_0_1298,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),insert_a(X2,X3)))
| ~ is_a(X1)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1018]) ).
cnf(i_0_1299,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),insert_a(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1019]) ).
cnf(i_0_1300,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1020]) ).
cnf(i_0_1301,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X3,X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1020]) ).
fof(i_0_1302,plain,
! [X3303,X3304,X3305] :
( ( is_pname(esk72_3(X3303,X3304,X3305))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(X3303,X3305)),X3304)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk72_3(X3303,X3304,X3305)),X3305))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(X3303,X3305)),X3304)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(X3303,esk72_3(X3303,X3304,X3305))),X3304))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(X3303,X3305)),X3304)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_360_image__subsetI])])])]) ).
fof(i_0_1303,plain,
! [X3311,X3312,X3313] :
( ( is_a(esk74_3(X3311,X3312,X3313))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(X3311,X3313)),X3312)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk74_3(X3311,X3312,X3313)),X3313))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(X3311,X3313)),X3312)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(X3311,esk74_3(X3311,X3312,X3313))),X3312))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(X3311,X3313)),X3312)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_362_image__subsetI])])])]) ).
fof(i_0_1304,plain,
! [X3319,X3320,X3321] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk76_3(X3319,X3320,X3321)),X3321))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_nat_pname(X3319,X3321)),X3320)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(X3319,esk76_3(X3319,X3320,X3321))),X3320))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_nat_pname(X3319,X3321)),X3320)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_364_image__subsetI])])])]) ).
fof(i_0_1305,plain,
! [X3307,X3308,X3309] :
( ( is_pname(esk73_3(X3307,X3308,X3309))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(X3307,X3309)),X3308)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk73_3(X3307,X3308,X3309)),X3309))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(X3307,X3309)),X3308)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(X3307,esk73_3(X3307,X3308,X3309))),X3308))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(X3307,X3309)),X3308)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_361_image__subsetI])])])]) ).
fof(i_0_1306,plain,
! [X3315,X3316,X3317] :
( ( is_a(esk75_3(X3315,X3316,X3317))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(X3315,X3317)),X3316)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk75_3(X3315,X3316,X3317)),X3317))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(X3315,X3317)),X3316)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_a_pname(X3315,esk75_3(X3315,X3316,X3317))),X3316))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(X3315,X3317)),X3316)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_363_image__subsetI])])])]) ).
fof(i_0_1307,plain,
! [X3323,X3324,X3325] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk77_3(X3323,X3324,X3325)),X3325))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(X3323,X3325)),X3324)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(X3323,esk77_3(X3323,X3324,X3325))),X3324))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(X3323,X3325)),X3324)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_365_image__subsetI])])])]) ).
fof(i_0_1308,plain,
! [X3327,X3328,X3329] :
( ( is_pname(esk78_3(X3327,X3328,X3329))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X3327,X3329)),X3328)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk78_3(X3327,X3328,X3329)),X3329))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X3327,X3329)),X3328)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X3327,esk78_3(X3327,X3328,X3329))),X3328))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X3327,X3329)),X3328)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_366_image__subsetI])])])]) ).
cnf(i_0_1309,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X3,X1)),insert_nat(X3,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1021]) ).
cnf(i_0_1310,plain,
( X1 = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,bot_bo844097828e_bool)))
| ~ is_pname(X1)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1022]) ).
cnf(i_0_1311,plain,
( X1 = X2
| ~ is_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,bot_bo844097828e_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_1023]) ).
cnf(i_0_1312,plain,
( X1 = X2
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,bot_bot_fun_a_bool)))
| ~ is_a(X1)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1024]) ).
cnf(i_0_1313,plain,
( X1 = X2
| ~ is_a(X1)
| ~ is_a(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,bot_bot_fun_a_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_1025]) ).
cnf(i_0_1314,plain,
( X1 = X3
| hBOOL(hAPP_pname_bool(X2,X3))
| ~ hBOOL(hAPP_pname_bool(insert_pname(X1,X2),X3))
| ~ is_pname(X1)
| ~ is_pname(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1026]) ).
cnf(i_0_1315,plain,
( X1 = X3
| hBOOL(hAPP_a_bool(X2,X3))
| ~ hBOOL(hAPP_a_bool(insert_a(X1,X2),X3))
| ~ is_a(X1)
| ~ is_a(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1027]) ).
cnf(i_0_1316,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1028]) ).
cnf(i_0_1317,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1029]) ).
cnf(i_0_1318,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1030]) ).
cnf(i_0_1319,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1031]) ).
cnf(i_0_1320,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk81_2(X1,X2)),u))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),insert_a(mgt(X2),bot_bot_fun_a_bool)))
| ~ hBOOL(wt(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_964]) ).
cnf(i_0_1321,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_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_1020]) ).
cnf(i_0_1322,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),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_1014]) ).
cnf(i_0_1323,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),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_1015]) ).
cnf(i_0_1324,plain,
( is_pname(esk81_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),insert_a(mgt(X2),bot_bot_fun_a_bool)))
| ~ hBOOL(wt(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_964]) ).
cnf(i_0_1325,plain,
insert_nat(X1,insert_nat(X2,X3)) = insert_nat(X2,insert_nat(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_1032]) ).
cnf(i_0_1326,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,insert_nat(X2,X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1033]) ).
cnf(i_0_1327,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X2,X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1034]) ).
cnf(i_0_1328,plain,
( insert_nat(X1,insert_nat(X3,bot_bot_fun_nat_bool)) = insert_nat(X4,insert_nat(X2,bot_bot_fun_nat_bool))
| X1 != X2
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[i_0_1010]) ).
cnf(i_0_1329,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),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_1016]) ).
cnf(i_0_1330,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),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_1018]) ).
cnf(i_0_1331,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X3,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1035]) ).
cnf(i_0_1332,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X3,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1036]) ).
cnf(i_0_1333,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X3,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1037]) ).
cnf(i_0_1334,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),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_1038]) ).
cnf(i_0_1335,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X3,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1039]) ).
cnf(i_0_1336,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X3,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1040]) ).
cnf(i_0_1337,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3)))
| X1 != X2
| ~ is_pname(X1)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1016]) ).
cnf(i_0_1338,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,X3)))
| X1 != X2
| ~ is_a(X1)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1018]) ).
cnf(i_0_1339,plain,
( hBOOL(hAPP_pname_bool(insert_pname(X3,X1),X2))
| ~ hBOOL(hAPP_pname_bool(X1,X2))
| ~ is_pname(X3)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1026]) ).
cnf(i_0_1340,plain,
( hBOOL(hAPP_a_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_1027]) ).
cnf(i_0_1341,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1037]) ).
cnf(i_0_1342,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1040]) ).
cnf(i_0_1343,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X2,X1))),
inference(split_conjunct,[status(thm)],[i_0_1041]) ).
cnf(i_0_1344,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_1042]) ).
cnf(i_0_1345,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),insert_a(X2,X1))),
inference(split_conjunct,[status(thm)],[i_0_1043]) ).
cnf(i_0_1346,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_1044]) ).
cnf(i_0_1347,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X2,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1028]) ).
cnf(i_0_1348,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X2,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1045]) ).
cnf(i_0_1349,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X2,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1029]) ).
cnf(i_0_1350,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X2,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1046]) ).
cnf(i_0_1351,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1030]) ).
cnf(i_0_1352,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1047]) ).
cnf(i_0_1353,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X2,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1031]) ).
cnf(i_0_1354,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X2,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1048]) ).
cnf(i_0_1355,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,bot_bo844097828e_bool)))
| X1 != X2
| ~ is_pname(X1)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1022]) ).
cnf(i_0_1356,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X2,bot_bot_fun_a_bool)))
| X1 != X2
| ~ is_a(X1)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1024]) ).
cnf(i_0_1357,plain,
image_pname_a(X1,insert_pname(X2,X3)) = insert_a(hAPP_pname_a(X1,X2),image_pname_a(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_1049]) ).
cnf(i_0_1358,plain,
image_a_pname(X1,insert_a(X2,X3)) = insert_pname(hAPP_a_pname(X1,X2),image_a_pname(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_1050]) ).
cnf(i_0_1359,plain,
( hBOOL(hAPP_pname_bool(insert_pname(X1,X3),X2))
| X1 != X2
| ~ is_pname(X1)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1026]) ).
cnf(i_0_1360,plain,
( hBOOL(hAPP_a_bool(insert_a(X1,X3),X2))
| X1 != X2
| ~ is_a(X1)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1027]) ).
cnf(i_0_1361,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),insert_nat(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1051]) ).
cnf(i_0_1362,plain,
( X1 = bot_bot_fun_nat_bool
| X1 = insert_nat(X2,bot_bot_fun_nat_bool)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X2,bot_bot_fun_nat_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_1052]) ).
cnf(i_0_1363,plain,
( X1 = X2
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1053]) ).
cnf(i_0_1364,plain,
( X1 = X2
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1054]) ).
cnf(i_0_1365,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))
| insert_pname(X1,X2) != insert_pname(X1,X3)
| ~ is_fun_pname_bool(X3)
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1055]) ).
cnf(i_0_1366,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))
| insert_a(X1,X2) != insert_a(X1,X3)
| ~ is_fun_a_bool(X3)
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1056]) ).
cnf(i_0_1367,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,bot_bot_fun_nat_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_1057]) ).
cnf(i_0_1368,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,bot_bot_fun_nat_bool))) ),
inference(split_conjunct,[status(thm)],[i_0_1058]) ).
fof(i_0_1369,plain,
! [X3351,X3352,X3353,X3354,X3355] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3351),X3352))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X3351,X3353)),hAPP_nat_bool(X3352,X3353))) )
& ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X3354,esk83_2(X3354,X3355))),hAPP_nat_bool(X3355,esk83_2(X3354,X3355))))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3354),X3355)) ) ),
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_375_le__fun__def])])])])]) ).
fof(i_0_1370,plain,
! [X3345,X3346,X3347,X3348,X3349] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3345),X3346))
| ~ is_pname(X3347)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(X3345,X3347)),hAPP_pname_bool(X3346,X3347))) )
& ( is_pname(esk82_2(X3348,X3349))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3348),X3349)) )
& ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(X3348,esk82_2(X3348,X3349))),hAPP_pname_bool(X3349,esk82_2(X3348,X3349))))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3348),X3349)) ) ),
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_374_le__fun__def])])])])])]) ).
fof(i_0_1371,plain,
! [X3357,X3358,X3359,X3360,X3361] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3357),X3358))
| ~ is_a(X3359)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X3357,X3359)),hAPP_a_bool(X3358,X3359))) )
& ( is_a(esk84_2(X3360,X3361))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3360),X3361)) )
& ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X3360,esk84_2(X3360,X3361))),hAPP_a_bool(X3361,esk84_2(X3360,X3361))))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3360),X3361)) ) ),
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_376_le__fun__def])])])])])]) ).
cnf(i_0_1372,plain,
( X1 = X3
| hBOOL(hAPP_nat_bool(X2,X3))
| ~ hBOOL(hAPP_nat_bool(insert_nat(X1,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1059]) ).
cnf(i_0_1373,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1060]) ).
cnf(i_0_1374,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1061]) ).
cnf(i_0_1375,plain,
image_nat_a(X1,insert_nat(X2,X3)) = insert_a(hAPP_nat_a(X1,X2),image_nat_a(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_1062]) ).
cnf(i_0_1376,plain,
( X1 = X2
| ~ is_pname(X1)
| ~ is_pname(X2)
| insert_pname(X1,bot_bo844097828e_bool) != insert_pname(X2,bot_bo844097828e_bool) ),
inference(split_conjunct,[status(thm)],[i_0_1063]) ).
cnf(i_0_1377,plain,
( X1 = X2
| ~ is_a(X1)
| ~ is_a(X2)
| insert_a(X1,bot_bot_fun_a_bool) != insert_a(X2,bot_bot_fun_a_bool) ),
inference(split_conjunct,[status(thm)],[i_0_1064]) ).
cnf(i_0_1378,plain,
image_a_nat(X1,insert_a(X2,X3)) = insert_nat(hAPP_a_nat(X1,X2),image_a_nat(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_1065]) ).
cnf(i_0_1379,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,esk121_2(X1,X2)),hAPP_nat_nat(X2,esk121_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1066]) ).
cnf(i_0_1380,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),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_1051]) ).
fof(i_0_1381,plain,
! [X4026,X4027,X4028] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X4028),X4027)),hAPP_nat_nat(minus_minus_nat(X4026),X4027)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4028),X4026))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4027),X4026))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4027),X4028)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4028),X4026))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X4028),X4027)),hAPP_nat_nat(minus_minus_nat(X4026),X4027)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4027),X4026))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4027),X4028)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_669_less__diff__iff])])]) ).
fof(i_0_1382,plain,
! [X2594,X2595,X2596] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2596),X2595)),hAPP_nat_nat(minus_minus_nat(X2594),X2595)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2596),X2594))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2595),X2594))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2595),X2596)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2596),X2594))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2596),X2595)),hAPP_nat_nat(minus_minus_nat(X2594),X2595)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2595),X2594))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2595),X2596)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_124_le__diff__iff])])]) ).
cnf(i_0_1383,plain,
insert_nat(X1,insert_nat(X1,X2)) = insert_nat(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1067]) ).
fof(i_0_1384,plain,
! [X2717,X2718,X2719] :
( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,esk9_3(X2717,X2718,X2719)),X2718))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2719),image_1921560913_pname(X2717,X2718)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2719))
| ~ is_fun_pname_bool(X2719) )
& ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk9_3(X2717,X2718,X2719)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2719),image_1921560913_pname(X2717,X2718)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2719))
| ~ is_fun_pname_bool(X2719) )
& ( X2719 = image_1921560913_pname(X2717,esk9_3(X2717,X2718,X2719))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2719),image_1921560913_pname(X2717,X2718)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2719))
| ~ is_fun_pname_bool(X2719) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_163_finite__subset__image])])])]) ).
fof(i_0_1385,plain,
! [X2685,X2686,X2687] :
( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,esk1_3(X2685,X2686,X2687)),X2686))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2687),image_fun_nat_bool_a(X2685,X2686)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2687))
| ~ is_fun_a_bool(X2687) )
& ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk1_3(X2685,X2686,X2687)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2687),image_fun_nat_bool_a(X2685,X2686)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2687))
| ~ is_fun_a_bool(X2687) )
& ( X2687 = image_fun_nat_bool_a(X2685,esk1_3(X2685,X2686,X2687))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2687),image_fun_nat_bool_a(X2685,X2686)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2687))
| ~ is_fun_a_bool(X2687) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_155_finite__subset__image])])])]) ).
fof(i_0_1386,plain,
! [X2721,X2722,X2723] :
( ( is_fun1661590463l_bool(esk10_3(X2721,X2722,X2723))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2723),image_1283814551_pname(X2721,X2722)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2723))
| ~ is_fun_pname_bool(X2723) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,esk10_3(X2721,X2722,X2723)),X2722))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2723),image_1283814551_pname(X2721,X2722)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2723))
| ~ is_fun_pname_bool(X2723) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk10_3(X2721,X2722,X2723)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2723),image_1283814551_pname(X2721,X2722)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2723))
| ~ is_fun_pname_bool(X2723) )
& ( X2723 = image_1283814551_pname(X2721,esk10_3(X2721,X2722,X2723))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2723),image_1283814551_pname(X2721,X2722)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2723))
| ~ is_fun_pname_bool(X2723) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_164_finite__subset__image])])])]) ).
fof(i_0_1387,plain,
! [X2689,X2690,X2691] :
( ( is_fun1661590463l_bool(esk2_3(X2689,X2690,X2691))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2691),image_876012084bool_a(X2689,X2690)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2691))
| ~ is_fun_a_bool(X2691) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,esk2_3(X2689,X2690,X2691)),X2690))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2691),image_876012084bool_a(X2689,X2690)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2691))
| ~ is_fun_a_bool(X2691) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk2_3(X2689,X2690,X2691)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2691),image_876012084bool_a(X2689,X2690)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2691))
| ~ is_fun_a_bool(X2691) )
& ( X2691 = image_876012084bool_a(X2689,esk2_3(X2689,X2690,X2691))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2691),image_876012084bool_a(X2689,X2690)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2691))
| ~ is_fun_a_bool(X2691) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_156_finite__subset__image])])])]) ).
fof(i_0_1388,plain,
! [X2725,X2726,X2727] :
( ( is_fun949378684l_bool(esk11_3(X2725,X2726,X2727))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2727),image_1854862208_pname(X2725,X2726)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2727))
| ~ is_fun_pname_bool(X2727) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,esk11_3(X2725,X2726,X2727)),X2726))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2727),image_1854862208_pname(X2725,X2726)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2727))
| ~ is_fun_pname_bool(X2727) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk11_3(X2725,X2726,X2727)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2727),image_1854862208_pname(X2725,X2726)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2727))
| ~ is_fun_pname_bool(X2727) )
& ( X2727 = image_1854862208_pname(X2725,esk11_3(X2725,X2726,X2727))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2727),image_1854862208_pname(X2725,X2726)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2727))
| ~ is_fun_pname_bool(X2727) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_165_finite__subset__image])])])]) ).
fof(i_0_1389,plain,
! [X2693,X2694,X2695] :
( ( is_fun949378684l_bool(esk3_3(X2693,X2694,X2695))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2695),image_fun_a_bool_a(X2693,X2694)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2695))
| ~ is_fun_a_bool(X2695) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,esk3_3(X2693,X2694,X2695)),X2694))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2695),image_fun_a_bool_a(X2693,X2694)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2695))
| ~ is_fun_a_bool(X2695) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk3_3(X2693,X2694,X2695)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2695),image_fun_a_bool_a(X2693,X2694)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2695))
| ~ is_fun_a_bool(X2695) )
& ( X2695 = image_fun_a_bool_a(X2693,esk3_3(X2693,X2694,X2695))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2695),image_fun_a_bool_a(X2693,X2694)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2695))
| ~ is_fun_a_bool(X2695) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_157_finite__subset__image])])])]) ).
fof(i_0_1390,plain,
! [X2781,X2782,X2783] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk25_3(X2781,X2782,X2783)),X2782))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2783),image_nat_pname(X2781,X2782)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2783))
| ~ is_fun_pname_bool(X2783) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk25_3(X2781,X2782,X2783)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2783),image_nat_pname(X2781,X2782)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2783))
| ~ is_fun_pname_bool(X2783) )
& ( X2783 = image_nat_pname(X2781,esk25_3(X2781,X2782,X2783))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2783),image_nat_pname(X2781,X2782)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2783))
| ~ is_fun_pname_bool(X2783) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_179_finite__subset__image])])])]) ).
fof(i_0_1391,plain,
! [X2777,X2778,X2779] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk24_3(X2777,X2778,X2779)),X2778))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2779),image_nat_fun_a_bool(X2777,X2778)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2779))
| ~ is_fun949378684l_bool(X2779) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk24_3(X2777,X2778,X2779)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2779),image_nat_fun_a_bool(X2777,X2778)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2779))
| ~ is_fun949378684l_bool(X2779) )
& ( X2779 = image_nat_fun_a_bool(X2777,esk24_3(X2777,X2778,X2779))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2779),image_nat_fun_a_bool(X2777,X2778)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2779))
| ~ is_fun949378684l_bool(X2779) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_178_finite__subset__image])])])]) ).
fof(i_0_1392,plain,
! [X2773,X2774,X2775] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk23_3(X2773,X2774,X2775)),X2774))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2775),image_1655916159e_bool(X2773,X2774)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2775))
| ~ is_fun1661590463l_bool(X2775) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk23_3(X2773,X2774,X2775)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2775),image_1655916159e_bool(X2773,X2774)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2775))
| ~ is_fun1661590463l_bool(X2775) )
& ( X2775 = image_1655916159e_bool(X2773,esk23_3(X2773,X2774,X2775))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2775),image_1655916159e_bool(X2773,X2774)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2775))
| ~ is_fun1661590463l_bool(X2775) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_177_finite__subset__image])])])]) ).
fof(i_0_1393,plain,
! [X2765,X2766,X2767] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk21_3(X2765,X2766,X2767)),X2766))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2767),image_nat_a(X2765,X2766)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2767))
| ~ is_fun_a_bool(X2767) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk21_3(X2765,X2766,X2767)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2767),image_nat_a(X2765,X2766)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2767))
| ~ is_fun_a_bool(X2767) )
& ( X2767 = image_nat_a(X2765,esk21_3(X2765,X2766,X2767))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2767),image_nat_a(X2765,X2766)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2767))
| ~ is_fun_a_bool(X2767) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_175_finite__subset__image])])])]) ).
fof(i_0_1394,plain,
! [X2789,X2790,X2791] :
( ( is_fun_pname_bool(esk27_3(X2789,X2790,X2791))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2791),image_pname_a(X2789,X2790)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2791))
| ~ is_fun_a_bool(X2791) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk27_3(X2789,X2790,X2791)),X2790))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2791),image_pname_a(X2789,X2790)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2791))
| ~ is_fun_a_bool(X2791) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk27_3(X2789,X2790,X2791)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2791),image_pname_a(X2789,X2790)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2791))
| ~ is_fun_a_bool(X2791) )
& ( X2791 = image_pname_a(X2789,esk27_3(X2789,X2790,X2791))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2791),image_pname_a(X2789,X2790)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2791))
| ~ is_fun_a_bool(X2791) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_181_finite__subset__image])])])]) ).
fof(i_0_1395,plain,
! [X2757,X2758,X2759] :
( ( is_fun_pname_bool(esk19_3(X2757,X2758,X2759))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2759),image_pname_pname(X2757,X2758)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2759))
| ~ is_fun_pname_bool(X2759) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk19_3(X2757,X2758,X2759)),X2758))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2759),image_pname_pname(X2757,X2758)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2759))
| ~ is_fun_pname_bool(X2759) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk19_3(X2757,X2758,X2759)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2759),image_pname_pname(X2757,X2758)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2759))
| ~ is_fun_pname_bool(X2759) )
& ( X2759 = image_pname_pname(X2757,esk19_3(X2757,X2758,X2759))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2759),image_pname_pname(X2757,X2758)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2759))
| ~ is_fun_pname_bool(X2759) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_173_finite__subset__image])])])]) ).
fof(i_0_1396,plain,
! [X2753,X2754,X2755] :
( ( is_fun_pname_bool(esk18_3(X2753,X2754,X2755))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2755),image_112932426a_bool(X2753,X2754)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2755))
| ~ is_fun949378684l_bool(X2755) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk18_3(X2753,X2754,X2755)),X2754))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2755),image_112932426a_bool(X2753,X2754)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2755))
| ~ is_fun949378684l_bool(X2755) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk18_3(X2753,X2754,X2755)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2755),image_112932426a_bool(X2753,X2754)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2755))
| ~ is_fun949378684l_bool(X2755) )
& ( X2755 = image_112932426a_bool(X2753,esk18_3(X2753,X2754,X2755))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2755),image_112932426a_bool(X2753,X2754)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2755))
| ~ is_fun949378684l_bool(X2755) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_172_finite__subset__image])])])]) ).
fof(i_0_1397,plain,
! [X2749,X2750,X2751] :
( ( is_fun_pname_bool(esk17_3(X2749,X2750,X2751))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2751),image_47868345e_bool(X2749,X2750)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2751))
| ~ is_fun1661590463l_bool(X2751) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk17_3(X2749,X2750,X2751)),X2750))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2751),image_47868345e_bool(X2749,X2750)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2751))
| ~ is_fun1661590463l_bool(X2751) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk17_3(X2749,X2750,X2751)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2751),image_47868345e_bool(X2749,X2750)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2751))
| ~ is_fun1661590463l_bool(X2751) )
& ( X2751 = image_47868345e_bool(X2749,esk17_3(X2749,X2750,X2751))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2751),image_47868345e_bool(X2749,X2750)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2751))
| ~ is_fun1661590463l_bool(X2751) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_171_finite__subset__image])])])]) ).
fof(i_0_1398,plain,
! [X2713,X2714,X2715] :
( ( is_fun_a_bool(esk8_3(X2713,X2714,X2715))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2715),image_a_pname(X2713,X2714)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2715))
| ~ is_fun_pname_bool(X2715) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk8_3(X2713,X2714,X2715)),X2714))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2715),image_a_pname(X2713,X2714)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2715))
| ~ is_fun_pname_bool(X2715) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk8_3(X2713,X2714,X2715)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2715),image_a_pname(X2713,X2714)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2715))
| ~ is_fun_pname_bool(X2715) )
& ( X2715 = image_a_pname(X2713,esk8_3(X2713,X2714,X2715))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2715),image_a_pname(X2713,X2714)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2715))
| ~ is_fun_pname_bool(X2715) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_162_finite__subset__image])])])]) ).
fof(i_0_1399,plain,
! [X2709,X2710,X2711] :
( ( is_fun_a_bool(esk7_3(X2709,X2710,X2711))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2711),image_a_fun_a_bool(X2709,X2710)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2711))
| ~ is_fun949378684l_bool(X2711) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk7_3(X2709,X2710,X2711)),X2710))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2711),image_a_fun_a_bool(X2709,X2710)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2711))
| ~ is_fun949378684l_bool(X2711) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk7_3(X2709,X2710,X2711)))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2711),image_a_fun_a_bool(X2709,X2710)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2711))
| ~ is_fun949378684l_bool(X2711) )
& ( X2711 = image_a_fun_a_bool(X2709,esk7_3(X2709,X2710,X2711))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2711),image_a_fun_a_bool(X2709,X2710)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2711))
| ~ is_fun949378684l_bool(X2711) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_161_finite__subset__image])])])]) ).
fof(i_0_1400,plain,
! [X2705,X2706,X2707] :
( ( is_fun_a_bool(esk6_3(X2705,X2706,X2707))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2707),image_819518260e_bool(X2705,X2706)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2707))
| ~ is_fun1661590463l_bool(X2707) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk6_3(X2705,X2706,X2707)),X2706))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2707),image_819518260e_bool(X2705,X2706)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2707))
| ~ is_fun1661590463l_bool(X2707) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk6_3(X2705,X2706,X2707)))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2707),image_819518260e_bool(X2705,X2706)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2707))
| ~ is_fun1661590463l_bool(X2707) )
& ( X2707 = image_819518260e_bool(X2705,esk6_3(X2705,X2706,X2707))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2707),image_819518260e_bool(X2705,X2706)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2707))
| ~ is_fun1661590463l_bool(X2707) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_160_finite__subset__image])])])]) ).
fof(i_0_1401,plain,
! [X2697,X2698,X2699] :
( ( is_fun_a_bool(esk4_3(X2697,X2698,X2699))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2699),image_a_a(X2697,X2698)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2699))
| ~ is_fun_a_bool(X2699) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk4_3(X2697,X2698,X2699)),X2698))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2699),image_a_a(X2697,X2698)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2699))
| ~ is_fun_a_bool(X2699) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk4_3(X2697,X2698,X2699)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2699),image_a_a(X2697,X2698)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2699))
| ~ is_fun_a_bool(X2699) )
& ( X2699 = image_a_a(X2697,esk4_3(X2697,X2698,X2699))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2699),image_a_a(X2697,X2698)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2699))
| ~ is_fun_a_bool(X2699) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_158_finite__subset__image])])])]) ).
fof(i_0_1402,plain,
! [X2733,X2734,X2735] :
( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,esk13_3(X2733,X2734,X2735)),X2734))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2735),image_496248727ol_nat(X2733,X2734)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2735)) )
& ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk13_3(X2733,X2734,X2735)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2735),image_496248727ol_nat(X2733,X2734)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2735)) )
& ( X2735 = image_496248727ol_nat(X2733,esk13_3(X2733,X2734,X2735))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2735),image_496248727ol_nat(X2733,X2734)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2735)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_167_finite__subset__image])])])]) ).
fof(i_0_1403,plain,
! [X2737,X2738,X2739] :
( ( is_fun1661590463l_bool(esk14_3(X2737,X2738,X2739))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2739),image_1551609309ol_nat(X2737,X2738)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2739)) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,esk14_3(X2737,X2738,X2739)),X2738))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2739),image_1551609309ol_nat(X2737,X2738)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2739)) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk14_3(X2737,X2738,X2739)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2739),image_1551609309ol_nat(X2737,X2738)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2739)) )
& ( X2739 = image_1551609309ol_nat(X2737,esk14_3(X2737,X2738,X2739))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2739),image_1551609309ol_nat(X2737,X2738)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2739)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_168_finite__subset__image])])])]) ).
fof(i_0_1404,plain,
! [X2741,X2742,X2743] :
( ( is_fun949378684l_bool(esk15_3(X2741,X2742,X2743))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2743),image_fun_a_bool_nat(X2741,X2742)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2743)) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,esk15_3(X2741,X2742,X2743)),X2742))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2743),image_fun_a_bool_nat(X2741,X2742)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2743)) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk15_3(X2741,X2742,X2743)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2743),image_fun_a_bool_nat(X2741,X2742)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2743)) )
& ( X2743 = image_fun_a_bool_nat(X2741,esk15_3(X2741,X2742,X2743))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2743),image_fun_a_bool_nat(X2741,X2742)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2743)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_169_finite__subset__image])])])]) ).
fof(i_0_1405,plain,
! [X2785,X2786,X2787] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk26_3(X2785,X2786,X2787)),X2786))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2787),image_nat_nat(X2785,X2786)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2787)) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk26_3(X2785,X2786,X2787)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2787),image_nat_nat(X2785,X2786)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2787)) )
& ( X2787 = image_nat_nat(X2785,esk26_3(X2785,X2786,X2787))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2787),image_nat_nat(X2785,X2786)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2787)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_180_finite__subset__image])])])]) ).
fof(i_0_1406,plain,
! [X2769,X2770,X2771] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk22_3(X2769,X2770,X2771)),X2770))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2771),image_26036933t_bool(X2769,X2770)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2771)) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk22_3(X2769,X2770,X2771)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2771),image_26036933t_bool(X2769,X2770)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2771)) )
& ( X2771 = image_26036933t_bool(X2769,esk22_3(X2769,X2770,X2771))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2771),image_26036933t_bool(X2769,X2770)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2771)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_176_finite__subset__image])])])]) ).
fof(i_0_1407,plain,
! [X2761,X2762,X2763] :
( ( is_fun_pname_bool(esk20_3(X2761,X2762,X2763))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2763),image_pname_nat(X2761,X2762)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2763)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk20_3(X2761,X2762,X2763)),X2762))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2763),image_pname_nat(X2761,X2762)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2763)) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk20_3(X2761,X2762,X2763)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2763),image_pname_nat(X2761,X2762)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2763)) )
& ( X2763 = image_pname_nat(X2761,esk20_3(X2761,X2762,X2763))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2763),image_pname_nat(X2761,X2762)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2763)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_174_finite__subset__image])])])]) ).
fof(i_0_1408,plain,
! [X2745,X2746,X2747] :
( ( is_fun_pname_bool(esk16_3(X2745,X2746,X2747))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2747),image_2129980159t_bool(X2745,X2746)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2747)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk16_3(X2745,X2746,X2747)),X2746))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2747),image_2129980159t_bool(X2745,X2746)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2747)) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk16_3(X2745,X2746,X2747)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2747),image_2129980159t_bool(X2745,X2746)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2747)) )
& ( X2747 = image_2129980159t_bool(X2745,esk16_3(X2745,X2746,X2747))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2747),image_2129980159t_bool(X2745,X2746)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2747)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_170_finite__subset__image])])])]) ).
fof(i_0_1409,plain,
! [X2729,X2730,X2731] :
( ( is_fun_a_bool(esk12_3(X2729,X2730,X2731))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2731),image_a_nat(X2729,X2730)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2731)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk12_3(X2729,X2730,X2731)),X2730))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2731),image_a_nat(X2729,X2730)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2731)) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk12_3(X2729,X2730,X2731)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2731),image_a_nat(X2729,X2730)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2731)) )
& ( X2731 = image_a_nat(X2729,esk12_3(X2729,X2730,X2731))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2731),image_a_nat(X2729,X2730)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2731)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_166_finite__subset__image])])])]) ).
fof(i_0_1410,plain,
! [X2701,X2702,X2703] :
( ( is_fun_a_bool(esk5_3(X2701,X2702,X2703))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2703),image_a_fun_nat_bool(X2701,X2702)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2703)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk5_3(X2701,X2702,X2703)),X2702))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2703),image_a_fun_nat_bool(X2701,X2702)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2703)) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk5_3(X2701,X2702,X2703)))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2703),image_a_fun_nat_bool(X2701,X2702)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2703)) )
& ( X2703 = image_a_fun_nat_bool(X2701,esk5_3(X2701,X2702,X2703))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2703),image_a_fun_nat_bool(X2701,X2702)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2703)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_159_finite__subset__image])])])]) ).
cnf(i_0_1411,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X3,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1068]) ).
cnf(i_0_1412,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X3,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1053]) ).
cnf(i_0_1413,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X3,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1069]) ).
cnf(i_0_1414,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X3,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1070]) ).
cnf(i_0_1415,plain,
( hAPP_f2009550088ol_nat(finite1306199131a_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_1071]) ).
cnf(i_0_1416,plain,
( hAPP_f55526627ol_nat(finite1340463720e_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_1072]) ).
cnf(i_0_1417,plain,
( hAPP_fun_a_bool_nat(finite_card_a,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_1073]) ).
cnf(i_0_1418,plain,
( hAPP_f921600141ol_nat(finite_card_pname,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_1074]) ).
cnf(i_0_1419,plain,
insert1325755072e_bool(X1,collec1974731493e_bool(X2)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1))),X2)),
inference(split_conjunct,[status(thm)],[i_0_1075]) ).
cnf(i_0_1420,plain,
insert_fun_a_bool(X1,collect_fun_a_bool(X2)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1))),X2)),
inference(split_conjunct,[status(thm)],[i_0_1076]) ).
cnf(i_0_1421,plain,
insert_pname(X1,collect_pname(X2)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),X2)),
inference(split_conjunct,[status(thm)],[i_0_1077]) ).
cnf(i_0_1422,plain,
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_1078]) ).
cnf(i_0_1423,plain,
( insert_pname(hAPP_pname_pname(X3,X1),image_pname_pname(X3,X2)) = image_pname_pname(X3,X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1079]) ).
cnf(i_0_1424,plain,
( insert_pname(hAPP_a_pname(X3,X1),image_a_pname(X3,X2)) = image_a_pname(X3,X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1080]) ).
cnf(i_0_1425,plain,
( insert_a(hAPP_nat_a(X3,X1),image_nat_a(X3,X2)) = image_nat_a(X3,X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1081]) ).
cnf(i_0_1426,plain,
( 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_1082]) ).
fof(i_0_1427,plain,
! [X3278,X3279,X3280] :
( ( X3278 = hAPP_nat_a(X3279,esk65_3(X3278,X3279,X3280))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3278),image_nat_a(X3279,X3280)))
| ~ is_a(X3278) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk65_3(X3278,X3279,X3280)),X3280))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3278),image_nat_a(X3279,X3280)))
| ~ is_a(X3278) ) ),
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_1083])])])])])]) ).
fof(i_0_1428,plain,
! [X3274,X3275,X3276] :
( ( X3274 = hAPP_nat_pname(X3275,esk64_3(X3274,X3275,X3276))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3274),image_nat_pname(X3275,X3276)))
| ~ is_pname(X3274) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk64_3(X3274,X3275,X3276)),X3276))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3274),image_nat_pname(X3275,X3276)))
| ~ is_pname(X3274) ) ),
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_1084])])])])])]) ).
fof(i_0_1429,plain,
! [X3233,X3234,X3235,X3237,X3238,X3239] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk60_3(X3233,X3234,X3235)),X3235))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3233),image_nat_a(X3234,X3235)))
| ~ is_fun_a_bool(X3233) )
& ( X3233 = image_nat_a(X3234,esk60_3(X3233,X3234,X3235))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3233),image_nat_a(X3234,X3235)))
| ~ is_fun_a_bool(X3233) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3239),X3238))
| X3233 != image_nat_a(X3237,X3239)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3233),image_nat_a(X3237,X3238)))
| ~ is_fun_a_bool(X3233) ) ),
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_344_subset__image__iff])])])])])]) ).
fof(i_0_1430,plain,
! [X3255,X3256,X3257,X3259,X3260,X3261] :
( ( is_fun_pname_bool(esk63_3(X3255,X3256,X3257))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3255),image_pname_a(X3256,X3257)))
| ~ is_fun_a_bool(X3255) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk63_3(X3255,X3256,X3257)),X3257))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3255),image_pname_a(X3256,X3257)))
| ~ is_fun_a_bool(X3255) )
& ( X3255 = image_pname_a(X3256,esk63_3(X3255,X3256,X3257))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3255),image_pname_a(X3256,X3257)))
| ~ is_fun_a_bool(X3255) )
& ( ~ is_fun_pname_bool(X3261)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3261),X3260))
| X3255 != image_pname_a(X3259,X3261)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3255),image_pname_a(X3259,X3260)))
| ~ is_fun_a_bool(X3255) ) ),
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_347_subset__image__iff])])])])])]) ).
fof(i_0_1431,plain,
! [X3290,X3291,X3292] :
( ( is_pname(esk68_3(X3290,X3291,X3292))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3290),image_pname_a(X3291,X3292)))
| ~ is_a(X3290) )
& ( X3290 = hAPP_pname_a(X3291,esk68_3(X3290,X3291,X3292))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3290),image_pname_a(X3291,X3292)))
| ~ is_a(X3290) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk68_3(X3290,X3291,X3292)),X3292))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3290),image_pname_a(X3291,X3292)))
| ~ is_a(X3290) ) ),
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_1085])])])])])]) ).
fof(i_0_1432,plain,
! [X3107,X3108,X3109,X3111,X3112,X3113] :
( ( is_pname(esk59_3(X3107,X3108,X3109))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3107),image_pname_a(X3108,X3109)))
| ~ is_a(X3107) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk59_3(X3107,X3108,X3109)),X3109))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3107),image_pname_a(X3108,X3109)))
| ~ is_a(X3107) )
& ( X3107 = hAPP_pname_a(X3108,esk59_3(X3107,X3108,X3109))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3107),image_pname_a(X3108,X3109)))
| ~ is_a(X3107) )
& ( ~ is_pname(X3113)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3113),X3112))
| X3107 != hAPP_pname_a(X3111,X3113)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3107),image_pname_a(X3111,X3112)))
| ~ is_a(X3107) ) ),
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_302_image__iff])])])])])]) ).
fof(i_0_1433,plain,
! [X3240,X3241,X3242,X3244,X3245,X3246] :
( ( is_fun_a_bool(esk61_3(X3240,X3241,X3242))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3240),image_a_pname(X3241,X3242)))
| ~ is_fun_pname_bool(X3240) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk61_3(X3240,X3241,X3242)),X3242))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3240),image_a_pname(X3241,X3242)))
| ~ is_fun_pname_bool(X3240) )
& ( X3240 = image_a_pname(X3241,esk61_3(X3240,X3241,X3242))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3240),image_a_pname(X3241,X3242)))
| ~ is_fun_pname_bool(X3240) )
& ( ~ is_fun_a_bool(X3246)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3246),X3245))
| X3240 != image_a_pname(X3244,X3246)
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3240),image_a_pname(X3244,X3245)))
| ~ is_fun_pname_bool(X3240) ) ),
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_345_subset__image__iff])])])])])]) ).
fof(i_0_1434,plain,
! [X3282,X3283,X3284] :
( ( is_pname(esk66_3(X3282,X3283,X3284))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3282),image_pname_nat(X3283,X3284))) )
& ( X3282 = hAPP_pname_nat(X3283,esk66_3(X3282,X3283,X3284))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3282),image_pname_nat(X3283,X3284))) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk66_3(X3282,X3283,X3284)),X3284))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3282),image_pname_nat(X3283,X3284))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1086])])])]) ).
fof(i_0_1435,plain,
! [X3247,X3248,X3249,X3251,X3252,X3253,X3254] :
( ( is_fun_a_bool(esk62_3(X3247,X3248,X3249))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3247),image_a_nat(X3248,X3249))) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk62_3(X3247,X3248,X3249)),X3249))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3247),image_a_nat(X3248,X3249))) )
& ( X3247 = image_a_nat(X3248,esk62_3(X3247,X3248,X3249))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3247),image_a_nat(X3248,X3249))) )
& ( ~ is_fun_a_bool(X3254)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3254),X3253))
| X3251 != image_a_nat(X3252,X3254)
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3251),image_a_nat(X3252,X3253))) ) ),
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_346_subset__image__iff])])])])])]) ).
fof(i_0_1436,plain,
! [X3286,X3287,X3288] :
( ( is_a(esk67_3(X3286,X3287,X3288))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3286),image_a_nat(X3287,X3288))) )
& ( X3286 = hAPP_a_nat(X3287,esk67_3(X3286,X3287,X3288))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3286),image_a_nat(X3287,X3288))) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk67_3(X3286,X3287,X3288)),X3288))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3286),image_a_nat(X3287,X3288))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1087])])])]) ).
fof(i_0_1437,plain,
! [X4035,X4036,X4037] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk128_3(X4035,X4036,X4037)),X4037))
| hBOOL(hAPP_nat_bool(X4035,X4036))
| ~ hBOOL(hAPP_nat_bool(X4035,X4037))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4036),X4037)) )
& ( hBOOL(hAPP_nat_bool(X4035,hAPP_nat_nat(suc,esk128_3(X4035,X4036,X4037))))
| hBOOL(hAPP_nat_bool(X4035,X4036))
| ~ hBOOL(hAPP_nat_bool(X4035,X4037))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4036),X4037)) )
& ( ~ hBOOL(hAPP_nat_bool(X4035,esk128_3(X4035,X4036,X4037)))
| hBOOL(hAPP_nat_bool(X4035,X4036))
| ~ hBOOL(hAPP_nat_bool(X4035,X4037))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4036),X4037)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_672_inc__induct])])])]) ).
cnf(i_0_1438,plain,
( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X1),X2))
| hAPP_f2009550088ol_nat(finite1306199131a_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_1071]) ).
cnf(i_0_1439,plain,
( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2),X1))
| hAPP_f2009550088ol_nat(finite1306199131a_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_1088]) ).
cnf(i_0_1440,plain,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X1),X2))
| hAPP_f55526627ol_nat(finite1340463720e_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_1072]) ).
cnf(i_0_1441,plain,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2),X1))
| hAPP_f55526627ol_nat(finite1340463720e_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_1089]) ).
cnf(i_0_1442,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hAPP_fun_a_bool_nat(finite_card_a,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_1073]) ).
cnf(i_0_1443,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| hAPP_fun_a_bool_nat(finite_card_a,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_1090]) ).
cnf(i_0_1444,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hAPP_f921600141ol_nat(finite_card_pname,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_1074]) ).
cnf(i_0_1445,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| hAPP_f921600141ol_nat(finite_card_pname,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_1091]) ).
fof(i_0_1446,plain,
! [X2938,X2939,X2940] :
( ( hBOOL(hAPP_nat_bool(X2939,hAPP_nat_nat(suc,esk57_3(X2938,X2939,X2940))))
| hBOOL(hAPP_nat_bool(X2939,hAPP_nat_nat(minus_minus_nat(X2940),X2938)))
| ~ hBOOL(hAPP_nat_bool(X2939,X2940)) )
& ( ~ hBOOL(hAPP_nat_bool(X2939,esk57_3(X2938,X2939,X2940)))
| hBOOL(hAPP_nat_bool(X2939,hAPP_nat_nat(minus_minus_nat(X2940),X2938)))
| ~ hBOOL(hAPP_nat_bool(X2939,X2940)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_228_zero__induct__lemma])])])]) ).
fof(i_0_1447,plain,
! [X3861,X3862,X3863] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3861),hAPP_nat_nat(minus_minus_nat(X3863),X3862)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3861),X3862)),X3863))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3862),X3863)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3861),X3862)),X3863))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3861),hAPP_nat_nat(minus_minus_nat(X3863),X3862)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3862),X3863)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_600_le__diff__conv2])])]) ).
cnf(i_0_1448,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1053]) ).
cnf(i_0_1449,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1069]) ).
cnf(i_0_1450,plain,
( hBOOL(hAPP_nat_bool(insert_nat(X3,X1),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1059]) ).
cnf(i_0_1451,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_1092]) ).
cnf(i_0_1452,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X2,X1))),
inference(split_conjunct,[status(thm)],[i_0_1093]) ).
cnf(i_0_1453,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X2,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1060]) ).
cnf(i_0_1454,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X2,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1094]) ).
cnf(i_0_1455,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1061]) ).
cnf(i_0_1456,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1095]) ).
cnf(i_0_1457,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,bot_bot_fun_nat_bool)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1057]) ).
fof(i_0_1458,plain,
! [X3869,X3870,X3871] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3870),X3871))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3869),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3871),X3869)),X3870))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_603_le__add__diff])]) ).
cnf(i_0_1459,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))
| insert_nat(X1,X2) != insert_nat(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1096]) ).
cnf(i_0_1460,plain,
( hBOOL(hAPP_nat_bool(insert_nat(X1,X3),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1059]) ).
fof(i_0_1461,plain,
! [X3922,X3923,X3924] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3922),X3923)),hAPP_nat_nat(plus_plus_nat(X3922),X3924)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3923),X3924)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3923),X3924))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3922),X3923)),hAPP_nat_nat(plus_plus_nat(X3922),X3924))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_623_nat__add__left__cancel__less])]) ).
fof(i_0_1462,plain,
! [X3822,X3823,X3824] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3822),X3823)),hAPP_nat_nat(plus_plus_nat(X3822),X3824)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3823),X3824)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3823),X3824))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3822),X3823)),hAPP_nat_nat(plus_plus_nat(X3822),X3824))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_587_nat__add__left__cancel__le])]) ).
cnf(i_0_1463,plain,
( is_fun1661590463l_bool(insert1325755072e_bool(X1,X2))
| ~ is_fun_pname_bool(X1)
| ~ is_fun1661590463l_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1097]) ).
cnf(i_0_1464,plain,
( is_fun949378684l_bool(insert_fun_a_bool(X1,X2))
| ~ is_fun_a_bool(X1)
| ~ is_fun949378684l_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1098]) ).
cnf(i_0_1465,plain,
( is_fun_pname_bool(insert_pname(X1,X2))
| ~ is_pname(X1)
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1099]) ).
cnf(i_0_1466,hypothesis,
( is_fun_a_bool(insert_a(X1,X2))
| ~ is_a(X1)
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1100]) ).
fof(i_0_1467,plain,
! [X2532,X2533] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2532)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X2532),X2533)))) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2533)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X2532),X2533)))) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2532)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2533)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X2532),X2533)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_93_finite__Collect__disjI])])]) ).
fof(i_0_1468,plain,
! [X2534,X2535] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2534)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X2534),X2535)))) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2535)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X2534),X2535)))) )
& ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2534)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2535)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X2534),X2535)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_94_finite__Collect__disjI])])]) ).
fof(i_0_1469,plain,
! [X2536,X2537] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2536)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X2536),X2537)))) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2537)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X2536),X2537)))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2536)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2537)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X2536),X2537)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_95_finite__Collect__disjI])])]) ).
fof(i_0_1470,plain,
! [X2528,X2529] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2528)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X2528),X2529)))) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2529)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X2528),X2529)))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2528)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2529)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X2528),X2529)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_91_finite__Collect__disjI])])]) ).
fof(i_0_1471,plain,
! [X3909,X3910,X3911,X3912] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3911),X3912))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3909),X3910))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3911),X3909)),hAPP_nat_nat(plus_plus_nat(X3912),X3910))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_619_add__less__mono])]) ).
fof(i_0_1472,plain,
! [X4023,X4024,X4025] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4024),X4025))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4023),X4024))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X4024),X4023)),hAPP_nat_nat(minus_minus_nat(X4025),X4023))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_668_diff__less__mono])]) ).
fof(i_0_1473,plain,
! [X3962,X3963,X3964] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3963),X3964))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3963),X3962))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X3962),X3964)),hAPP_nat_nat(minus_minus_nat(X3962),X3963))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_642_diff__less__mono2])]) ).
fof(i_0_1474,plain,
! [X3834,X3835,X3836,X3837] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3836),X3837))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3834),X3835))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3836),X3834)),hAPP_nat_nat(plus_plus_nat(X3837),X3835))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_591_add__le__mono])]) ).
fof(i_0_1475,plain,
! [X2447,X2448] :
( ~ is_fun1661590463l_bool(X2447)
| ~ is_fun1661590463l_bool(X2448)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2448))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2447),X2448))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2448)),hAPP_f55526627ol_nat(finite1340463720e_bool,X2447)))
| X2447 = X2448 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_49_card__seteq])]) ).
fof(i_0_1476,plain,
! [X2449,X2450] :
( ~ is_fun949378684l_bool(X2449)
| ~ is_fun949378684l_bool(X2450)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2450))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2449),X2450))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2450)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2449)))
| X2449 = X2450 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_50_card__seteq])]) ).
fof(i_0_1477,plain,
! [X2451,X2452] :
( ~ is_fun_pname_bool(X2451)
| ~ is_fun_pname_bool(X2452)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2452))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2451),X2452))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2452)),hAPP_f921600141ol_nat(finite_card_pname,X2451)))
| X2451 = X2452 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_51_card__seteq])]) ).
fof(i_0_1478,plain,
! [X2453,X2454] :
( ~ is_fun_a_bool(X2453)
| ~ is_fun_a_bool(X2454)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2454))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2453),X2454))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2454)),hAPP_fun_a_bool_nat(finite_card_a,X2453)))
| X2453 = X2454 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_52_card__seteq])]) ).
cnf(i_0_1479,plain,
( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X2)),X1)) = insert1325755072e_bool(X2,bot_bo1649642514l_bool)
| ~ hBOOL(hAPP_f1664156314l_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1101]) ).
cnf(i_0_1480,plain,
( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X2)),X1)) = insert_fun_a_bool(X2,bot_bo1389914601l_bool)
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1102]) ).
cnf(i_0_1481,plain,
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),X1)) = insert_pname(X2,bot_bo844097828e_bool)
| ~ hBOOL(hAPP_pname_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1103]) ).
cnf(i_0_1482,plain,
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),X1)) = insert_a(X2,bot_bot_fun_a_bool)
| ~ hBOOL(hAPP_a_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1104]) ).
fof(i_0_1483,plain,
! [X4020,X4021,X4022] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4020),hAPP_nat_nat(minus_minus_nat(X4021),X4022)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X4020),X4022)),X4021)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X4020),X4022)),X4021))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4020),hAPP_nat_nat(minus_minus_nat(X4021),X4022))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_667_less__diff__conv])]) ).
fof(i_0_1484,plain,
! [X3872,X3873,X3874] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X3872),X3873)),X3874))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3872),hAPP_nat_nat(plus_plus_nat(X3874),X3873))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3872),hAPP_nat_nat(plus_plus_nat(X3874),X3873)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X3872),X3873)),X3874)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_604_le__diff__conv])]) ).
fof(i_0_1485,plain,
! [X2445,X2446] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2446))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2445),X2446))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X2446)),hAPP_f696928925ol_nat(finite346522414t_bool,X2445)))
| X2445 = X2446 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_48_card__seteq])]) ).
fof(i_0_1486,plain,
! [X2455,X2456] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2456))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2455),X2456))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X2456)),hAPP_f22106695ol_nat(finite_card_nat,X2455)))
| X2455 = X2456 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_53_card__seteq])]) ).
cnf(i_0_1487,plain,
( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,X2)),X1)) = insert1325755072e_bool(X2,bot_bo1649642514l_bool)
| ~ hBOOL(hAPP_f1664156314l_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1105]) ).
cnf(i_0_1488,plain,
( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,X2)),X1)) = insert_fun_a_bool(X2,bot_bo1389914601l_bool)
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1106]) ).
cnf(i_0_1489,plain,
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,X2)),X1)) = insert_pname(X2,bot_bo844097828e_bool)
| ~ hBOOL(hAPP_pname_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1107]) ).
cnf(i_0_1490,plain,
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X2)),X1)) = insert_a(X2,bot_bot_fun_a_bool)
| ~ hBOOL(hAPP_a_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1108]) ).
fof(i_0_1491,plain,
! [X2417,X2418] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2418))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X2417,X2418))),hAPP_f921600141ol_nat(finite_card_pname,X2418))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_34_card__image__le])]) ).
fof(i_0_1492,plain,
! [X2425,X2426] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2426))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X2425,X2426))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2426))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_38_card__image__le])]) ).
fof(i_0_1493,plain,
! [X2423,X2424] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2424))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X2423,X2424))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2424))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_37_card__image__le])]) ).
fof(i_0_1494,plain,
! [X2421,X2422] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2422))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X2421,X2422))),hAPP_f696928925ol_nat(finite346522414t_bool,X2422))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_36_card__image__le])]) ).
fof(i_0_1495,plain,
! [X2419,X2420] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2420))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X2419,X2420))),hAPP_fun_a_bool_nat(finite_card_a,X2420))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_35_card__image__le])]) ).
fof(i_0_1496,plain,
! [X2411,X2412] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2412))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X2411,X2412))),hAPP_f696928925ol_nat(finite346522414t_bool,X2412))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_31_card__image__le])]) ).
fof(i_0_1497,plain,
! [X2413,X2414] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2414))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X2413,X2414))),hAPP_f55526627ol_nat(finite1340463720e_bool,X2414))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_32_card__image__le])]) ).
fof(i_0_1498,plain,
! [X2415,X2416] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2416))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X2415,X2416))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2416))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_33_card__image__le])]) ).
fof(i_0_1499,plain,
! [X2431,X2432] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2432))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X2431,X2432))),hAPP_f921600141ol_nat(finite_card_pname,X2432))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_41_card__image__le])]) ).
fof(i_0_1500,plain,
! [X2409,X2410] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2410))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X2409,X2410))),hAPP_fun_a_bool_nat(finite_card_a,X2410))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_30_card__image__le])]) ).
fof(i_0_1501,plain,
! [X2429,X2430] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2430))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X2429,X2430))),hAPP_f22106695ol_nat(finite_card_nat,X2430))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_40_card__image__le])]) ).
fof(i_0_1502,plain,
! [X2407,X2408] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2408))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X2407,X2408))),hAPP_f921600141ol_nat(finite_card_pname,X2408))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_29_card__image__le])]) ).
fof(i_0_1503,plain,
! [X2427,X2428] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2428))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X2427,X2428))),hAPP_fun_a_bool_nat(finite_card_a,X2428))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_39_card__image__le])]) ).
cnf(i_0_1504,plain,
( hAPP_f22106695ol_nat(finite_card_nat,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_1109]) ).
cnf(i_0_1505,plain,
( hAPP_f696928925ol_nat(finite346522414t_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_1110]) ).
fof(i_0_1506,plain,
! [X3880,X3881,X3882] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3881),X3882))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X3882),X3881))),X3880) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X3882)),hAPP_nat_nat(plus_plus_nat(X3881),X3880)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_608_diff__Suc__diff__eq2])]) ).
fof(i_0_1507,plain,
! [X3902,X3903,X3904] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3902),X3903)),X3904))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3902),X3904)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_617_add__lessD1])]) ).
fof(i_0_1508,plain,
! [X3844,X3845,X3846] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3844),X3846))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3844),X3845)),X3846)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3845),X3846))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3844),X3845)),X3846)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1111])])]) ).
fof(i_0_1509,plain,
! [X3841,X3842,X3843] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3841),X3842)),X3843))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3841),X3843)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_593_add__leD1])]) ).
fof(i_0_1510,plain,
! [X3838,X3839,X3840] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3838),X3839)),X3840))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3839),X3840)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_592_add__leD2])]) ).
fof(i_0_1511,plain,
! [X3777,X3778] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X3777)),X3778))
| hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X3777)),X3778)) )
& ( ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,X3777)),X3778))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X3777)),X3778)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_570_less__eq__nat_Osimps_I2_J])]) ).
cnf(i_0_1512,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hAPP_f22106695ol_nat(finite_card_nat,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_1109]) ).
cnf(i_0_1513,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| hAPP_f22106695ol_nat(finite_card_nat,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_1112]) ).
cnf(i_0_1514,plain,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1),X2))
| hAPP_f696928925ol_nat(finite346522414t_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_1110]) ).
cnf(i_0_1515,plain,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2),X1))
| hAPP_f696928925ol_nat(finite346522414t_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_1113]) ).
fof(i_0_1516,plain,
! [X3913,X3914,X3915] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3914),X3915))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3914),X3913)),hAPP_nat_nat(plus_plus_nat(X3915),X3913))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_620_add__less__mono1])]) ).
fof(i_0_1517,plain,
! [X3831,X3832,X3833] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3832),X3833))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3832),X3831)),hAPP_nat_nat(plus_plus_nat(X3833),X3831))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_590_add__le__mono1])]) ).
fof(i_0_1518,plain,
! [X2605,X2606,X2607] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2606),X2607))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2606),X2605)),hAPP_nat_nat(minus_minus_nat(X2607),X2605))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_128_diff__le__mono])]) ).
fof(i_0_1519,plain,
! [X2608,X2609,X2610] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2609),X2610))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2608),X2610)),hAPP_nat_nat(minus_minus_nat(X2608),X2609))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_129_diff__le__mono2])]) ).
cnf(i_0_1520,plain,
( insert_nat(hAPP_pname_nat(X3,X1),image_pname_nat(X3,X2)) = image_pname_nat(X3,X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1114]) ).
cnf(i_0_1521,plain,
( insert_nat(hAPP_a_nat(X3,X1),image_a_nat(X3,X2)) = image_a_nat(X3,X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1115]) ).
cnf(i_0_1522,plain,
insert_pname(X1,X2) != bot_bo844097828e_bool,
inference(split_conjunct,[status(thm)],[i_0_1116]) ).
cnf(i_0_1523,plain,
insert_a(X1,X2) != bot_bot_fun_a_bool,
inference(split_conjunct,[status(thm)],[i_0_1117]) ).
cnf(i_0_1524,plain,
bot_bo844097828e_bool != insert_pname(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1118]) ).
cnf(i_0_1525,plain,
bot_bot_fun_a_bool != insert_a(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1119]) ).
fof(i_0_1526,plain,
! [X3946,X3947] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X3946)),hAPP_nat_nat(suc,X3947)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3946),X3947)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3946),X3947))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X3946)),hAPP_nat_nat(suc,X3947))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_634_Suc__less__eq])]) ).
fof(i_0_1527,plain,
! [X3929,X3930] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X3929)),hAPP_nat_nat(suc,X3930)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3929),X3930)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_626_Suc__less__SucD])]) ).
fof(i_0_1528,plain,
! [X2582,X2583] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2582)),hAPP_nat_nat(suc,X2583)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2582),X2583)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2582),X2583))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2582)),hAPP_nat_nat(suc,X2583))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_118_Suc__le__mono])]) ).
cnf(i_0_1529,plain,
( X1 = X2
| insert_nat(X1,bot_bot_fun_nat_bool) != insert_nat(X2,bot_bot_fun_nat_bool) ),
inference(split_conjunct,[status(thm)],[i_0_1120]) ).
fof(i_0_1530,plain,
! [X3935,X3936,X3937] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3936),X3937))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3937),X3935))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X3936)),X3935)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_629_less__trans__Suc])]) ).
cnf(i_0_1531,plain,
( image_pname_a(cOMBK_a_pname(X3),X2) = 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_1121]) ).
fof(i_0_1532,plain,
! [X2589,X2590,X2591] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2589)),X2590)),hAPP_nat_nat(suc,X2591)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2589),X2590)),X2591),
inference(variable_rename,[status(thm)],[fact_122_Suc__diff__diff]) ).
cnf(i_0_1533,plain,
( 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_1122]) ).
cnf(i_0_1534,plain,
( 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_1123]) ).
fof(i_0_1535,plain,
! [X2597,X2598,X2599] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2598),X2599))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2598),X2597))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2599),X2598)),hAPP_nat_nat(minus_minus_nat(X2597),X2598)) = hAPP_nat_nat(minus_minus_nat(X2599),X2597) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_125_Nat_Odiff__diff__eq])]) ).
fof(i_0_1536,plain,
! [X4050,X4051] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4050),esk133_2(X4050,X4051)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X4050)),X4051)) )
& ( X4051 = hAPP_nat_nat(suc,esk133_2(X4050,X4051))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X4050)),X4051)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_676_Suc__lessE])])])]) ).
fof(i_0_1537,plain,
! [X2497,X2498] :
( ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2498)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X2498),X2497)))) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X2497)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X2498),X2497)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_74_finite__Collect__conjI])])]) ).
fof(i_0_1538,plain,
! [X2499,X2500] :
( ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2500)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X2500),X2499)))) )
& ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X2499)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X2500),X2499)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_75_finite__Collect__conjI])])]) ).
fof(i_0_1539,plain,
! [X2501,X2502] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2502)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X2502),X2501)))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X2501)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X2502),X2501)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_76_finite__Collect__conjI])])]) ).
fof(i_0_1540,plain,
! [X2493,X2494] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2494)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X2494),X2493)))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X2493)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X2494),X2493)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_72_finite__Collect__conjI])])]) ).
fof(i_0_1541,plain,
! [X2586,X2587] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2586),X2587))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2587)),X2586)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2587)),X2586))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2586),X2587)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1124])]) ).
fof(i_0_1542,plain,
! [X2443,X2444] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2444))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2443),X2444))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X2443)),hAPP_f22106695ol_nat(finite_card_nat,X2444))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_47_card__mono])]) ).
fof(i_0_1543,plain,
! [X2437,X2438] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2438))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2437),X2438))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X2437)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X2438))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_44_card__mono])]) ).
fof(i_0_1544,plain,
! [X2435,X2436] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2436))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2435),X2436))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X2435)),hAPP_f55526627ol_nat(finite1340463720e_bool,X2436))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_43_card__mono])]) ).
fof(i_0_1545,plain,
! [X2433,X2434] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2434))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2433),X2434))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X2433)),hAPP_f696928925ol_nat(finite346522414t_bool,X2434))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_42_card__mono])]) ).
fof(i_0_1546,plain,
! [X2441,X2442] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2442))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2441),X2442))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X2441)),hAPP_fun_a_bool_nat(finite_card_a,X2442))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_46_card__mono])]) ).
fof(i_0_1547,plain,
! [X2439,X2440] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2440))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2439),X2440))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X2439)),hAPP_f921600141ol_nat(finite_card_pname,X2440))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_45_card__mono])]) ).
fof(i_0_1548,plain,
! [X3927,X3928] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3927),X3928)),X3927)),
inference(variable_rename,[status(thm)],[i_0_1125]) ).
fof(i_0_1549,plain,
! [X3925,X3926] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3925),X3926)),X3926)),
inference(variable_rename,[status(thm)],[i_0_1126]) ).
fof(i_0_1550,plain,
! [X3294,X3295] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk69_2(X3294,X3295)),X3295))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3295),X3294)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk69_2(X3294,X3295)),X3294))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3295),X3294)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_357_subsetI])])])]) ).
fof(i_0_1551,plain,
! [X3297,X3298] :
( ( is_pname(esk70_2(X3297,X3298))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3298),X3297)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk70_2(X3297,X3298)),X3298))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3298),X3297)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk70_2(X3297,X3298)),X3297))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3298),X3297)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_358_subsetI])])])]) ).
fof(i_0_1552,plain,
! [X3300,X3301] :
( ( is_a(esk71_2(X3300,X3301))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3301),X3300)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk71_2(X3300,X3301)),X3301))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3301),X3300)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk71_2(X3300,X3301)),X3300))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3301),X3300)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_359_subsetI])])])]) ).
fof(i_0_1553,plain,
! [X3883,X3884,X3885] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3884),X3885))
| hAPP_nat_nat(minus_minus_nat(X3883),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X3885),X3884))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3883),X3884)),hAPP_nat_nat(suc,X3885)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_609_diff__Suc__diff__eq1])]) ).
fof(i_0_1554,plain,
! [X3114,X3115,X3116] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3115),X3116))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(X3114,X3115)),image_pname_nat(X3114,X3116))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_303_imageI])]) ).
fof(i_0_1555,plain,
! [X3117,X3118,X3119] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3118),X3119))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(X3117,X3118)),image_a_nat(X3117,X3119))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_304_imageI])]) ).
fof(i_0_1556,plain,
! [X3265,X3266,X3267] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3266),X3267))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(X3265,X3266)),image_a_nat(X3265,X3267))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_349_image__mono])]) ).
fof(i_0_1557,plain,
! [X3262,X3263,X3264] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3263),X3264))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(X3262,X3263)),image_a_pname(X3262,X3264))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_348_image__mono])]) ).
fof(i_0_1558,plain,
! [X3120,X3121,X3122] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3121),X3122))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(X3120,X3121)),image_nat_pname(X3120,X3122))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_305_imageI])]) ).
fof(i_0_1559,plain,
! [X3268,X3269,X3270] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3269),X3270))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(X3268,X3269)),image_nat_a(X3268,X3270))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_350_image__mono])]) ).
fof(i_0_1560,plain,
! [X3271,X3272,X3273] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3272),X3273))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X3271,X3272)),image_pname_a(X3271,X3273))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_351_image__mono])]) ).
fof(i_0_1561,plain,
! [X3123,X3124,X3125] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3124),X3125))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(X3123,X3124)),image_nat_a(X3123,X3125))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_306_imageI])]) ).
fof(i_0_1562,plain,
! [X3126,X3127,X3128] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3127),X3128))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X3126,X3127)),image_pname_a(X3126,X3128))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_307_imageI])]) ).
fof(i_0_1563,plain,
! [X3375,X3376,X3377] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3376),X3377))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X3376,X3375)),hAPP_nat_bool(X3377,X3375))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_381_le__funE])]) ).
fof(i_0_1564,plain,
! [X3366,X3367,X3368] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3367),X3368))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(X3367,X3366)),hAPP_nat_bool(X3368,X3366))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_378_le__funD])]) ).
fof(i_0_1565,plain,
! [X3372,X3373,X3374] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3373),X3374))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(X3373,X3372)),hAPP_pname_bool(X3374,X3372))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_380_le__funE])]) ).
fof(i_0_1566,plain,
! [X3363,X3364,X3365] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3364),X3365))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(X3364,X3363)),hAPP_pname_bool(X3365,X3363))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_377_le__funD])]) ).
fof(i_0_1567,plain,
! [X3378,X3379,X3380] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3379),X3380))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X3379,X3378)),hAPP_a_bool(X3380,X3378))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_382_le__funE])]) ).
fof(i_0_1568,plain,
! [X3369,X3370,X3371] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3370),X3371))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(X3370,X3369)),hAPP_a_bool(X3371,X3369))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_379_le__funD])]) ).
fof(i_0_1569,plain,
! [X3965,X3966,X3967] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3966),X3967))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X3966),X3965)),X3967)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_643_less__imp__diff__less])]) ).
cnf(i_0_1570,plain,
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_1127]) ).
cnf(i_0_1571,plain,
insert_fun_nat_bool(X1,collect_fun_nat_bool(X2)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X2)),
inference(split_conjunct,[status(thm)],[i_0_1128]) ).
fof(i_0_1572,plain,
! [X3931,X3932] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X3931)),X3932))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3931),X3932)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_627_Suc__lessD])]) ).
fof(i_0_1573,plain,
! [X4014,X4015] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X4014)),X4015))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4014),X4015)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_664_Suc__le__lessD])]) ).
fof(i_0_1574,plain,
! [X4006,X4007] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X4006)),X4007))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4006),X4007)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4006),X4007))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X4006)),X4007)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_660_Suc__le__eq])]) ).
fof(i_0_1575,plain,
! [X4002,X4003] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4002),X4003))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X4002)),X4003)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X4002)),X4003))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4002),X4003)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_658_less__eq__Suc__le])]) ).
fof(i_0_1576,plain,
! [X2576,X2577] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2576)),X2577))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2576),X2577)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_115_Suc__leD])]) ).
fof(i_0_1577,plain,
! [X3893,X3894] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3893),X3894))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X3893)),hAPP_nat_nat(suc,X3894))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_613_Suc__mono])]) ).
fof(i_0_1578,plain,
! [X3062,X3063,X3064] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3063),X3064))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3064),X3062))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3063),X3062)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_281_set__rev__mp])]) ).
fof(i_0_1579,plain,
! [X3071,X3072,X3073] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3072),X3073))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3071),X3072))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3071),X3073)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_284_set__mp])]) ).
fof(i_0_1580,plain,
! [X3053,X3054,X3055] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3054),X3055))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3053),X3054))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3053),X3055)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_278_in__mono])]) ).
fof(i_0_1581,plain,
! [X2911,X2912,X2913] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2912),X2913))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2911),X2912))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2911),X2913)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_219_subsetD])]) ).
fof(i_0_1582,plain,
! [X3612,X3613,X3614] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3613),X3614))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3614),X3612))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3613),X3612)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_511_order__trans])]) ).
fof(i_0_1583,plain,
! [X3095,X3096,X3097] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3096),X3097))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3097),X3095))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3096),X3095)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_297_subset__trans])]) ).
fof(i_0_1584,plain,
! [X3587,X3588,X3589] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3588),X3589))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3587),X3588))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3587),X3589)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_501_xt1_I6_J])]) ).
fof(i_0_1585,plain,
! [X3615,X3616,X3617] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3616),X3617))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3617),X3615))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3616),X3615)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_512_order__trans])]) ).
fof(i_0_1586,plain,
! [X3092,X3093,X3094] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3093),X3094))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3094),X3092))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3093),X3092)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_296_subset__trans])]) ).
fof(i_0_1587,plain,
! [X3590,X3591,X3592] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3591),X3592))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3590),X3591))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3590),X3592)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_502_xt1_I6_J])]) ).
fof(i_0_1588,plain,
! [X3065,X3066,X3067] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3066),X3067))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3067),X3065))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3066),X3065)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_282_set__rev__mp])]) ).
fof(i_0_1589,plain,
! [X3074,X3075,X3076] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3075),X3076))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3074),X3075))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3074),X3076)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_285_set__mp])]) ).
fof(i_0_1590,plain,
! [X3056,X3057,X3058] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3057),X3058))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3056),X3057))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3056),X3058)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_279_in__mono])]) ).
fof(i_0_1591,plain,
! [X2914,X2915,X2916] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2915),X2916))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2914),X2915))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2914),X2916)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_220_subsetD])]) ).
fof(i_0_1592,plain,
! [X3621,X3622,X3623] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3622),X3623))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3623),X3621))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3622),X3621)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_514_order__trans])]) ).
fof(i_0_1593,plain,
! [X3098,X3099,X3100] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3099),X3100))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3100),X3098))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3099),X3098)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_298_subset__trans])]) ).
fof(i_0_1594,plain,
! [X3596,X3597,X3598] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3597),X3598))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3596),X3597))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3596),X3598)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_504_xt1_I6_J])]) ).
fof(i_0_1595,plain,
! [X3068,X3069,X3070] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3069),X3070))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3070),X3068))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3069),X3068)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_283_set__rev__mp])]) ).
fof(i_0_1596,plain,
! [X3077,X3078,X3079] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3078),X3079))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3077),X3078))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3077),X3079)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_286_set__mp])]) ).
fof(i_0_1597,plain,
! [X3059,X3060,X3061] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3060),X3061))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3059),X3060))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3059),X3061)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_280_in__mono])]) ).
fof(i_0_1598,plain,
! [X2917,X2918,X2919] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2918),X2919))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2917),X2918))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2917),X2919)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_221_subsetD])]) ).
fof(i_0_1599,plain,
! [X3618,X3619,X3620] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3619),X3620))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3620),X3618))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3619),X3618)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_513_order__trans])]) ).
fof(i_0_1600,plain,
! [X2517,X2518,X2519] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2518),X2519))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2519),X2517))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2518),X2517)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_86_le__trans])]) ).
fof(i_0_1601,plain,
! [X3593,X3594,X3595] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3594),X3595))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3593),X3594))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3593),X3595)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_503_xt1_I6_J])]) ).
fof(i_0_1602,plain,
! [X3609,X3610,X3611] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3610),X3611))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3611),X3609))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3610),X3609)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_510_order__trans])]) ).
fof(i_0_1603,plain,
! [X3584,X3585,X3586] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3585),X3586))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3584),X3585))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3584),X3586)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_500_xt1_I6_J])]) ).
fof(i_0_1604,plain,
! [X4012,X4013] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4013),hAPP_nat_nat(suc,X4012)))
| X4013 = X4012
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4012),X4013)) )
& ( X4013 != X4012
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4013),hAPP_nat_nat(suc,X4012)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4012),X4013)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_663_le__less__Suc__eq])])]) ).
fof(i_0_1605,plain,
! [X3850,X3851,X3852] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3851),X3852))
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X3852),X3851)),X3850) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3852),X3850)),X3851) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_596_add__diff__assoc2])]) ).
fof(i_0_1606,plain,
! [X3847,X3848,X3849] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3848),X3849))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3849),X3847)),X3848) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X3849),X3848)),X3847) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_595_diff__add__assoc2])]) ).
fof(i_0_1607,plain,
! [X3950,X3951] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3950),X3951))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3951),hAPP_nat_nat(suc,X3950))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3951),hAPP_nat_nat(suc,X3950)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3950),X3951)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1129])]) ).
fof(i_0_1608,plain,
! [X3983,X3985,X3986,X3987] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3983))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3985),X3983))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3985),esk123_1(X3983))) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk124_2(X3986,X3987)),X3986))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3986)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk124_2(X3986,X3987)),X3987))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3986)) ) ),
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_652_finite__nat__set__iff__bounded])])])])])]) ).
fof(i_0_1609,plain,
! [X3336,X3338,X3339,X3340] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3336))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3338),X3336))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3338),esk79_1(X3336))) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk80_2(X3339,X3340)),X3339))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3339)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk80_2(X3339,X3340)),X3340))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3339)) ) ),
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_372_finite__nat__set__iff__bounded__le])])])])])]) ).
fof(i_0_1610,plain,
! [X4042,X4043] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk130_2(X4042,X4043)),X4043))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4043)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk130_2(X4042,X4043)),X4042))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X4043)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_674_bounded__nat__set__is__finite])])])]) ).
fof(i_0_1611,plain,
! [X2600,X2601,X2602] :
( ( hAPP_nat_nat(minus_minus_nat(X2602),X2601) != hAPP_nat_nat(minus_minus_nat(X2600),X2601)
| X2602 = X2600
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2601),X2600))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2601),X2602)) )
& ( X2602 != X2600
| hAPP_nat_nat(minus_minus_nat(X2602),X2601) = hAPP_nat_nat(minus_minus_nat(X2600),X2601)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2601),X2600))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2601),X2602)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_126_eq__diff__iff])])]) ).
fof(i_0_1612,plain,
! [X2942,X2943] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2942)),X2943))
| X2943 = hAPP_nat_nat(suc,esk58_2(X2942,X2943)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_229_Suc__le__D])])]) ).
fof(i_0_1613,plain,
! [X3938,X3939] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3938),X3939))
| hAPP_nat_nat(suc,X3938) = X3939
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X3938)),X3939)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_630_Suc__lessI])]) ).
cnf(i_0_1614,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_1130]) ).
cnf(i_0_1615,plain,
collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)) = insert1325755072e_bool(X1,bot_bo1649642514l_bool),
inference(split_conjunct,[status(thm)],[i_0_1131]) ).
cnf(i_0_1616,plain,
collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)) = insert_fun_a_bool(X1,bot_bo1389914601l_bool),
inference(split_conjunct,[status(thm)],[i_0_1132]) ).
cnf(i_0_1617,plain,
collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)) = insert_pname(X1,bot_bo844097828e_bool),
inference(split_conjunct,[status(thm)],[i_0_1133]) ).
cnf(i_0_1618,plain,
collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)) = insert_a(X1,bot_bot_fun_a_bool),
inference(split_conjunct,[status(thm)],[i_0_1134]) ).
cnf(i_0_1619,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_1135]) ).
cnf(i_0_1620,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_1135]) ).
cnf(i_0_1621,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_1136]) ).
cnf(i_0_1622,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_1136]) ).
cnf(i_0_1623,plain,
( X1 = bot_bo844097828e_bool
| image_pname_a(cOMBK_a_pname(X2),X1) = insert_a(X2,bot_bot_fun_a_bool)
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1137]) ).
cnf(i_0_1624,plain,
collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1)) = insert1325755072e_bool(X1,bot_bo1649642514l_bool),
inference(split_conjunct,[status(thm)],[i_0_1138]) ).
cnf(i_0_1625,plain,
collect_fun_a_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1)) = insert_fun_a_bool(X1,bot_bo1389914601l_bool),
inference(split_conjunct,[status(thm)],[i_0_1139]) ).
cnf(i_0_1626,plain,
collect_pname(hAPP_p61793385e_bool(fequal_pname,X1)) = insert_pname(X1,bot_bo844097828e_bool),
inference(split_conjunct,[status(thm)],[i_0_1140]) ).
cnf(i_0_1627,plain,
collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) = insert_a(X1,bot_bot_fun_a_bool),
inference(split_conjunct,[status(thm)],[i_0_1141]) ).
fof(i_0_1628,plain,
! [X4010,X4011] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4010),X4011))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X4010)),X4011)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_662_Suc__leI])]) ).
fof(i_0_1629,plain,
! [X2584,X2585] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2584),hAPP_nat_nat(suc,X2585)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2584),X2585))
| X2584 = hAPP_nat_nat(suc,X2585) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2584),X2585))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2584),hAPP_nat_nat(suc,X2585))) )
& ( X2584 != hAPP_nat_nat(suc,X2585)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2584),hAPP_nat_nat(suc,X2585))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_119_le__Suc__eq])])]) ).
fof(i_0_1630,plain,
! [X2578,X2579] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2578),hAPP_nat_nat(suc,X2579)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2578),X2579))
| X2578 = hAPP_nat_nat(suc,X2579) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1142])]) ).
cnf(i_0_1631,plain,
( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),X1)) = insert_nat(X2,bot_bot_fun_nat_bool)
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1143]) ).
cnf(i_0_1632,plain,
( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X2)),X1)) = insert_fun_nat_bool(X2,bot_bo1701429464l_bool)
| ~ hBOOL(hAPP_f54304608l_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1144]) ).
fof(i_0_1633,plain,
! [X3853,X3854,X3855] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3854),X3855))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3853),X3855)),X3854) = hAPP_nat_nat(plus_plus_nat(X3853),hAPP_nat_nat(minus_minus_nat(X3855),X3854)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_597_diff__add__assoc])]) ).
fof(i_0_1634,plain,
! [X3864,X3865,X3866] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3865),X3866))
| hAPP_nat_nat(plus_plus_nat(X3864),hAPP_nat_nat(minus_minus_nat(X3866),X3865)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3864),X3866)),X3865) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_601_add__diff__assoc])]) ).
fof(i_0_1635,plain,
! [X3875,X3876,X3877] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3876),X3877))
| hAPP_nat_nat(minus_minus_nat(X3875),hAPP_nat_nat(minus_minus_nat(X3877),X3876)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3875),X3876)),X3877) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_605_diff__diff__right])]) ).
fof(i_0_1636,plain,
! [X4016,X4017] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X4016),X4017)),hAPP_nat_nat(suc,X4016))),
inference(variable_rename,[status(thm)],[fact_665_diff__less__Suc]) ).
fof(i_0_1637,plain,
! [X3992,X3993] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3992),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X3992),X3993)))),
inference(variable_rename,[status(thm)],[fact_655_less__add__Suc1]) ).
fof(i_0_1638,plain,
! [X3994,X3995] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3994),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X3995),X3994)))),
inference(variable_rename,[status(thm)],[fact_656_less__add__Suc2]) ).
fof(i_0_1639,plain,
! [X3919,X3920,X3921] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3920),X3921))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3920),hAPP_nat_nat(plus_plus_nat(X3921),X3919))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_622_trans__less__add1])]) ).
fof(i_0_1640,plain,
! [X3896,X3897,X3898] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3897),X3898))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3897),hAPP_nat_nat(plus_plus_nat(X3898),X3896))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_615_termination__basic__simps_I1_J])]) ).
fof(i_0_1641,plain,
! [X3916,X3917,X3918] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3917),X3918))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3917),hAPP_nat_nat(plus_plus_nat(X3916),X3918))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_621_trans__less__add2])]) ).
fof(i_0_1642,plain,
! [X3899,X3900,X3901] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3900),X3901))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3900),hAPP_nat_nat(plus_plus_nat(X3899),X3901))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_616_termination__basic__simps_I2_J])]) ).
fof(i_0_1643,plain,
! [X3886,X3887,X3888] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3887),X3888))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3887),hAPP_nat_nat(plus_plus_nat(X3888),X3886))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_610_termination__basic__simps_I3_J])]) ).
fof(i_0_1644,plain,
! [X3825,X3826,X3827] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3826),X3827))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3826),hAPP_nat_nat(plus_plus_nat(X3827),X3825))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_588_trans__le__add1])]) ).
fof(i_0_1645,plain,
! [X3889,X3890,X3891] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3890),X3891))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3890),hAPP_nat_nat(plus_plus_nat(X3889),X3891))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_611_termination__basic__simps_I4_J])]) ).
fof(i_0_1646,plain,
! [X3828,X3829,X3830] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3829),X3830))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3829),hAPP_nat_nat(plus_plus_nat(X3828),X3830))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_589_trans__le__add2])]) ).
fof(i_0_1647,plain,
! [X2643,X2644,X2645] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2645))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2643),image_26036933t_bool(X2644,X2645)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2643)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_141_finite__surj])]) ).
fof(i_0_1648,plain,
! [X2625,X2626,X2627] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2627))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2625),image_2129980159t_bool(X2626,X2627)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2625)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_135_finite__surj])]) ).
fof(i_0_1649,plain,
! [X2646,X2647,X2648] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2648))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2646),image_1655916159e_bool(X2647,X2648)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2646)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_142_finite__surj])]) ).
fof(i_0_1650,plain,
! [X2628,X2629,X2630] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2630))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2628),image_47868345e_bool(X2629,X2630)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2628)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_136_finite__surj])]) ).
fof(i_0_1651,plain,
! [X2649,X2650,X2651] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2651))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2649),image_nat_fun_a_bool(X2650,X2651)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2649)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_143_finite__surj])]) ).
fof(i_0_1652,plain,
! [X2631,X2632,X2633] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2633))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2631),image_112932426a_bool(X2632,X2633)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2631)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_137_finite__surj])]) ).
fof(i_0_1653,plain,
! [X2673,X2674,X2675] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2675))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2673),image_496248727ol_nat(X2674,X2675)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2673)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_151_finite__surj])]) ).
fof(i_0_1654,plain,
! [X2676,X2677,X2678] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2678))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2676),image_1551609309ol_nat(X2677,X2678)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2676)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_152_finite__surj])]) ).
fof(i_0_1655,plain,
! [X2679,X2680,X2681] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2681))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2679),image_fun_a_bool_nat(X2680,X2681)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2679)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_153_finite__surj])]) ).
fof(i_0_1656,plain,
! [X2655,X2656,X2657] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2657))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2655),image_nat_nat(X2656,X2657)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2655)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_145_finite__surj])]) ).
fof(i_0_1657,plain,
! [X2637,X2638,X2639] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2639))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2637),image_pname_nat(X2638,X2639)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2637)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_139_finite__surj])]) ).
fof(i_0_1658,plain,
! [X2670,X2671,X2672] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2672))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2670),image_a_nat(X2671,X2672)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2670)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_150_finite__surj])]) ).
fof(i_0_1659,plain,
! [X2661,X2662,X2663] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2663))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2661),image_1921560913_pname(X2662,X2663)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2661)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_147_finite__surj])]) ).
fof(i_0_1660,plain,
! [X2664,X2665,X2666] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2666))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2664),image_1283814551_pname(X2665,X2666)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2664)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_148_finite__surj])]) ).
fof(i_0_1661,plain,
! [X2667,X2668,X2669] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2669))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2667),image_1854862208_pname(X2668,X2669)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2667)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_149_finite__surj])]) ).
fof(i_0_1662,plain,
! [X2652,X2653,X2654] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2654))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2652),image_nat_pname(X2653,X2654)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2652)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_144_finite__surj])]) ).
fof(i_0_1663,plain,
! [X2634,X2635,X2636] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2636))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2634),image_pname_pname(X2635,X2636)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2634)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_138_finite__surj])]) ).
fof(i_0_1664,plain,
! [X2658,X2659,X2660] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2660))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2658),image_a_pname(X2659,X2660)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2658)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_146_finite__surj])]) ).
fof(i_0_1665,plain,
! [X2616,X2617,X2618] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2618))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2616),image_fun_nat_bool_a(X2617,X2618)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2616)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_132_finite__surj])]) ).
fof(i_0_1666,plain,
! [X2619,X2620,X2621] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2621))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2619),image_876012084bool_a(X2620,X2621)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2619)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_133_finite__surj])]) ).
fof(i_0_1667,plain,
! [X2622,X2623,X2624] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2624))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2622),image_fun_a_bool_a(X2623,X2624)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2622)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_134_finite__surj])]) ).
fof(i_0_1668,plain,
! [X2640,X2641,X2642] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2642))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2640),image_nat_a(X2641,X2642)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2640)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_140_finite__surj])]) ).
fof(i_0_1669,plain,
! [X2682,X2683,X2684] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2684))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2682),image_pname_a(X2683,X2684)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2682)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_154_finite__surj])]) ).
fof(i_0_1670,plain,
! [X2613,X2614,X2615] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2615))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2613),image_a_a(X2614,X2615)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2613)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_131_finite__surj])]) ).
fof(i_0_1671,plain,
! [X2885,X2886,X2887,X2888] :
( X2886 != hAPP_pname_nat(X2887,X2888)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2888),X2885))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2886),image_pname_nat(X2887,X2885))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_211_image__eqI])]) ).
fof(i_0_1672,plain,
! [X2889,X2890,X2891,X2892] :
( X2890 != hAPP_a_nat(X2891,X2892)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2892),X2889))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2890),image_a_nat(X2891,X2889))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_212_image__eqI])]) ).
fof(i_0_1673,plain,
! [X3129,X3130,X3131,X3132] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3131),X3132))
| X3129 != hAPP_pname_nat(X3130,X3131)
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3129),image_pname_nat(X3130,X3132))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_308_rev__image__eqI])]) ).
fof(i_0_1674,plain,
! [X3133,X3134,X3135,X3136] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3135),X3136))
| X3133 != hAPP_a_nat(X3134,X3135)
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3133),image_a_nat(X3134,X3136))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_309_rev__image__eqI])]) ).
fof(i_0_1675,plain,
! [X2893,X2894,X2895,X2896] :
( X2894 != hAPP_nat_pname(X2895,X2896)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2896),X2893))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2894),image_nat_pname(X2895,X2893))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_213_image__eqI])]) ).
fof(i_0_1676,plain,
! [X3137,X3138,X3139,X3140] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3139),X3140))
| X3137 != hAPP_nat_pname(X3138,X3139)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3137),image_nat_pname(X3138,X3140))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_310_rev__image__eqI])]) ).
fof(i_0_1677,plain,
! [X2897,X2898,X2899,X2900] :
( X2898 != hAPP_nat_a(X2899,X2900)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2900),X2897))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2898),image_nat_a(X2899,X2897))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_214_image__eqI])]) ).
fof(i_0_1678,plain,
! [X2901,X2902,X2903,X2904] :
( X2902 != hAPP_pname_a(X2903,X2904)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2904),X2901))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2902),image_pname_a(X2903,X2901))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_215_image__eqI])]) ).
fof(i_0_1679,plain,
! [X3141,X3142,X3143,X3144] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3143),X3144))
| X3141 != hAPP_nat_a(X3142,X3143)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3141),image_nat_a(X3142,X3144))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_311_rev__image__eqI])]) ).
fof(i_0_1680,plain,
! [X3145,X3146,X3147,X3148] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3147),X3148))
| X3145 != hAPP_pname_a(X3146,X3147)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3145),image_pname_a(X3146,X3148))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_312_rev__image__eqI])]) ).
fof(i_0_1681,plain,
! [X3948,X3949] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3948),hAPP_nat_nat(suc,X3949)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3948),X3949))
| X3948 = X3949 )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3948),X3949))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3948),hAPP_nat_nat(suc,X3949))) )
& ( X3948 != X3949
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3948),hAPP_nat_nat(suc,X3949))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_635_less__Suc__eq])])]) ).
fof(i_0_1682,plain,
! [X3944,X3945] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3944),hAPP_nat_nat(suc,X3945)))
| X3944 = X3945
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3944),X3945)) )
& ( X3944 != X3945
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3944),hAPP_nat_nat(suc,X3945)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3944),X3945)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1145])])]) ).
fof(i_0_1683,plain,
! [X3942,X3943] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3942),X3943))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3942),hAPP_nat_nat(suc,X3943)))
| X3943 = X3942 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1146])]) ).
fof(i_0_1684,plain,
! [X3933,X3934] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3933),hAPP_nat_nat(suc,X3934)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3933),X3934))
| X3933 = X3934 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1147])]) ).
fof(i_0_1685,plain,
! [X4004,X4005] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4004),hAPP_nat_nat(suc,X4005)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4004),X4005)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4004),X4005))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4004),hAPP_nat_nat(suc,X4005))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_659_less__Suc__eq__le])]) ).
fof(i_0_1686,plain,
! [X2588] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X2588)),X2588)),
inference(variable_rename,[status(thm)],[i_0_1148]) ).
fof(i_0_1687,plain,
! [X4053,X4054] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4053),esk134_2(X4053,X4054)))
| X4054 = hAPP_nat_nat(suc,X4053)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4053),X4054)) )
& ( X4054 = hAPP_nat_nat(suc,esk134_2(X4053,X4054))
| X4054 = hAPP_nat_nat(suc,X4053)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4053),X4054)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_677_lessE])])])]) ).
cnf(i_0_1688,plain,
( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X2)),X1)) = insert_nat(X2,bot_bot_fun_nat_bool)
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1149]) ).
cnf(i_0_1689,plain,
( collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,X2)),X1)) = insert_fun_nat_bool(X2,bot_bo1701429464l_bool)
| ~ hBOOL(hAPP_f54304608l_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1150]) ).
fof(i_0_1690,plain,
! [X3905,X3906,X3907,X3908] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3907),X3908))
| hAPP_nat_nat(plus_plus_nat(X3905),X3908) != hAPP_nat_nat(plus_plus_nat(X3907),X3906)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3905),X3906)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_618_less__add__eq__less])]) ).
cnf(i_0_1691,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_1135]) ).
cnf(i_0_1692,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_1136]) ).
fof(i_0_1693,plain,
! [X3718,X3719] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3718),X3719))
| X3718 != X3719
| ~ is_fun_pname_bool(X3718)
| ~ is_fun_pname_bool(X3719) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3719),X3718))
| X3718 != X3719
| ~ is_fun_pname_bool(X3718)
| ~ is_fun_pname_bool(X3719) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3718),X3719))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3719),X3718))
| X3718 = X3719
| ~ is_fun_pname_bool(X3718)
| ~ is_fun_pname_bool(X3719) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_552_order__eq__iff])])]) ).
fof(i_0_1694,plain,
! [X3698,X3699] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3699),X3698))
| X3699 = X3698
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3698),X3699))
| ~ is_fun_pname_bool(X3698)
| ~ is_fun_pname_bool(X3699) )
& ( X3699 != X3698
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3699),X3698))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3698),X3699))
| ~ is_fun_pname_bool(X3698)
| ~ is_fun_pname_bool(X3699) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_542_order__antisym__conv])])]) ).
fof(i_0_1695,plain,
! [X3628,X3629] :
( ~ is_fun_pname_bool(X3628)
| ~ is_fun_pname_bool(X3629)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3628),X3629))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3629),X3628))
| X3628 = X3629 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_517_order__antisym])]) ).
fof(i_0_1696,plain,
! [X3603,X3604] :
( ~ is_fun_pname_bool(X3603)
| ~ is_fun_pname_bool(X3604)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3603),X3604))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3604),X3603))
| X3604 = X3603 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_507_xt1_I5_J])]) ).
fof(i_0_1697,plain,
! [X3035,X3036] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3035),X3036))
| X3035 != X3036
| ~ is_fun_pname_bool(X3035)
| ~ is_fun_pname_bool(X3036) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3036),X3035))
| X3035 != X3036
| ~ is_fun_pname_bool(X3035)
| ~ is_fun_pname_bool(X3036) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3035),X3036))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3036),X3035))
| X3035 = X3036
| ~ is_fun_pname_bool(X3035)
| ~ is_fun_pname_bool(X3036) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_269_set__eq__subset])])]) ).
fof(i_0_1698,plain,
! [X2905,X2906] :
( ~ is_fun_pname_bool(X2905)
| ~ is_fun_pname_bool(X2906)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2905),X2906))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2906),X2905))
| X2905 = X2906 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_216_equalityI])]) ).
fof(i_0_1699,plain,
! [X3722,X3723] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3722),X3723))
| X3722 != X3723
| ~ is_fun_a_bool(X3722)
| ~ is_fun_a_bool(X3723) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3723),X3722))
| X3722 != X3723
| ~ is_fun_a_bool(X3722)
| ~ is_fun_a_bool(X3723) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3722),X3723))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3723),X3722))
| X3722 = X3723
| ~ is_fun_a_bool(X3722)
| ~ is_fun_a_bool(X3723) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_554_order__eq__iff])])]) ).
fof(i_0_1700,plain,
! [X3702,X3703] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3703),X3702))
| X3703 = X3702
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3702),X3703))
| ~ is_fun_a_bool(X3702)
| ~ is_fun_a_bool(X3703) )
& ( X3703 != X3702
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3703),X3702))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3702),X3703))
| ~ is_fun_a_bool(X3702)
| ~ is_fun_a_bool(X3703) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_544_order__antisym__conv])])]) ).
fof(i_0_1701,plain,
! [X3632,X3633] :
( ~ is_fun_a_bool(X3632)
| ~ is_fun_a_bool(X3633)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3632),X3633))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3633),X3632))
| X3632 = X3633 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_519_order__antisym])]) ).
fof(i_0_1702,plain,
! [X3607,X3608] :
( ~ is_fun_a_bool(X3607)
| ~ is_fun_a_bool(X3608)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3607),X3608))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3608),X3607))
| X3608 = X3607 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_509_xt1_I5_J])]) ).
fof(i_0_1703,plain,
! [X3039,X3040] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3039),X3040))
| X3039 != X3040
| ~ is_fun_a_bool(X3039)
| ~ is_fun_a_bool(X3040) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3040),X3039))
| X3039 != X3040
| ~ is_fun_a_bool(X3039)
| ~ is_fun_a_bool(X3040) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3039),X3040))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3040),X3039))
| X3039 = X3040
| ~ is_fun_a_bool(X3039)
| ~ is_fun_a_bool(X3040) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_271_set__eq__subset])])]) ).
fof(i_0_1704,plain,
! [X2909,X2910] :
( ~ is_fun_a_bool(X2909)
| ~ is_fun_a_bool(X2910)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2909),X2910))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2910),X2909))
| X2909 = X2910 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_218_equalityI])]) ).
cnf(i_0_1705,plain,
( insert_nat(X1,X2) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1151]) ).
fof(i_0_1706,plain,
! [X3714,X3715] :
( ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3715),X3714))
| ~ hBOOL(X3715)
| ~ hBOOL(X3714) )
& ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3714),X3715))
| ~ hBOOL(X3715)
| ~ hBOOL(X3714) )
& ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3715),X3714))
| hBOOL(X3715)
| hBOOL(X3714) )
& ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3714),X3715))
| hBOOL(X3715)
| hBOOL(X3714) )
& ( ~ hBOOL(X3715)
| hBOOL(X3714)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3715),X3714))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3714),X3715)) )
& ( ~ hBOOL(X3714)
| hBOOL(X3715)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3715),X3714))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3714),X3715)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_550_order__eq__iff])])]) ).
fof(i_0_1707,plain,
! [X3694,X3695] :
( ( ~ hBOOL(X3695)
| hBOOL(X3694)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3695),X3694))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3694),X3695)) )
& ( ~ hBOOL(X3694)
| hBOOL(X3695)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3695),X3694))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3694),X3695)) )
& ( ~ hBOOL(X3695)
| ~ hBOOL(X3694)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3695),X3694))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3694),X3695)) )
& ( hBOOL(X3695)
| hBOOL(X3694)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3695),X3694))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3694),X3695)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_540_order__antisym__conv])])]) ).
fof(i_0_1708,plain,
! [X3624,X3625] :
( ( ~ hBOOL(X3624)
| hBOOL(X3625)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3625),X3624))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3624),X3625)) )
& ( ~ hBOOL(X3625)
| hBOOL(X3624)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3625),X3624))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3624),X3625)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_515_order__antisym])])]) ).
fof(i_0_1709,plain,
! [X3599,X3600] :
( ( ~ hBOOL(X3600)
| hBOOL(X3599)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3600),X3599))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3599),X3600)) )
& ( ~ hBOOL(X3599)
| hBOOL(X3600)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3600),X3599))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3599),X3600)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_505_xt1_I5_J])])]) ).
fof(i_0_1710,plain,
! [X3716,X3717] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3716),X3717))
| X3716 != X3717 )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3717),X3716))
| X3716 != X3717 )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3716),X3717))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3717),X3716))
| X3716 = X3717 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_551_order__eq__iff])])]) ).
fof(i_0_1711,plain,
! [X3696,X3697] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3697),X3696))
| X3697 = X3696
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3696),X3697)) )
& ( X3697 != X3696
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3697),X3696))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3696),X3697)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_541_order__antisym__conv])])]) ).
fof(i_0_1712,plain,
! [X3626,X3627] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3626),X3627))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3627),X3626))
| X3626 = X3627 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_516_order__antisym])]) ).
fof(i_0_1713,plain,
! [X3601,X3602] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3601),X3602))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3602),X3601))
| X3602 = X3601 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_506_xt1_I5_J])]) ).
fof(i_0_1714,plain,
! [X3037,X3038] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3037),X3038))
| X3037 != X3038 )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3038),X3037))
| X3037 != X3038 )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3037),X3038))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3038),X3037))
| X3037 = X3038 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_270_set__eq__subset])])]) ).
fof(i_0_1715,plain,
! [X2907,X2908] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2907),X2908))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2908),X2907))
| X2907 = X2908 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_217_equalityI])]) ).
fof(i_0_1716,plain,
! [X3720,X3721] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3720),X3721))
| X3720 != X3721 )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3721),X3720))
| X3720 != X3721 )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3720),X3721))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3721),X3720))
| X3720 = X3721 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_553_order__eq__iff])])]) ).
fof(i_0_1717,plain,
! [X3700,X3701] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3701),X3700))
| X3701 = X3700
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3700),X3701)) )
& ( X3701 != X3700
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3701),X3700))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3700),X3701)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_543_order__antisym__conv])])]) ).
fof(i_0_1718,plain,
! [X3630,X3631] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3630),X3631))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3631),X3630))
| X3630 = X3631 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_518_order__antisym])]) ).
fof(i_0_1719,plain,
! [X3605,X3606] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3605),X3606))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3606),X3605))
| X3606 = X3605 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_508_xt1_I5_J])]) ).
fof(i_0_1720,plain,
! [X2515,X2516] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2515),X2516))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2516),X2515))
| X2515 = X2516 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_85_le__antisym])]) ).
fof(i_0_1721,plain,
! [X3940,X3941] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3940),X3941))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3940),hAPP_nat_nat(suc,X3941))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_631_less__SucI])]) ).
fof(i_0_1722,plain,
! [X4008,X4009] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4008),X4009))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4008),hAPP_nat_nat(suc,X4009))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_661_le__imp__less__Suc])]) ).
fof(i_0_1723,plain,
! [X2580,X2581] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2580),X2581))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2580),hAPP_nat_nat(suc,X2581))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_117_le__SucI])]) ).
fof(i_0_1724,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_1725,plain,
! [X3980,X3981,X3982] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3982),X3981))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| X3981 = X3982
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3981),X3982)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| X3981 = X3982
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3981),X3982)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3982),X3981))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3981),X3982)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3981),X3982)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3982),X3981))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| X3981 = X3982
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| X3981 = X3982
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981)) )
& ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3982),X3981))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(X3980,X3982),X3981)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_651_nat__less__cases])])]) ).
fof(i_0_1726,plain,
! [X2505,X2506] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2505),X2506))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2506)),X2505) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X2506),X2505)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_78_Suc__diff__le])]) ).
fof(i_0_1727,plain,
! [X2611,X2612] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X2611),X2612)),X2611)),
inference(variable_rename,[status(thm)],[fact_130_diff__le__self]) ).
fof(i_0_1728,plain,
! [X4039,X4040] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4039),X4040))
| X4040 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X4039),esk129_2(X4039,X4040))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_673_less__imp__Suc__add])])]) ).
fof(i_0_1729,plain,
! [X3996,X3997,X3999,X4000,X4001] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3996),X3997))
| X3997 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X3996),esk125_2(X3996,X3997))) )
& ( X4000 != hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X3999),X4001))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3999),X4000)) ) ),
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_657_less__iff__Suc__add])])])])]) ).
fof(i_0_1730,plain,
! [X3859,X3860] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3859),X3860))
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X3860),X3859)),X3859) = X3860 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_599_le__add__diff__inverse2])]) ).
cnf(i_0_1731,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_1152]) ).
cnf(i_0_1732,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_1152]) ).
cnf(i_0_1733,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_1153]) ).
cnf(i_0_1734,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_1153]) ).
fof(i_0_1735,plain,
! [X2357] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2357))
| hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X2357)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1_finite__Collect__subsets])]) ).
fof(i_0_1736,plain,
! [X2358] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2358))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X2358)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2_finite__Collect__subsets])]) ).
fof(i_0_1737,plain,
! [X2359] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2359))
| hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X2359)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_3_finite__Collect__subsets])]) ).
fof(i_0_1738,plain,
! [X2361] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2361))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X2361)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_finite__Collect__subsets])]) ).
fof(i_0_1739,plain,
! [X2360] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2360))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X2360)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_finite__Collect__subsets])]) ).
fof(i_0_1740,plain,
! [X3679,X3680,X3681] :
( ( ~ hBOOL(X3681)
| ~ hBOOL(X3680)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3680),X3679))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3681),X3679)) )
& ( hBOOL(X3681)
| hBOOL(X3680)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3680),X3679))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3681),X3679)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_535_ord__eq__le__trans])])]) ).
fof(i_0_1741,plain,
! [X3634,X3635,X3636] :
( ( ~ hBOOL(X3635)
| ~ hBOOL(X3634)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3634),X3636))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3635),X3636)) )
& ( hBOOL(X3635)
| hBOOL(X3634)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3634),X3636))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3635),X3636)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_520_xt1_I4_J])])]) ).
fof(i_0_1742,plain,
! [X3664,X3665,X3666] :
( ( ~ hBOOL(X3666)
| ~ hBOOL(X3665)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3664),X3665))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3664),X3666)) )
& ( hBOOL(X3666)
| hBOOL(X3665)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3664),X3665))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3664),X3666)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_530_xt1_I3_J])])]) ).
fof(i_0_1743,plain,
! [X3649,X3650,X3651] :
( ( ~ hBOOL(X3651)
| ~ hBOOL(X3649)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3650),X3649))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3650),X3651)) )
& ( hBOOL(X3651)
| hBOOL(X3649)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3650),X3649))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3650),X3651)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_525_ord__le__eq__trans])])]) ).
cnf(i_0_1744,plain,
insert_nat(X1,X2) != bot_bot_fun_nat_bool,
inference(split_conjunct,[status(thm)],[i_0_1154]) ).
cnf(i_0_1745,plain,
bot_bot_fun_nat_bool != insert_nat(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1155]) ).
fof(i_0_1746,plain,
! [X3960,X3961] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3960),X3961))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3960),X3961)) )
& ( X3960 != X3961
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3960),X3961)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3960),X3961))
| X3960 = X3961
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3960),X3961)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_641_nat__less__le])])]) ).
fof(i_0_1747,plain,
! [X3958,X3959] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3958),X3959))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3958),X3959))
| X3958 = X3959 )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3958),X3959))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3958),X3959)) )
& ( X3958 != X3959
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3958),X3959)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_640_le__eq__less__or__eq])])]) ).
fof(i_0_1748,plain,
! [X3954,X3955] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3954),X3955))
| X3954 = X3955
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3954),X3955)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_638_le__neq__implies__less])]) ).
fof(i_0_1749,plain,
! [X3968,X3969] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3968),X3969))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3968),X3969)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_644_termination__basic__simps_I5_J])]) ).
fof(i_0_1750,plain,
! [X3956,X3957] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3956),X3957))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3956),X3957)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_639_less__imp__le__nat])]) ).
fof(i_0_1751,plain,
! [X3952,X3953] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3952),X3953))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3952),X3953)) )
& ( X3952 != X3953
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3952),X3953)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_637_less__or__eq__imp__le])])]) ).
fof(i_0_1752,plain,
! [X2525,X2526,X2527] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2525),X2526)),X2527) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2525),X2527)),X2526),
inference(variable_rename,[status(thm)],[fact_90_diff__commute]) ).
fof(i_0_1753,plain,
! [X2552,X2553] :
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2552),X2553))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2553))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2552)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_103_finite__subset])]) ).
fof(i_0_1754,plain,
! [X2564,X2565] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2565))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X2564),X2565))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2564)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_109_rev__finite__subset])]) ).
fof(i_0_1755,plain,
! [X2554,X2555] :
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2554),X2555))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2555))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2554)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_104_finite__subset])]) ).
fof(i_0_1756,plain,
! [X2566,X2567] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2567))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X2566),X2567))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2566)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_110_rev__finite__subset])]) ).
fof(i_0_1757,plain,
! [X2556,X2557] :
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2556),X2557))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2557))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2556)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_105_finite__subset])]) ).
fof(i_0_1758,plain,
! [X2568,X2569] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2569))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X2568),X2569))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2568)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_111_rev__finite__subset])]) ).
fof(i_0_1759,plain,
! [X2562,X2563] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2562),X2563))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2563))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_108_finite__subset])]) ).
fof(i_0_1760,plain,
! [X2574,X2575] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2575))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2574),X2575))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2574)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_114_rev__finite__subset])]) ).
fof(i_0_1761,plain,
! [X2560,X2561] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2560),X2561))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2561))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2560)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_107_finite__subset])]) ).
fof(i_0_1762,plain,
! [X2572,X2573] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2573))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2572),X2573))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2572)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_113_rev__finite__subset])]) ).
fof(i_0_1763,plain,
! [X2558,X2559] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2558),X2559))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2559))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2558)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_106_finite__subset])]) ).
fof(i_0_1764,plain,
! [X2570,X2571] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2571))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2570),X2571))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2570)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_112_rev__finite__subset])]) ).
fof(i_0_1765,plain,
! [X3867,X3868] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3867),X3868))
| hAPP_nat_nat(plus_plus_nat(X3867),hAPP_nat_nat(minus_minus_nat(X3868),X3867)) = X3868 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_602_le__add__diff__inverse])]) ).
fof(i_0_1766,plain,
! [X2603,X2604] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2603),X2604))
| hAPP_nat_nat(minus_minus_nat(X2604),hAPP_nat_nat(minus_minus_nat(X2604),X2603)) = X2603 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_127_diff__diff__cancel])]) ).
fof(i_0_1767,plain,
! [X3856,X3857,X3858] :
( ( hAPP_nat_nat(minus_minus_nat(X3858),X3857) != X3856
| X3858 = hAPP_nat_nat(plus_plus_nat(X3856),X3857)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3857),X3858)) )
& ( X3858 != hAPP_nat_nat(plus_plus_nat(X3856),X3857)
| hAPP_nat_nat(minus_minus_nat(X3858),X3857) = X3856
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3857),X3858)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_598_le__imp__diff__is__add])])]) ).
fof(i_0_1768,plain,
! [X3816,X3817,X3819,X3820,X3821] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3816),X3817))
| X3817 = hAPP_nat_nat(plus_plus_nat(X3816),esk122_2(X3816,X3817)) )
& ( X3820 != hAPP_nat_nat(plus_plus_nat(X3819),X3821)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3819),X3820)) ) ),
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_586_le__iff__add])])])])]) ).
fof(i_0_1769,plain,
! [X2355,X2356] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2355),X2356))
| hBOOL(hAPP_fun_a_bool_bool(p(X2356),X2355)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_assms_I1_J])]) ).
fof(i_0_1770,plain,
! [X3773] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3773),u))
| hBOOL(wt(the_com(body(X3773)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_567_assms_I4_J])]) ).
fof(i_0_1771,plain,
! [X3973,X3974] :
( X3973 = X3974
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3973),X3974))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3974),X3973)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1156])]) ).
fof(i_0_1772,plain,
! [X3971,X3972] :
( ( X3971 = X3972
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3971),X3972))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3972),X3971)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3971),X3972))
| X3971 != X3972 )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3972),X3971))
| X3971 != X3972 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_646_nat__neq__iff])])]) ).
fof(i_0_1773,plain,
! [X3806,X3807,X3808] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3806),X3807)),hAPP_nat_nat(plus_plus_nat(X3806),X3808)) = hAPP_nat_nat(minus_minus_nat(X3807),X3808),
inference(variable_rename,[status(thm)],[fact_582_diff__cancel]) ).
fof(i_0_1774,plain,
! [X3809,X3810,X3811] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3809),X3810)),hAPP_nat_nat(plus_plus_nat(X3811),X3810)) = hAPP_nat_nat(minus_minus_nat(X3809),X3811),
inference(variable_rename,[status(thm)],[fact_583_diff__cancel2]) ).
fof(i_0_1775,plain,
! [X3791,X3792,X3793] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X3791),X3792)),X3793) = hAPP_nat_nat(plus_plus_nat(X3791),hAPP_nat_nat(plus_plus_nat(X3792),X3793)),
inference(variable_rename,[status(thm)],[fact_576_nat__add__assoc]) ).
fof(i_0_1776,plain,
! [X3803,X3804,X3805] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X3803),X3804)),X3805) = hAPP_nat_nat(minus_minus_nat(X3803),hAPP_nat_nat(plus_plus_nat(X3804),X3805)),
inference(variable_rename,[status(thm)],[fact_581_diff__diff__left]) ).
fof(i_0_1777,plain,
! [X3724,X3725] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3724),X3725))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3725),X3724)) ),
inference(variable_rename,[status(thm)],[fact_555_linorder__linear]) ).
fof(i_0_1778,plain,
! [X3582,X3583] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3582),X3583))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3583),X3582)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1157])]) ).
fof(i_0_1779,plain,
! [X2522,X2523] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2522),X2523))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2523),X2522)) ),
inference(variable_rename,[status(thm)],[fact_88_nat__le__linear]) ).
fof(i_0_1780,plain,
! [X3814,X3815] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3814),hAPP_nat_nat(plus_plus_nat(X3814),X3815))),
inference(variable_rename,[status(thm)],[fact_585_le__add1]) ).
fof(i_0_1781,plain,
! [X3812,X3813] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3812),hAPP_nat_nat(plus_plus_nat(X3813),X3812))),
inference(variable_rename,[status(thm)],[fact_584_le__add2]) ).
fof(i_0_1782,plain,
! [X3080,X3081] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3080),X3081))
| hBOOL(hAPP_nat_bool(X3081,X3080)) )
& ( ~ hBOOL(hAPP_nat_bool(X3081,X3080))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3080),X3081)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_287_mem__def])]) ).
fof(i_0_1783,plain,
! [X3082,X3083] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3082),X3083))
| hBOOL(hAPP_pname_bool(X3083,X3082)) )
& ( ~ hBOOL(hAPP_pname_bool(X3083,X3082))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3082),X3083)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_288_mem__def])]) ).
fof(i_0_1784,plain,
! [X3084,X3085] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3084),X3085))
| hBOOL(hAPP_a_bool(X3085,X3084)) )
& ( ~ hBOOL(hAPP_a_bool(X3085,X3084))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3084),X3085)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_289_mem__def])]) ).
cnf(i_0_1785,plain,
collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1)) = insert_nat(X1,bot_bot_fun_nat_bool),
inference(split_conjunct,[status(thm)],[i_0_1158]) ).
cnf(i_0_1786,plain,
collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)) = insert_fun_nat_bool(X1,bot_bo1701429464l_bool),
inference(split_conjunct,[status(thm)],[i_0_1159]) ).
cnf(i_0_1787,plain,
collect_nat(hAPP_n1699378549t_bool(fequal_nat,X1)) = insert_nat(X1,bot_bot_fun_nat_bool),
inference(split_conjunct,[status(thm)],[i_0_1160]) ).
cnf(i_0_1788,plain,
collect_fun_nat_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1)) = insert_fun_nat_bool(X1,bot_bo1701429464l_bool),
inference(split_conjunct,[status(thm)],[i_0_1161]) ).
fof(i_0_1789,plain,
! [X4067,X4068] :
( ( hAPP_nat_nat(minus_minus_nat(X4067),X4068) != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4067),X4068)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4067),X4068))
| hAPP_nat_nat(minus_minus_nat(X4067),X4068) = zero_zero_nat ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_685_diff__is__0__eq])]) ).
fof(i_0_1790,plain,
! [X4065,X4066] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4065),X4066))
| hAPP_nat_nat(minus_minus_nat(X4065),X4066) = zero_zero_nat ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_684_diff__is__0__eq_H])]) ).
fof(i_0_1791,plain,
! [X3458,X3460] :
( ( is_pname(esk101_1(X3458))
| X3458 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X3458) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk101_1(X3458)),X3458))
| X3458 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X3458) )
& ( X3458 != bot_bo844097828e_bool
| ~ is_pname(X3460)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3460),X3458))
| ~ is_fun_pname_bool(X3458) ) ),
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_1162])])])])]) ).
fof(i_0_1792,plain,
! [X3461,X3463] :
( ( is_a(esk102_1(X3461))
| X3461 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X3461) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk102_1(X3461)),X3461))
| X3461 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X3461) )
& ( X3461 != bot_bot_fun_a_bool
| ~ is_a(X3463)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3463),X3461))
| ~ is_fun_a_bool(X3461) ) ),
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_1163])])])])]) ).
fof(i_0_1793,plain,
! [X3448,X3449] :
( ( ~ is_pname(X3449)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3449),X3448))
| X3448 != bot_bo844097828e_bool
| ~ is_fun_pname_bool(X3448) )
& ( is_pname(esk98_1(X3448))
| X3448 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X3448) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk98_1(X3448)),X3448))
| X3448 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X3448) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_414_ex__in__conv])])])])]) ).
fof(i_0_1794,plain,
! [X3451,X3452] :
( ( ~ is_a(X3452)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3452),X3451))
| X3451 != bot_bot_fun_a_bool
| ~ is_fun_a_bool(X3451) )
& ( is_a(esk99_1(X3451))
| X3451 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X3451) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk99_1(X3451)),X3451))
| X3451 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X3451) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_415_ex__in__conv])])])])]) ).
fof(i_0_1795,plain,
! [X4111,X4112] :
( ~ is_pname(X4111)
| ~ is_pname(X4112)
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X4111),X4112))
| X4111 = X4112 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1164])]) ).
fof(i_0_1796,plain,
! [X4103,X4104] :
( ~ is_a(X4103)
| ~ is_a(X4104)
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X4103),X4104))
| X4103 = X4104 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1165])]) ).
fof(i_0_1797,plain,
! [X4152,X4153] :
( ~ is_fun_pname_bool(X4152)
| ~ is_fun_pname_bool(X4153)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X4152),X4153))
| X4152 = X4153 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1166])]) ).
fof(i_0_1798,plain,
! [X4124,X4125] :
( ~ is_fun_a_bool(X4124)
| ~ is_fun_a_bool(X4125)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X4124),X4125))
| X4124 = X4125 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1167])]) ).
fof(i_0_1799,plain,
! [X4018,X4019] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4018),X4019))
| hAPP_nat_nat(plus_plus_nat(X4019),hAPP_nat_nat(minus_minus_nat(X4018),X4019)) = X4018 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1168])]) ).
cnf(i_0_1800,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_1169]) ).
fof(i_0_1801,plain,
! [X3774,X3775] : hAPP_nat_nat(minus_minus_nat(X3774),hAPP_nat_nat(suc,X3775)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X3774),one_one_nat)),X3775),
inference(variable_rename,[status(thm)],[fact_568_diff__Suc__eq__diff__pred]) ).
cnf(i_0_1802,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_1143]) ).
cnf(i_0_1803,plain,
( hBOOL(hAPP_f54304608l_bool(X1,X2))
| collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X2)),X1)) = bot_bo1701429464l_bool ),
inference(split_conjunct,[status(thm)],[i_0_1144]) ).
fof(i_0_1804,plain,
! [X4101,X4102] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X4101),X4102))
| ~ hBOOL(X4101)
| hBOOL(X4102) ),
inference(variable_rename,[status(thm)],[i_0_1170]) ).
fof(i_0_1805,plain,
! [X4094,X4095] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X4094),X4095))
| hBOOL(X4094)
| hBOOL(X4095) ),
inference(variable_rename,[status(thm)],[i_0_1171]) ).
fof(i_0_1806,plain,
! [X3476] :
( ( ~ hBOOL(X3476)
| hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3476),bot_bot_bool)) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(X3476)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3476),bot_bot_bool)) )
& ( ~ hBOOL(X3476)
| ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3476),bot_bot_bool)) )
& ( hBOOL(X3476)
| hBOOL(bot_bot_bool)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3476),bot_bot_bool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_437_bot__unique])])]) ).
fof(i_0_1807,plain,
! [X3471] :
( ( ~ hBOOL(X3471)
| hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3471),bot_bot_bool)) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(X3471)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3471),bot_bot_bool)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_432_le__bot])])]) ).
fof(i_0_1808,plain,
! [X4086,X4087] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X4086),X4087))
| hBOOL(X4086) ),
inference(variable_rename,[status(thm)],[i_0_1172]) ).
fof(i_0_1809,plain,
! [X4088,X4089] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X4088),X4089))
| hBOOL(X4089) ),
inference(variable_rename,[status(thm)],[i_0_1173]) ).
fof(i_0_1810,plain,
! [X3528] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3528),bot_bo844097828e_bool))
| X3528 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X3528) )
& ( X3528 != bot_bo844097828e_bool
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3528),bot_bo844097828e_bool))
| ~ is_fun_pname_bool(X3528) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_465_subset__empty])])]) ).
fof(i_0_1811,plain,
! [X3475] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3475),bot_bo844097828e_bool))
| X3475 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X3475) )
& ( X3475 != bot_bo844097828e_bool
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3475),bot_bo844097828e_bool))
| ~ is_fun_pname_bool(X3475) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_436_bot__unique])])]) ).
fof(i_0_1812,plain,
! [X3470] :
( ~ is_fun_pname_bool(X3470)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3470),bot_bo844097828e_bool))
| X3470 = bot_bo844097828e_bool ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_431_le__bot])]) ).
fof(i_0_1813,plain,
! [X3529] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3529),bot_bot_fun_a_bool))
| X3529 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X3529) )
& ( X3529 != bot_bot_fun_a_bool
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3529),bot_bot_fun_a_bool))
| ~ is_fun_a_bool(X3529) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_466_subset__empty])])]) ).
fof(i_0_1814,plain,
! [X3478] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3478),bot_bot_fun_a_bool))
| X3478 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X3478) )
& ( X3478 != bot_bot_fun_a_bool
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3478),bot_bot_fun_a_bool))
| ~ is_fun_a_bool(X3478) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_439_bot__unique])])]) ).
fof(i_0_1815,plain,
! [X3473] :
( ~ is_fun_a_bool(X3473)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3473),bot_bot_fun_a_bool))
| X3473 = bot_bot_fun_a_bool ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_434_le__bot])]) ).
fof(i_0_1816,plain,
! [X3978,X3979] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3978),X3979))
| X3978 != X3979 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_650_less__not__refl3])]) ).
fof(i_0_1817,plain,
! [X3976,X3977] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3976),X3977))
| X3977 != X3976 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_649_less__not__refl2])]) ).
fof(i_0_1818,plain,
! [X2371,X2372] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2372))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X2371,X2372))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_11_finite__imageI])]) ).
fof(i_0_1819,plain,
! [X2363,X2364] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2364))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X2363,X2364))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_7_finite__imageI])]) ).
fof(i_0_1820,plain,
! [X2373,X2374] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2374))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X2373,X2374))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_12_finite__imageI])]) ).
fof(i_0_1821,plain,
! [X2365,X2366] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2366))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X2365,X2366))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_8_finite__imageI])]) ).
fof(i_0_1822,plain,
! [X2375,X2376] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2376))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X2375,X2376))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_13_finite__imageI])]) ).
fof(i_0_1823,plain,
! [X2367,X2368] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2368))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X2367,X2368))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_9_finite__imageI])]) ).
fof(i_0_1824,plain,
! [X2391,X2392] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2392))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X2391,X2392))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_21_finite__imageI])]) ).
fof(i_0_1825,plain,
! [X2389,X2390] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2390))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X2389,X2390))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_20_finite__imageI])]) ).
fof(i_0_1826,plain,
! [X2387,X2388] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2388))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X2387,X2388))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_19_finite__imageI])]) ).
fof(i_0_1827,plain,
! [X2385,X2386] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2386))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X2385,X2386))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_18_finite__imageI])]) ).
fof(i_0_1828,plain,
! [X2379,X2380] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2380))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X2379,X2380))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_15_finite__imageI])]) ).
fof(i_0_1829,plain,
! [X2381,X2382] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2382))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X2381,X2382))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_16_finite__imageI])]) ).
fof(i_0_1830,plain,
! [X2383,X2384] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2384))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X2383,X2384))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_17_finite__imageI])]) ).
fof(i_0_1831,plain,
! [X2377,X2378] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2378))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X2377,X2378))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_14_finite__imageI])]) ).
fof(i_0_1832,plain,
! [X2369,X2370] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2370))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X2369,X2370))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_10_finite__imageI])]) ).
fof(i_0_1833,plain,
! [X2393,X2394] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2394))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2393,X2394))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_finite__imageI])]) ).
fof(i_0_1834,plain,
! [X3454,X3456,X3457] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk100_1(X3454)),X3454))
| X3454 = bot_bot_fun_nat_bool )
& ( X3456 != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3457),X3456)) ) ),
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_1174])])])])]) ).
fof(i_0_1835,plain,
! [X3387,X3388] :
( X3388 != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3387),X3388)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1175])]) ).
fof(i_0_1836,plain,
! [X3389,X3390] :
( X3390 != bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3389),X3390)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1176])]) ).
fof(i_0_1837,plain,
! [X3391,X3392] :
( X3392 != bot_bot_fun_a_bool
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3391),X3392)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1177])]) ).
fof(i_0_1838,plain,
! [X3444,X3445,X3446] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3445),X3444))
| X3444 != bot_bot_fun_nat_bool )
& ( X3446 = bot_bot_fun_nat_bool
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk97_1(X3446)),X3446)) ) ),
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_413_ex__in__conv])])])])]) ).
fof(i_0_1839,plain,
! [X4148,X4149] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X4148),X4149))
| X4148 = X4149 ),
inference(variable_rename,[status(thm)],[i_0_1178]) ).
fof(i_0_1840,plain,
! [X4107,X4108] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X4107),X4108))
| X4107 = X4108 ),
inference(variable_rename,[status(thm)],[i_0_1179]) ).
fof(i_0_1841,plain,
! [X3892] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3892),hAPP_nat_nat(suc,X3892))),
inference(variable_rename,[status(thm)],[fact_612_lessI]) ).
fof(i_0_1842,plain,
! [X3975] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3975),X3975)),
inference(variable_rename,[status(thm)],[i_0_1180]) ).
fof(i_0_1843,plain,
! [X3970] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X3970),X3970)),
inference(variable_rename,[status(thm)],[i_0_1181]) ).
fof(i_0_1844,plain,
! [X3794,X3795,X3796] : hAPP_nat_nat(plus_plus_nat(X3794),hAPP_nat_nat(plus_plus_nat(X3795),X3796)) = hAPP_nat_nat(plus_plus_nat(X3795),hAPP_nat_nat(plus_plus_nat(X3794),X3796)),
inference(variable_rename,[status(thm)],[fact_577_nat__add__left__commute]) ).
fof(i_0_1845,plain,
! [X3781,X3782] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,X3781)),X3782) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X3781),X3782)),
inference(variable_rename,[status(thm)],[fact_572_add__Suc]) ).
fof(i_0_1846,plain,
! [X4080] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4080),zero_zero_nat))
| X4080 = zero_zero_nat )
& ( X4080 != zero_zero_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X4080),zero_zero_nat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_698_le__0__eq])]) ).
fof(i_0_1847,plain,
! [X3479] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3479),bot_bot_nat))
| X3479 = bot_bot_nat )
& ( X3479 != bot_bot_nat
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3479),bot_bot_nat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_440_bot__unique])]) ).
fof(i_0_1848,plain,
! [X3474] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3474),bot_bot_nat))
| X3474 = bot_bot_nat ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_435_le__bot])]) ).
fof(i_0_1849,plain,
! [X3527] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3527),bot_bot_fun_nat_bool))
| X3527 = bot_bot_fun_nat_bool )
& ( X3527 != bot_bot_fun_nat_bool
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3527),bot_bot_fun_nat_bool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_464_subset__empty])]) ).
fof(i_0_1850,plain,
! [X3477] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3477),bot_bot_fun_nat_bool))
| X3477 = bot_bot_fun_nat_bool )
& ( X3477 != bot_bot_fun_nat_bool
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3477),bot_bot_fun_nat_bool)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_438_bot__unique])]) ).
fof(i_0_1851,plain,
! [X3472] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3472),bot_bot_fun_nat_bool))
| X3472 = bot_bot_fun_nat_bool ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_433_le__bot])]) ).
fof(i_0_1852,plain,
! [X4058] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,X4058))),
inference(variable_rename,[status(thm)],[fact_680_zero__less__Suc]) ).
fof(i_0_1853,plain,
! [X3417] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3417),bot_bot_fun_nat_bool)),
inference(variable_rename,[status(thm)],[i_0_1182]) ).
fof(i_0_1854,plain,
! [X3381] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3381),bot_bot_fun_nat_bool)),
inference(variable_rename,[status(thm)],[i_0_1183]) ).
fof(i_0_1855,plain,
! [X3418] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3418),bot_bo844097828e_bool)),
inference(variable_rename,[status(thm)],[i_0_1184]) ).
fof(i_0_1856,plain,
! [X3382] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3382),bot_bo844097828e_bool)),
inference(variable_rename,[status(thm)],[i_0_1185]) ).
fof(i_0_1857,plain,
! [X3419] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3419),bot_bot_fun_a_bool)),
inference(variable_rename,[status(thm)],[i_0_1186]) ).
fof(i_0_1858,plain,
! [X3383] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3383),bot_bot_fun_a_bool)),
inference(variable_rename,[status(thm)],[i_0_1187]) ).
fof(i_0_1859,plain,
! [X4056] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X4056),zero_zero_nat)),
inference(variable_rename,[status(thm)],[i_0_1188]) ).
cnf(i_0_1860,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_1149]) ).
cnf(i_0_1861,plain,
( hBOOL(hAPP_f54304608l_bool(X1,X2))
| collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,X2)),X1)) = bot_bo1701429464l_bool ),
inference(split_conjunct,[status(thm)],[i_0_1150]) ).
fof(i_0_1862,plain,
! [X2592,X2593] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2592)),hAPP_nat_nat(suc,X2593)) = hAPP_nat_nat(minus_minus_nat(X2592),X2593),
inference(variable_rename,[status(thm)],[fact_123_diff__Suc__Suc]) ).
fof(i_0_1863,plain,
! [X3783,X3784] : hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,X3783)),X3784) = hAPP_nat_nat(plus_plus_nat(X3783),hAPP_nat_nat(suc,X3784)),
inference(variable_rename,[status(thm)],[fact_573_add__Suc__shift]) ).
fof(i_0_1864,plain,
! [X4249,X4250,X4251] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X4249,X4250),X4251) = hAPP_bool_bool(hAPP_f1748468828l_bool(X4249,X4251),hAPP_f54304608l_bool(X4250,X4251)),
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_1865,plain,
! [X4273,X4274,X4275] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X4273,X4274),X4275) = hAPP_bool_bool(hAPP_f1476298914l_bool(X4273,X4275),hAPP_f1664156314l_bool(X4274,X4275)),
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_1866,plain,
! [X4216,X4217,X4218] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X4216,X4217),X4218) = hAPP_bool_bool(hAPP_f198738859l_bool(X4216,X4218),hAPP_fun_a_bool_bool(X4217,X4218)),
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_1867,plain,
! [X4167,X4168,X4169] : hAPP_nat_bool(cOMBS_nat_bool_bool(X4167,X4168),X4169) = hAPP_bool_bool(hAPP_n1006566506l_bool(X4167,X4169),hAPP_nat_bool(X4168,X4169)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).
fof(i_0_1868,plain,
! [X4179,X4180,X4181] : hAPP_pname_bool(cOMBS_568398431l_bool(X4179,X4180),X4181) = hAPP_bool_bool(hAPP_p393069232l_bool(X4179,X4181),hAPP_pname_bool(X4180,X4181)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).
fof(i_0_1869,plain,
! [X4139,X4140,X4141] : hAPP_a_bool(cOMBS_a_bool_bool(X4139,X4140),X4141) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X4139,X4141),hAPP_a_bool(X4140,X4141)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).
fof(i_0_1870,plain,
! [X3801,X3802] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3801),X3802)),X3801) = X3802,
inference(variable_rename,[status(thm)],[fact_580_diff__add__inverse]) ).
fof(i_0_1871,plain,
! [X3799,X3800] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3799),X3800)),X3800) = X3799,
inference(variable_rename,[status(thm)],[fact_579_diff__add__inverse2]) ).
fof(i_0_1872,plain,
! [X3779,X3780] : hAPP_nat_nat(plus_plus_nat(X3779),hAPP_nat_nat(suc,X3780)) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X3779),X3780)),
inference(variable_rename,[status(thm)],[fact_571_add__Suc__right]) ).
fof(i_0_1873,plain,
! [X4360,X4361,X4362] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X4360),X4361),X4362) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X4360,X4362),X4361),
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_1874,plain,
! [X4363,X4364,X4365] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X4363),X4364),X4365) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X4363,X4365),X4364),
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_1875,plain,
! [X4357,X4358,X4359] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X4357),X4358),X4359) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X4357,X4359),X4358),
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_1876,plain,
! [X4261,X4262,X4263] : hAPP_f54304608l_bool(hAPP_p130839763l_bool(cOMBC_615407716e_bool(X4261),X4262),X4263) = hAPP_pname_bool(hAPP_f654413245e_bool(X4261,X4263),X4262),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opn]) ).
fof(i_0_1877,plain,
! [X4342,X4343,X4344] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X4342),X4343),X4344) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X4342,X4344),X4343),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__021]) ).
fof(i_0_1878,plain,
! [X4237,X4238,X4239] : hAPP_f54304608l_bool(hAPP_n215258509l_bool(cOMBC_385542954t_bool(X4237),X4238),X4239) = hAPP_nat_bool(hAPP_f800510211t_bool(X4237,X4239),X4238),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona]) ).
fof(i_0_1879,plain,
! [X4303,X4304,X4305] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X4303),X4304),X4305) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X4303,X4305),X4304),
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_1880,plain,
! [X4351,X4352,X4353] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X4351),X4352),X4353) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X4351,X4353),X4352),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_024]) ).
fof(i_0_1881,plain,
! [X4318,X4319,X4320] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X4318),X4319),X4320) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X4318,X4320),X4319),
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_1882,plain,
! [X4258,X4259,X4260] : hAPP_f1664156314l_bool(hAPP_n850744903l_bool(cOMBC_1666426608t_bool(X4258),X4259),X4260) = hAPP_nat_bool(hAPP_f1066163005t_bool(X4258,X4260),X4259),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Nat__O]) ).
fof(i_0_1883,plain,
! [X4279,X4280,X4281] : hAPP_f1664156314l_bool(hAPP_p338031245l_bool(cOMBC_1004116266e_bool(X4279),X4280),X4281) = hAPP_pname_bool(hAPP_f759274231e_bool(X4279,X4281),X4280),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O]) ).
fof(i_0_1884,plain,
! [X4327,X4328,X4329] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X4327),X4328),X4329) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X4327,X4329),X4328),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__]) ).
fof(i_0_1885,plain,
! [X4285,X4286,X4287] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X4285),X4286),X4287) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X4285,X4287),X4286),
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_1886,plain,
! [X4207,X4208,X4209] : hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(cOMBC_619334683t_bool(X4207),X4208),X4209) = hAPP_nat_bool(hAPP_f282463732t_bool(X4207,X4209),X4208),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat_000tc__]) ).
fof(i_0_1887,plain,
! [X4225,X4226,X4227] : hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(X4225),X4226),X4227) = hAPP_pname_bool(hAPP_f1794073134e_bool(X4225,X4227),X4226),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname_000tc]) ).
fof(i_0_1888,plain,
! [X4204,X4205,X4206] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(X4204),X4205),X4206) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(X4204,X4206),X4205),
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_1889,plain,
! [X4255,X4256,X4257] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(X4255),X4256),X4257) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(X4255,X4257),X4256),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo]) ).
fof(i_0_1890,plain,
! [X4133,X4134,X4135] : hAPP_nat_bool(hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(X4133),X4134),X4135) = hAPP_a_bool(hAPP_nat_fun_a_bool(X4133,X4135),X4134),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000t__a_000tc__HOL__Obool_U]) ).
fof(i_0_1891,plain,
! [X4173,X4174,X4175] : hAPP_nat_bool(hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(X4173),X4174),X4175) = hAPP_pname_bool(hAPP_n1025906991e_bool(X4173,X4175),X4174),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U]) ).
fof(i_0_1892,plain,
! [X4234,X4235,X4236] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X4234),X4235),X4236) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X4234,X4236),X4235),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).
fof(i_0_1893,plain,
! [X4159,X4160,X4161] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X4159),X4160),X4161) = hAPP_nat_bool(hAPP_n1699378549t_bool(X4159,X4161),X4160),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U]) ).
fof(i_0_1894,plain,
! [X4252,X4253,X4254] : hAPP_pname_bool(hAPP_f654413245e_bool(cOMBC_267053842l_bool(X4252),X4253),X4254) = hAPP_f54304608l_bool(hAPP_p130839763l_bool(X4252,X4254),X4253),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Oboo]) ).
fof(i_0_1895,plain,
! [X4276,X4277,X4278] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X4276),X4277),X4278) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X4276,X4278),X4277),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob]) ).
fof(i_0_1896,plain,
! [X4222,X4223,X4224] : hAPP_pname_bool(hAPP_f1794073134e_bool(cOMBC_445755039l_bool(X4222),X4223),X4224) = hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(X4222,X4224),X4223),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc]) ).
fof(i_0_1897,plain,
! [X4170,X4171,X4172] : hAPP_pname_bool(hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(X4170),X4171),X4172) = hAPP_nat_bool(hAPP_p1499970991t_bool(X4170,X4172),X4171),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U]) ).
fof(i_0_1898,plain,
! [X4182,X4183,X4184] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X4182),X4183),X4184) = hAPP_pname_bool(hAPP_p61793385e_bool(X4182,X4184),X4183),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U]) ).
fof(i_0_1899,plain,
! [X4145,X4146,X4147] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X4145),X4146),X4147) = hAPP_a_bool(hAPP_p1534023578a_bool(X4145,X4147),X4146),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U]) ).
fof(i_0_1900,plain,
! [X4201,X4202,X4203] : hAPP_a_bool(hAPP_f1549043526a_bool(cOMBC_777206479l_bool(X4201),X4202),X4203) = hAPP_f54304608l_bool(hAPP_a1392362872l_bool(X4201,X4203),X4202),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__]) ).
fof(i_0_1901,plain,
! [X4219,X4220,X4221] : hAPP_a_bool(hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(X4219),X4220),X4221) = hAPP_f1664156314l_bool(hAPP_a217006258l_bool(X4219,X4221),X4220),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc]) ).
fof(i_0_1902,plain,
! [X4188,X4189,X4190] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X4188),X4189),X4190) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X4188,X4190),X4189),
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_1903,plain,
! [X4130,X4131,X4132] : hAPP_a_bool(hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(X4130),X4131),X4132) = hAPP_nat_bool(hAPP_a_fun_nat_bool(X4130,X4132),X4131),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000tc__Nat__Onat_000tc__HOL__Obool_U]) ).
fof(i_0_1904,plain,
! [X4142,X4143,X4144] : hAPP_a_bool(hAPP_p1534023578a_bool(cOMBC_a_pname_bool(X4142),X4143),X4144) = hAPP_pname_bool(hAPP_a93125764e_bool(X4142,X4144),X4143),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000tc__Com__Opname_000tc__HOL__Obool_U]) ).
fof(i_0_1905,plain,
! [X4119,X4120,X4121] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X4119),X4120),X4121) = hAPP_a_bool(hAPP_a_fun_a_bool(X4119,X4121),X4120),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U]) ).
cnf(i_0_1906,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_1189]) ).
cnf(i_0_1907,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_1190]) ).
fof(i_0_1908,plain,
! [X3704,X3705] :
( ( ~ hBOOL(X3705)
| ~ hBOOL(X3704)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3705),X3704)) )
& ( hBOOL(X3705)
| hBOOL(X3704)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3705),X3704)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_545_order__eq__refl])])]) ).
fof(i_0_1909,plain,
! [X4084,X4085] :
( ~ hBOOL(X4085)
| ~ hBOOL(X4084)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X4085),X4084)) ),
inference(variable_rename,[status(thm)],[i_0_1191]) ).
fof(i_0_1910,plain,
! [X4099,X4100] :
( ~ hBOOL(X4100)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X4099),X4100)) ),
inference(variable_rename,[status(thm)],[i_0_1192]) ).
fof(i_0_1911,plain,
! [X4090,X4091] :
( ~ hBOOL(X4091)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X4091),X4090)) ),
inference(variable_rename,[status(thm)],[i_0_1193]) ).
fof(i_0_1912,plain,
! [X4092,X4093] :
( ~ hBOOL(X4093)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X4092),X4093)) ),
inference(variable_rename,[status(thm)],[i_0_1194]) ).
fof(i_0_1913,plain,
! [X4097,X4098] :
( hBOOL(X4098)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X4098),X4097)) ),
inference(variable_rename,[status(thm)],[help_fimplies_1_1_U]) ).
fof(i_0_1914,plain,
! [X4315,X4316,X4317] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X4315,X4316),X4317) = hAPP_b589554111l_bool(X4315,hAPP_f1664156314l_bool(X4316,X4317)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_016]) ).
fof(i_0_1915,plain,
! [X4306,X4307,X4308] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X4306,X4307),X4308) = hAPP_b589554111l_bool(X4306,hAPP_f54304608l_bool(X4307,X4308)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_013]) ).
fof(i_0_1916,plain,
! [X4291,X4292,X4293] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X4291,X4292),X4293) = hAPP_b589554111l_bool(X4291,hAPP_fun_a_bool_bool(X4292,X4293)),
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_1917,plain,
! [X4333,X4334,X4335] : hAPP_a1392362872l_bool(cOMBB_743407885bool_a(X4333,X4334),X4335) = hAPP_f103356543l_bool(X4333,hAPP_a_fun_nat_bool(X4334,X4335)),
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_1918,plain,
! [X4270,X4271,X4272] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X4270,X4271),X4272) = hAPP_b589554111l_bool(X4270,hAPP_pname_bool(X4271,X4272)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007]) ).
fof(i_0_1919,plain,
! [X4243,X4244,X4245] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X4243,X4244),X4245) = hAPP_b589554111l_bool(X4243,hAPP_nat_bool(X4244,X4245)),
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_1920,plain,
! [X4213,X4214,X4215] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X4213,X4214),X4215) = hAPP_b589554111l_bool(X4213,hAPP_a_bool(X4214,X4215)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo]) ).
fof(i_0_1921,plain,
! [X4288,X4289,X4290] : hAPP_f282463732t_bool(cOMBB_164527437a_bool(X4288,X4289),X4290) = hAPP_n1699378549t_bool(X4288,hAPP_fun_a_bool_nat(X4289,X4290)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__009]) ).
fof(i_0_1922,plain,
! [X4309,X4310,X4311] : hAPP_f1066163005t_bool(cOMBB_1896684278e_bool(X4309,X4310),X4311) = hAPP_n1699378549t_bool(X4309,hAPP_f921600141ol_nat(X4310,X4311)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__014]) ).
fof(i_0_1923,plain,
! [X4198,X4199,X4200] : hAPP_a_fun_nat_bool(cOMBB_1321347587bool_a(X4198,X4199),X4200) = hAPP_n1699378549t_bool(X4198,hAPP_a_nat(X4199,X4200)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).
fof(i_0_1924,plain,
! [X4345,X4346,X4347] : hAPP_p130839763l_bool(cOMBB_928955006_pname(X4345,X4346),X4347) = hAPP_f103356543l_bool(X4345,hAPP_p1499970991t_bool(X4346,X4347)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__022]) ).
fof(i_0_1925,plain,
! [X4246,X4247,X4248] : hAPP_p1499970991t_bool(cOMBB_523834888_pname(X4246,X4247),X4248) = hAPP_n1699378549t_bool(X4246,hAPP_pname_nat(X4247,X4248)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__005]) ).
fof(i_0_1926,plain,
! [X4297,X4298,X4299] : hAPP_f800510211t_bool(cOMBB_1250273980t_bool(X4297,X4298),X4299) = hAPP_n1699378549t_bool(X4297,hAPP_f22106695ol_nat(X4298,X4299)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__012]) ).
fof(i_0_1927,plain,
! [X4339,X4340,X4341] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(X4339,X4340),X4341) = hAPP_f103356543l_bool(X4339,hAPP_n1699378549t_bool(X4340,X4341)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__020]) ).
fof(i_0_1928,plain,
! [X4231,X4232,X4233] : hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(X4231,X4232),X4233) = hAPP_n1699378549t_bool(X4231,hAPP_nat_nat(X4232,X4233)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__003]) ).
fof(i_0_1929,plain,
! [X4312,X4313,X4314] : hAPP_f654413245e_bool(cOMBB_141086128t_bool(X4312,X4313),X4314) = hAPP_p61793385e_bool(X4312,hAPP_f1291551745_pname(X4313,X4314)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_015]) ).
fof(i_0_1930,plain,
! [X4240,X4241,X4242] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(X4240,X4241),X4242) = hAPP_bool_bool(X4240,hAPP_f54304608l_bool(X4241,X4242)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On]) ).
fof(i_0_1931,plain,
! [X4321,X4322,X4323] : hAPP_f759274231e_bool(cOMBB_598082538e_bool(X4321,X4322),X4323) = hAPP_p61793385e_bool(X4321,hAPP_f1297739591_pname(X4322,X4323)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_017]) ).
fof(i_0_1932,plain,
! [X4267,X4268,X4269] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X4267,X4268),X4269) = hAPP_bool_bool(X4267,hAPP_f1664156314l_bool(X4268,X4269)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op]) ).
fof(i_0_1933,plain,
! [X4294,X4295,X4296] : hAPP_f1794073134e_bool(cOMBB_1693087065a_bool(X4294,X4295),X4296) = hAPP_p61793385e_bool(X4294,hAPP_f1128469712_pname(X4295,X4296)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_011]) ).
fof(i_0_1934,plain,
! [X4210,X4211,X4212] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X4210,X4211),X4212) = hAPP_bool_bool(X4210,hAPP_fun_a_bool_bool(X4211,X4212)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H]) ).
fof(i_0_1935,plain,
! [X4348,X4349,X4350] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(X4348,X4349),X4350) = hAPP_f434788991l_bool(X4348,hAPP_n1025906991e_bool(X4349,X4350)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_023]) ).
fof(i_0_1936,plain,
! [X4324,X4325,X4326] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(X4324,X4325),X4326) = hAPP_f1631501043l_bool(X4324,hAPP_nat_fun_a_bool(X4325,X4326)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___018]) ).
fof(i_0_1937,plain,
! [X4264,X4265,X4266] : hAPP_n1025906991e_bool(cOMBB_1212655066ol_nat(X4264,X4265),X4266) = hAPP_p61793385e_bool(X4264,hAPP_nat_pname(X4265,X4266)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_006]) ).
fof(i_0_1938,plain,
! [X4185,X4186,X4187] : hAPP_nat_fun_a_bool(cOMBB_1885489796ol_nat(X4185,X4186),X4187) = hAPP_a_fun_a_bool(X4185,hAPP_nat_a(X4186,X4187)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat]) ).
fof(i_0_1939,plain,
! [X4162,X4163,X4164] : hAPP_nat_bool(cOMBB_bool_bool_nat(X4162,X4163),X4164) = hAPP_bool_bool(X4162,hAPP_nat_bool(X4163,X4164)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U]) ).
fof(i_0_1940,plain,
! [X4354,X4355,X4356] : hAPP_p338031245l_bool(cOMBB_408569982_pname(X4354,X4355),X4356) = hAPP_f434788991l_bool(X4354,hAPP_p61793385e_bool(X4355,X4356)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_025]) ).
fof(i_0_1941,plain,
! [X4330,X4331,X4332] : hAPP_p1824510254l_bool(cOMBB_392435466_pname(X4330,X4331),X4332) = hAPP_f1631501043l_bool(X4330,hAPP_p1534023578a_bool(X4331,X4332)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___019]) ).
fof(i_0_1942,plain,
! [X4282,X4283,X4284] : hAPP_p61793385e_bool(cOMBB_542850580_pname(X4282,X4283),X4284) = hAPP_p61793385e_bool(X4282,hAPP_pname_pname(X4283,X4284)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_008]) ).
fof(i_0_1943,plain,
! [X4191,X4192,X4193] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X4191,X4192),X4193) = hAPP_a_fun_a_bool(X4191,hAPP_pname_a(X4192,X4193)),
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_1944,plain,
! [X4176,X4177,X4178] : hAPP_pname_bool(cOMBB_647938656_pname(X4176,X4177),X4178) = hAPP_bool_bool(X4176,hAPP_pname_bool(X4177,X4178)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U]) ).
fof(i_0_1945,plain,
! [X4336,X4337,X4338] : hAPP_a217006258l_bool(cOMBB_1137537805bool_a(X4336,X4337),X4338) = hAPP_f434788991l_bool(X4336,hAPP_a93125764e_bool(X4337,X4338)),
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_1946,plain,
! [X4300,X4301,X4302] : hAPP_a85458249l_bool(cOMBB_472261505bool_a(X4300,X4301),X4302) = hAPP_f1631501043l_bool(X4300,hAPP_a_fun_a_bool(X4301,X4302)),
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_1947,plain,
! [X4228,X4229,X4230] : hAPP_a93125764e_bool(cOMBB_610033911bool_a(X4228,X4229),X4230) = hAPP_p61793385e_bool(X4228,hAPP_a_pname(X4229,X4230)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob]) ).
fof(i_0_1948,plain,
! [X4156,X4157,X4158] : hAPP_a_fun_a_bool(cOMBB_a_fun_a_bool_a(X4156,X4157),X4158) = hAPP_a_fun_a_bool(X4156,hAPP_a_a(X4157,X4158)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a_U]) ).
fof(i_0_1949,plain,
! [X4136,X4137,X4138] : hAPP_a_bool(cOMBB_bool_bool_a(X4136,X4137),X4138) = hAPP_bool_bool(X4136,hAPP_a_bool(X4137,X4138)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U]) ).
fof(i_0_1950,plain,
! [X4150,X4151] :
( X4150 != X4151
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X4150),X4151)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T]) ).
fof(i_0_1951,plain,
! [X3706,X3707] :
( X3706 != X3707
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3706),X3707)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_546_order__eq__refl])]) ).
fof(i_0_1952,plain,
! [X3103,X3104] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3103),X3104))
| X3103 != X3104 )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3104),X3103))
| X3103 != X3104 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1195])])]) ).
fof(i_0_1953,plain,
! [X3043,X3044] :
( X3043 != X3044
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3043),X3044)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_273_equalityD1])]) ).
fof(i_0_1954,plain,
! [X3049,X3050] :
( X3049 != X3050
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3050),X3049)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_276_equalityD2])]) ).
fof(i_0_1955,plain,
! [X4154,X4155] :
( X4154 != X4155
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X4154),X4155)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T]) ).
fof(i_0_1956,plain,
! [X3708,X3709] :
( X3708 != X3709
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3708),X3709)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_547_order__eq__refl])]) ).
fof(i_0_1957,plain,
! [X3101,X3102] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3101),X3102))
| X3101 != X3102 )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3102),X3101))
| X3101 != X3102 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1196])])]) ).
fof(i_0_1958,plain,
! [X3041,X3042] :
( X3041 != X3042
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3041),X3042)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_272_equalityD1])]) ).
fof(i_0_1959,plain,
! [X3047,X3048] :
( X3047 != X3048
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3048),X3047)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_275_equalityD2])]) ).
fof(i_0_1960,plain,
! [X4126,X4127] :
( X4126 != X4127
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X4126),X4127)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T]) ).
fof(i_0_1961,plain,
! [X3712,X3713] :
( X3712 != X3713
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3712),X3713)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_549_order__eq__refl])]) ).
fof(i_0_1962,plain,
! [X3105,X3106] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3105),X3106))
| X3105 != X3106 )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3106),X3105))
| X3105 != X3106 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1197])])]) ).
fof(i_0_1963,plain,
! [X3045,X3046] :
( X3045 != X3046
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3045),X3046)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_274_equalityD1])]) ).
fof(i_0_1964,plain,
! [X3051,X3052] :
( X3051 != X3052
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3052),X3051)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_277_equalityD2])]) ).
fof(i_0_1965,plain,
! [X4109,X4110] :
( X4109 != X4110
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X4109),X4110)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__Nat__Onat_T]) ).
fof(i_0_1966,plain,
! [X3710,X3711] :
( X3710 != X3711
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3710),X3711)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_548_order__eq__refl])]) ).
fof(i_0_1967,plain,
! [X2520,X2521] :
( X2520 != X2521
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2520),X2521)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_87_eq__imp__le])]) ).
fof(i_0_1968,plain,
! [X4113,X4114] :
( X4113 != X4114
| hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X4113),X4114)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__Com__Opname_T]) ).
fof(i_0_1969,plain,
! [X4105,X4106] :
( X4105 != X4106
| hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X4105),X4106)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000t__a_T]) ).
fof(i_0_1970,plain,
! [X3333] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3333),X3333)),
inference(variable_rename,[status(thm)],[fact_369_order__refl]) ).
fof(i_0_1971,plain,
! [X3033] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3033),X3033)),
inference(variable_rename,[status(thm)],[fact_267_subset__refl]) ).
fof(i_0_1972,plain,
! [X3332] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3332),X3332)),
inference(variable_rename,[status(thm)],[fact_368_order__refl]) ).
fof(i_0_1973,plain,
! [X3032] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3032),X3032)),
inference(variable_rename,[status(thm)],[fact_266_subset__refl]) ).
fof(i_0_1974,plain,
! [X3334] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3334),X3334)),
inference(variable_rename,[status(thm)],[fact_370_order__refl]) ).
fof(i_0_1975,plain,
! [X3034] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3034),X3034)),
inference(variable_rename,[status(thm)],[fact_268_subset__refl]) ).
fof(i_0_1976,plain,
! [X3335] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3335),X3335)),
inference(variable_rename,[status(thm)],[fact_371_order__refl]) ).
fof(i_0_1977,plain,
! [X2524] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2524),X2524)),
inference(variable_rename,[status(thm)],[fact_89_le__refl]) ).
fof(i_0_1978,plain,
! [X3331] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3331),X3331)),
inference(variable_rename,[status(thm)],[fact_367_order__refl]) ).
fof(i_0_1979,plain,
! [X4059,X4060] :
( ( X4059 = zero_zero_nat
| X4059 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(plus_plus_nat(X4059),X4060) != hAPP_nat_nat(suc,zero_zero_nat) )
& ( X4060 = hAPP_nat_nat(suc,zero_zero_nat)
| X4059 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(plus_plus_nat(X4059),X4060) != hAPP_nat_nat(suc,zero_zero_nat) )
& ( X4059 = zero_zero_nat
| X4060 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X4059),X4060) != hAPP_nat_nat(suc,zero_zero_nat) )
& ( X4060 = hAPP_nat_nat(suc,zero_zero_nat)
| X4060 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X4059),X4060) != hAPP_nat_nat(suc,zero_zero_nat) )
& ( X4059 != hAPP_nat_nat(suc,zero_zero_nat)
| X4060 != zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X4059),X4060) = hAPP_nat_nat(suc,zero_zero_nat) )
& ( X4059 != zero_zero_nat
| X4060 != hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(plus_plus_nat(X4059),X4060) = hAPP_nat_nat(suc,zero_zero_nat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_681_add__is__1])])]) ).
fof(i_0_1980,plain,
! [X4061,X4062] :
( ( X4061 = zero_zero_nat
| X4061 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(plus_plus_nat(X4061),X4062) )
& ( X4062 = hAPP_nat_nat(suc,zero_zero_nat)
| X4061 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(plus_plus_nat(X4061),X4062) )
& ( X4061 = zero_zero_nat
| X4062 = zero_zero_nat
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(plus_plus_nat(X4061),X4062) )
& ( X4062 = hAPP_nat_nat(suc,zero_zero_nat)
| X4062 = zero_zero_nat
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(plus_plus_nat(X4061),X4062) )
& ( X4061 != hAPP_nat_nat(suc,zero_zero_nat)
| X4062 != zero_zero_nat
| hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(plus_plus_nat(X4061),X4062) )
& ( X4061 != zero_zero_nat
| X4062 != hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(plus_plus_nat(X4061),X4062) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_682_one__is__add])])]) ).
fof(i_0_1981,plain,
! [X3482] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X3482)),
inference(variable_rename,[status(thm)],[fact_443_bot__least]) ).
fof(i_0_1982,plain,
! [X3385] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X3385)),
inference(variable_rename,[status(thm)],[fact_393_empty__subsetI]) ).
fof(i_0_1983,plain,
! [X3480] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),X3480)),
inference(variable_rename,[status(thm)],[fact_441_bot__least]) ).
fof(i_0_1984,plain,
! [X3384] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),X3384)),
inference(variable_rename,[status(thm)],[fact_392_empty__subsetI]) ).
fof(i_0_1985,plain,
! [X3483] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X3483)),
inference(variable_rename,[status(thm)],[fact_444_bot__least]) ).
fof(i_0_1986,plain,
! [X3386] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),X3386)),
inference(variable_rename,[status(thm)],[fact_394_empty__subsetI]) ).
fof(i_0_1987,plain,
! [X4081] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X4081)),
inference(variable_rename,[status(thm)],[fact_699_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_1988,plain,
! [X4057] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X4057)),
inference(variable_rename,[status(thm)],[fact_679_le0]) ).
fof(i_0_1989,plain,
! [X3484] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),X3484)),
inference(variable_rename,[status(thm)],[fact_445_bot__least]) ).
fof(i_0_1990,plain,
! [X3481] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),X3481)),
inference(variable_rename,[status(thm)],[fact_442_bot__least]) ).
fof(i_0_1991,plain,
! [X4069,X4070] :
( hAPP_nat_nat(minus_minus_nat(X4069),X4070) != zero_zero_nat
| hAPP_nat_nat(minus_minus_nat(X4070),X4069) != zero_zero_nat
| X4069 = X4070 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_687_diffs0__imp__equal])]) ).
fof(i_0_1992,plain,
! [X3785,X3786,X3787] :
( ( hAPP_nat_nat(plus_plus_nat(X3785),X3786) != hAPP_nat_nat(plus_plus_nat(X3787),X3786)
| X3785 = X3787 )
& ( X3785 != X3787
| hAPP_nat_nat(plus_plus_nat(X3785),X3786) = hAPP_nat_nat(plus_plus_nat(X3787),X3786) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_574_nat__add__right__cancel])]) ).
fof(i_0_1993,plain,
! [X3788,X3789,X3790] :
( ( hAPP_nat_nat(plus_plus_nat(X3788),X3789) != hAPP_nat_nat(plus_plus_nat(X3788),X3790)
| X3789 = X3790 )
& ( X3789 != X3790
| hAPP_nat_nat(plus_plus_nat(X3788),X3789) = hAPP_nat_nat(plus_plus_nat(X3788),X3790) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_575_nat__add__left__cancel])]) ).
fof(i_0_1994,plain,
! [X3776] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X3776)),one_one_nat) = X3776,
inference(variable_rename,[status(thm)],[fact_569_diff__Suc__1]) ).
fof(i_0_1995,plain,
! [X3401,X3402,X3403] :
( ( collec1974731493e_bool(X3401) != bot_bo1649642514l_bool
| ~ is_fun_pname_bool(X3402)
| ~ hBOOL(hAPP_f1664156314l_bool(X3401,X3402)) )
& ( is_fun_pname_bool(esk87_1(X3403))
| collec1974731493e_bool(X3403) = bot_bo1649642514l_bool )
& ( hBOOL(hAPP_f1664156314l_bool(X3403,esk87_1(X3403)))
| collec1974731493e_bool(X3403) = bot_bo1649642514l_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_1198])])])])])]) ).
fof(i_0_1996,plain,
! [X3405,X3406,X3407] :
( ( collect_fun_a_bool(X3405) != bot_bo1389914601l_bool
| ~ is_fun_a_bool(X3406)
| ~ hBOOL(hAPP_fun_a_bool_bool(X3405,X3406)) )
& ( is_fun_a_bool(esk88_1(X3407))
| collect_fun_a_bool(X3407) = bot_bo1389914601l_bool )
& ( hBOOL(hAPP_fun_a_bool_bool(X3407,esk88_1(X3407)))
| collect_fun_a_bool(X3407) = bot_bo1389914601l_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_1199])])])])])]) ).
fof(i_0_1997,plain,
! [X3393,X3394,X3395] :
( ( collect_pname(X3393) != bot_bo844097828e_bool
| ~ is_pname(X3394)
| ~ hBOOL(hAPP_pname_bool(X3393,X3394)) )
& ( is_pname(esk85_1(X3395))
| collect_pname(X3395) = bot_bo844097828e_bool )
& ( hBOOL(hAPP_pname_bool(X3395,esk85_1(X3395)))
| collect_pname(X3395) = bot_bo844097828e_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_1200])])])])])]) ).
fof(i_0_1998,plain,
! [X3409,X3410,X3411] :
( ( collect_a(X3409) != bot_bot_fun_a_bool
| ~ is_a(X3410)
| ~ hBOOL(hAPP_a_bool(X3409,X3410)) )
& ( is_a(esk89_1(X3411))
| collect_a(X3411) = bot_bot_fun_a_bool )
& ( hBOOL(hAPP_a_bool(X3411,esk89_1(X3411)))
| collect_a(X3411) = 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_1201])])])])])]) ).
fof(i_0_1999,plain,
! [X3428,X3429,X3430] :
( ( bot_bo1649642514l_bool != collec1974731493e_bool(X3428)
| ~ is_fun_pname_bool(X3429)
| ~ hBOOL(hAPP_f1664156314l_bool(X3428,X3429)) )
& ( is_fun_pname_bool(esk93_1(X3430))
| bot_bo1649642514l_bool = collec1974731493e_bool(X3430) )
& ( hBOOL(hAPP_f1664156314l_bool(X3430,esk93_1(X3430)))
| bot_bo1649642514l_bool = collec1974731493e_bool(X3430) ) ),
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_1202])])])])])]) ).
fof(i_0_2000,plain,
! [X3432,X3433,X3434] :
( ( bot_bo1389914601l_bool != collect_fun_a_bool(X3432)
| ~ is_fun_a_bool(X3433)
| ~ hBOOL(hAPP_fun_a_bool_bool(X3432,X3433)) )
& ( is_fun_a_bool(esk94_1(X3434))
| bot_bo1389914601l_bool = collect_fun_a_bool(X3434) )
& ( hBOOL(hAPP_fun_a_bool_bool(X3434,esk94_1(X3434)))
| bot_bo1389914601l_bool = collect_fun_a_bool(X3434) ) ),
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_1203])])])])])]) ).
fof(i_0_2001,plain,
! [X3420,X3421,X3422] :
( ( bot_bo844097828e_bool != collect_pname(X3420)
| ~ is_pname(X3421)
| ~ hBOOL(hAPP_pname_bool(X3420,X3421)) )
& ( is_pname(esk91_1(X3422))
| bot_bo844097828e_bool = collect_pname(X3422) )
& ( hBOOL(hAPP_pname_bool(X3422,esk91_1(X3422)))
| bot_bo844097828e_bool = collect_pname(X3422) ) ),
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_1204])])])])])]) ).
fof(i_0_2002,plain,
! [X3436,X3437,X3438] :
( ( bot_bot_fun_a_bool != collect_a(X3436)
| ~ is_a(X3437)
| ~ hBOOL(hAPP_a_bool(X3436,X3437)) )
& ( is_a(esk95_1(X3438))
| bot_bot_fun_a_bool = collect_a(X3438) )
& ( hBOOL(hAPP_a_bool(X3438,esk95_1(X3438)))
| bot_bot_fun_a_bool = collect_a(X3438) ) ),
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_1205])])])])])]) ).
fof(i_0_2003,plain,
! [X4063,X4064] : hAPP_nat_nat(minus_minus_nat(X4063),hAPP_nat_nat(plus_plus_nat(X4063),X4064)) = zero_zero_nat,
inference(variable_rename,[status(thm)],[fact_683_diff__add__0]) ).
cnf(i_0_2004,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_1206]) ).
fof(i_0_2005,plain,
! [X4082] :
( ~ hBOOL(hAPP_bool_bool(fNot,X4082))
| ~ hBOOL(X4082) ),
inference(variable_rename,[status(thm)],[i_0_1207]) ).
cnf(i_0_2006,plain,
( bot_bo1701429464l_bool != collect_fun_nat_bool(X1)
| ~ hBOOL(hAPP_f54304608l_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1208]) ).
cnf(i_0_2007,plain,
( bot_bot_fun_nat_bool != collect_nat(X1)
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1209]) ).
cnf(i_0_2008,plain,
( collect_fun_nat_bool(X1) != bot_bo1701429464l_bool
| ~ hBOOL(hAPP_f54304608l_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1210]) ).
cnf(i_0_2009,plain,
( collect_nat(X1) != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1211]) ).
fof(i_0_2010,plain,
! [X4029] : hAPP_n1699378549t_bool(ord_less_nat,X4029) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X4029)),
inference(variable_rename,[status(thm)],[fact_670_less__eq__Suc__le__raw]) ).
fof(i_0_2011,plain,
! [X3468] :
( ( ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X3468))
| hBOOL(bot_bot_bool) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X3468)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_429_bot__apply])]) ).
fof(i_0_2012,plain,
! [X3465] :
( ( ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X3465))
| hBOOL(bot_bot_bool) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X3465)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_426_bot__fun__def])]) ).
fof(i_0_2013,plain,
! [X3467] :
( ( ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X3467))
| hBOOL(bot_bot_bool) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X3467)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_428_bot__apply])]) ).
fof(i_0_2014,plain,
! [X3464] :
( ( ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X3464))
| hBOOL(bot_bot_bool) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X3464)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_425_bot__fun__def])]) ).
fof(i_0_2015,plain,
! [X3469] :
( ( ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X3469))
| hBOOL(bot_bot_bool) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X3469)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_430_bot__apply])]) ).
fof(i_0_2016,plain,
! [X3466] :
( ( ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X3466))
| hBOOL(bot_bot_bool) )
& ( ~ hBOOL(bot_bot_bool)
| hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X3466)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_427_bot__fun__def])]) ).
cnf(i_0_2017,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_1212]) ).
fof(i_0_2018,hypothesis,
! [X2320,X2321] :
( ~ is_fun1661590463l_bool(X2320)
| ~ is_fun_pname_bool(X2321)
| is_bool(hAPP_f1664156314l_bool(X2320,X2321)) ),
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_2019,hypothesis,
! [X2310,X2311] :
( ~ is_fun949378684l_bool(X2310)
| ~ is_fun_a_bool(X2311)
| is_bool(hAPP_fun_a_bool_bool(X2310,X2311)) ),
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_2020,plain,
! [X2282,X2283] :
( ~ is_fun_pname_bool(X2282)
| ~ is_pname(X2283)
| is_bool(hAPP_pname_bool(X2282,X2283)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool])]) ).
fof(i_0_2021,plain,
! [X2268,X2269] :
( ~ is_fun_a_bool(X2268)
| ~ is_a(X2269)
| is_bool(hAPP_a_bool(X2268,X2269)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__HOL__Obool])]) ).
cnf(i_0_2022,plain,
( hBOOL(hAPP_f54304608l_bool(X1,esk92_1(X1)))
| bot_bo1701429464l_bool = collect_fun_nat_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1208]) ).
cnf(i_0_2023,plain,
( hBOOL(hAPP_nat_bool(X1,esk96_1(X1)))
| bot_bot_fun_nat_bool = collect_nat(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1209]) ).
cnf(i_0_2024,plain,
( hBOOL(hAPP_f54304608l_bool(X1,esk86_1(X1)))
| collect_fun_nat_bool(X1) = bot_bo1701429464l_bool ),
inference(split_conjunct,[status(thm)],[i_0_1210]) ).
cnf(i_0_2025,plain,
( hBOOL(hAPP_nat_bool(X1,esk90_1(X1)))
| collect_nat(X1) = bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_1211]) ).
fof(i_0_2026,plain,
! [X2511,X2512] :
( ( hAPP_nat_nat(suc,X2511) != hAPP_nat_nat(suc,X2512)
| X2511 = X2512 )
& ( X2511 != X2512
| hAPP_nat_nat(suc,X2511) = hAPP_nat_nat(suc,X2512) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_82_nat_Oinject])]) ).
fof(i_0_2027,plain,
! [X2509,X2510] :
( hAPP_nat_nat(suc,X2509) != hAPP_nat_nat(suc,X2510)
| X2509 = X2510 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_81_Suc__inject])]) ).
fof(i_0_2028,plain,
! [X3797,X3798] : hAPP_nat_nat(plus_plus_nat(X3797),X3798) = hAPP_nat_nat(plus_plus_nat(X3798),X3797),
inference(variable_rename,[status(thm)],[fact_578_nat__add__commute]) ).
fof(i_0_2029,plain,
! [X2318,X2319] :
( ~ is_fun_pname_bool(X2319)
| is_pname(hAPP_f1297739591_pname(X2318,X2319)) ),
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_2030,plain,
! [X2308,X2309] :
( ~ is_fun_a_bool(X2309)
| is_pname(hAPP_f1128469712_pname(X2308,X2309)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname])]) ).
fof(i_0_2031,plain,
! [X2280,X2281] :
( ~ is_pname(X2281)
| is_pname(hAPP_pname_pname(X2280,X2281)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname])]) ).
fof(i_0_2032,plain,
! [X2266,X2267] :
( ~ is_a(X2267)
| is_pname(hAPP_a_pname(X2266,X2267)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__Com__Opname])]) ).
fof(i_0_2033,hypothesis,
! [X2278,X2279] :
( ~ is_pname(X2279)
| is_a(hAPP_pname_a(X2278,X2279)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000t__a])]) ).
fof(i_0_2034,plain,
! [X2264,X2265] :
( ~ is_a(X2265)
| is_a(hAPP_a_a(X2264,X2265)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000t__a])]) ).
fof(i_0_2035,plain,
! [X2340,X2341] :
( ~ is_fun1661590463l_bool(X2341)
| is_bool(hAPP_f1935102916l_bool(X2340,X2341)) ),
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_2036,plain,
! [X2336,X2337] :
( ~ is_fun949378684l_bool(X2337)
| is_bool(hAPP_f621171935l_bool(X2336,X2337)) ),
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_2037,plain,
! [X2292,X2293] :
( ~ is_bool(X2293)
| is_bool(hAPP_bool_bool(X2292,X2293)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool])]) ).
fof(i_0_2038,plain,
! [X2342,X2343] :
( ~ is_fun1661590463l_bool(X2343)
| is_fun1661590463l_bool(hAPP_f559147733l_bool(X2342,X2343)) ),
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_2039,plain,
! [X2326,X2327] :
( ~ is_fun_pname_bool(X2327)
| is_fun1661590463l_bool(hAPP_f434788991l_bool(X2326,X2327)) ),
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_2040,hypothesis,
! [X2290,X2291] :
( ~ is_pname(X2291)
| is_fun1661590463l_bool(hAPP_p338031245l_bool(X2290,X2291)) ),
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_2041,plain,
! [X2276,X2277] :
( ~ is_a(X2277)
| is_fun1661590463l_bool(hAPP_a217006258l_bool(X2276,X2277)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__H])]) ).
fof(i_0_2042,plain,
! [X2234,X2235] :
( ~ is_fun_pname_bool(X2235)
| is_fun1661590463l_bool(image_47868345e_bool(X2234,X2235)) ),
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_2043,plain,
! [X2226,X2227] :
( ~ is_fun_a_bool(X2227)
| is_fun1661590463l_bool(image_819518260e_bool(X2226,X2227)) ),
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_2044,plain,
! [X2214,X2215] :
( ~ is_fun1661590463l_bool(X2215)
| is_fun1661590463l_bool(cOMBS_350070575l_bool(X2214,X2215)) ),
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_2045,plain,
! [X2202,X2203] :
( ~ is_fun1661590463l_bool(X2203)
| is_fun1661590463l_bool(cOMBB_307249310e_bool(X2202,X2203)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_])]) ).
fof(i_0_2046,plain,
! [X2338,X2339] :
( ~ is_fun949378684l_bool(X2339)
| is_fun949378684l_bool(hAPP_f2117159681l_bool(X2338,X2339)) ),
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_2047,hypothesis,
! [X2316,X2317] :
( ~ is_fun_a_bool(X2317)
| is_fun949378684l_bool(hAPP_f1631501043l_bool(X2316,X2317)) ),
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_2048,plain,
! [X2288,X2289] :
( ~ is_pname(X2289)
| is_fun949378684l_bool(hAPP_p1824510254l_bool(X2288,X2289)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H])]) ).
fof(i_0_2049,hypothesis,
! [X2274,X2275] :
( ~ is_a(X2275)
| is_fun949378684l_bool(hAPP_a85458249l_bool(X2274,X2275)) ),
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_2050,plain,
! [X2232,X2233] :
( ~ is_fun_pname_bool(X2233)
| is_fun949378684l_bool(image_112932426a_bool(X2232,X2233)) ),
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_2051,plain,
! [X2224,X2225] :
( ~ is_fun_a_bool(X2225)
| is_fun949378684l_bool(image_a_fun_a_bool(X2224,X2225)) ),
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_2052,plain,
! [X2212,X2213] :
( ~ is_fun949378684l_bool(X2213)
| is_fun949378684l_bool(cOMBS_1035972772l_bool(X2212,X2213)) ),
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_2053,plain,
! [X2200,X2201] :
( ~ is_fun949378684l_bool(X2201)
| is_fun949378684l_bool(cOMBB_2140588453a_bool(X2200,X2201)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool])]) ).
fof(i_0_2054,plain,
! [X2324,X2325] :
( ~ is_fun_pname_bool(X2325)
| is_fun_pname_bool(hAPP_f759274231e_bool(X2324,X2325)) ),
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_2055,plain,
! [X2314,X2315] :
( ~ is_fun_a_bool(X2315)
| is_fun_pname_bool(hAPP_f1794073134e_bool(X2314,X2315)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opname_Mtc__H])]) ).
fof(i_0_2056,plain,
! [X2286,X2287] :
( ~ is_pname(X2287)
| is_fun_pname_bool(hAPP_p61793385e_bool(X2286,X2287)) ),
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_2057,plain,
! [X2272,X2273] :
( ~ is_a(X2273)
| is_fun_pname_bool(hAPP_a93125764e_bool(X2272,X2273)) ),
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_2058,plain,
! [X2250,X2251] :
( ~ is_fun1661590463l_bool(X2251)
| is_fun_pname_bool(image_1283814551_pname(X2250,X2251)) ),
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_2059,plain,
! [X2246,X2247] :
( ~ is_fun949378684l_bool(X2247)
| is_fun_pname_bool(image_1854862208_pname(X2246,X2247)) ),
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_2060,plain,
! [X2230,X2231] :
( ~ is_fun_pname_bool(X2231)
| is_fun_pname_bool(image_pname_pname(X2230,X2231)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname])]) ).
fof(i_0_2061,plain,
! [X2222,X2223] :
( ~ is_fun_a_bool(X2223)
| is_fun_pname_bool(image_a_pname(X2222,X2223)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000t__a_000tc__Com__Opname])]) ).
fof(i_0_2062,plain,
! [X2210,X2211] :
( ~ is_fun_pname_bool(X2211)
| is_fun_pname_bool(cOMBS_568398431l_bool(X2210,X2211)) ),
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_2063,plain,
! [X2198,X2199] :
( ~ is_fun_pname_bool(X2199)
| is_fun_pname_bool(cOMBB_647938656_pname(X2198,X2199)) ),
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_2064,plain,
! [X2322,X2323] :
( ~ is_fun_pname_bool(X2323)
| is_fun_a_bool(hAPP_f1051908748a_bool(X2322,X2323)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__H])]) ).
fof(i_0_2065,plain,
! [X2312,X2313] :
( ~ is_fun_a_bool(X2313)
| is_fun_a_bool(hAPP_f2050579477a_bool(X2312,X2313)) ),
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_2066,plain,
! [X2284,X2285] :
( ~ is_pname(X2285)
| is_fun_a_bool(hAPP_p1534023578a_bool(X2284,X2285)) ),
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_2067,plain,
! [X2270,X2271] :
( ~ is_a(X2271)
| is_fun_a_bool(hAPP_a_fun_a_bool(X2270,X2271)) ),
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_2068,plain,
! [X2248,X2249] :
( ~ is_fun1661590463l_bool(X2249)
| is_fun_a_bool(image_876012084bool_a(X2248,X2249)) ),
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_2069,plain,
! [X2244,X2245] :
( ~ is_fun949378684l_bool(X2245)
| is_fun_a_bool(image_fun_a_bool_a(X2244,X2245)) ),
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_2070,hypothesis,
! [X2228,X2229] :
( ~ is_fun_pname_bool(X2229)
| is_fun_a_bool(image_pname_a(X2228,X2229)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000t__a])]) ).
fof(i_0_2071,plain,
! [X2220,X2221] :
( ~ is_fun_a_bool(X2221)
| is_fun_a_bool(image_a_a(X2220,X2221)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000t__a_000t__a])]) ).
fof(i_0_2072,plain,
! [X2208,X2209] :
( ~ is_fun_a_bool(X2209)
| is_fun_a_bool(cOMBS_a_bool_bool(X2208,X2209)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool])]) ).
fof(i_0_2073,plain,
! [X2196,X2197] :
( ~ is_fun_a_bool(X2197)
| is_fun_a_bool(cOMBB_bool_bool_a(X2196,X2197)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a])]) ).
fof(i_0_2074,plain,
! [X4083] :
( hBOOL(X4083)
| hBOOL(hAPP_bool_bool(fNot,X4083)) ),
inference(variable_rename,[status(thm)],[help_fNot_2_1_U]) ).
fof(i_0_2075,plain,
! [X3530,X3531] :
( ( image_pname_a(X3530,X3531) != bot_bot_fun_a_bool
| X3531 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X3531) )
& ( X3531 != bot_bo844097828e_bool
| image_pname_a(X3530,X3531) = bot_bot_fun_a_bool
| ~ is_fun_pname_bool(X3531) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_467_image__is__empty])])]) ).
fof(i_0_2076,plain,
! [X3533,X3534] :
( ( bot_bot_fun_a_bool != image_pname_a(X3533,X3534)
| X3534 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X3534) )
& ( X3534 != bot_bo844097828e_bool
| bot_bot_fun_a_bool = image_pname_a(X3533,X3534)
| ~ is_fun_pname_bool(X3534) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_469_empty__is__image])])]) ).
fof(i_0_2077,plain,
! [X3878] : hAPP_nat_nat(suc,X3878) = hAPP_nat_nat(plus_plus_nat(X3878),one_one_nat),
inference(variable_rename,[status(thm)],[fact_606_Suc__eq__plus1]) ).
fof(i_0_2078,plain,
! [X2328,X2329] : is_pname(hAPP_f1291551745_pname(X2328,X2329)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname]) ).
fof(i_0_2079,plain,
! [X2296,X2297] : is_pname(hAPP_nat_pname(X2296,X2297)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__Com__Opname]) ).
fof(i_0_2080,plain,
! [X2294,X2295] : is_a(hAPP_nat_a(X2294,X2295)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000t__a]) ).
fof(i_0_2081,plain,
! [X2350,X2351] : is_bool(hAPP_f937997336l_bool(X2350,X2351)),
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_2082,plain,
! [X2348,X2349] : is_bool(hAPP_f389811538l_bool(X2348,X2349)),
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_2083,plain,
! [X2346,X2347] : is_bool(hAPP_f292226953l_bool(X2346,X2347)),
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_2084,plain,
! [X2344,X2345] : is_bool(hAPP_f1637334154l_bool(X2344,X2345)),
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_2085,plain,
! [X2330,X2331] : is_bool(hAPP_f54304608l_bool(X2330,X2331)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).
fof(i_0_2086,hypothesis,
! [X2298,X2299] : is_bool(hAPP_nat_bool(X2298,X2299)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool]) ).
fof(i_0_2087,plain,
! [X2306,X2307] : is_fun1661590463l_bool(hAPP_n850744903l_bool(X2306,X2307)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool]) ).
fof(i_0_2088,plain,
! [X2242,X2243] : is_fun1661590463l_bool(image_1655916159e_bool(X2242,X2243)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).
fof(i_0_2089,plain,
! [X2304,X2305] : is_fun949378684l_bool(hAPP_n1414589940l_bool(X2304,X2305)),
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_2090,plain,
! [X2240,X2241] : is_fun949378684l_bool(image_nat_fun_a_bool(X2240,X2241)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).
fof(i_0_2091,plain,
! [X2334,X2335] : is_fun_pname_bool(hAPP_f654413245e_bool(X2334,X2335)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Opna]) ).
fof(i_0_2092,plain,
! [X2302,X2303] : is_fun_pname_bool(hAPP_n1025906991e_bool(X2302,X2303)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).
fof(i_0_2093,plain,
! [X2254,X2255] : is_fun_pname_bool(image_1921560913_pname(X2254,X2255)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname]) ).
fof(i_0_2094,plain,
! [X2238,X2239] : is_fun_pname_bool(image_nat_pname(X2238,X2239)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname]) ).
fof(i_0_2095,plain,
! [X2332,X2333] : is_fun_a_bool(hAPP_f1549043526a_bool(X2332,X2333)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL]) ).
fof(i_0_2096,plain,
! [X2300,X2301] : is_fun_a_bool(hAPP_nat_fun_a_bool(X2300,X2301)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).
fof(i_0_2097,plain,
! [X2252,X2253] : is_fun_a_bool(image_fun_nat_bool_a(X2252,X2253)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a]) ).
fof(i_0_2098,plain,
! [X2236,X2237] : is_fun_a_bool(image_nat_a(X2236,X2237)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a]) ).
fof(i_0_2099,plain,
! [X3879] : hAPP_nat_nat(suc,X3879) = hAPP_nat_nat(plus_plus_nat(one_one_nat),X3879),
inference(variable_rename,[status(thm)],[fact_607_Suc__eq__plus1__left]) ).
fof(i_0_2100,plain,
! [X4194,X4195] :
( ~ is_bool(X4194)
| hAPP_f54304608l_bool(cOMBK_1994329625t_bool(X4194),X4195) = X4194 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool])]) ).
fof(i_0_2101,plain,
! [X4196,X4197] :
( ~ is_bool(X4196)
| hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(X4196),X4197) = X4196 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo])]) ).
fof(i_0_2102,plain,
! [X4165,X4166] :
( ~ is_bool(X4165)
| hAPP_fun_a_bool_bool(cOMBK_324466864a_bool(X4165),X4166) = X4165 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U])]) ).
fof(i_0_2103,plain,
! [X4122,X4123] :
( ~ is_bool(X4122)
| hAPP_nat_bool(cOMBK_bool_nat(X4122),X4123) = X4122 ),
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_2104,plain,
! [X4128,X4129] :
( ~ is_bool(X4128)
| hAPP_pname_bool(cOMBK_bool_pname(X4128),X4129) = X4128 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U])]) ).
fof(i_0_2105,plain,
! [X4117,X4118] :
( ~ is_a(X4117)
| hAPP_pname_a(cOMBK_a_pname(X4117),X4118) = X4117 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U])]) ).
fof(i_0_2106,plain,
! [X4115,X4116] :
( ~ is_bool(X4115)
| hAPP_a_bool(cOMBK_bool_a(X4115),X4116) = X4115 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U])]) ).
fof(i_0_2107,plain,
! [X2513] : hAPP_nat_nat(suc,X2513) != X2513,
inference(variable_rename,[status(thm)],[fact_83_Suc__n__not__n]) ).
fof(i_0_2108,plain,
! [X2514] : X2514 != hAPP_nat_nat(suc,X2514),
inference(variable_rename,[status(thm)],[fact_84_n__not__Suc__n]) ).
fof(i_0_2109,plain,
! [X4071] : hAPP_nat_nat(minus_minus_nat(X4071),X4071) = zero_zero_nat,
inference(variable_rename,[status(thm)],[fact_688_diff__self__eq__0]) ).
fof(i_0_2110,plain,
! [X4077] : hAPP_nat_nat(suc,X4077) != zero_zero_nat,
inference(variable_rename,[status(thm)],[fact_694_Suc__not__Zero]) ).
fof(i_0_2111,plain,
! [X4076] : hAPP_nat_nat(suc,X4076) != zero_zero_nat,
inference(variable_rename,[status(thm)],[fact_693_nat_Osimps_I3_J]) ).
fof(i_0_2112,plain,
! [X4074] : hAPP_nat_nat(suc,X4074) != zero_zero_nat,
inference(variable_rename,[status(thm)],[fact_691_Suc__neq__Zero]) ).
fof(i_0_2113,plain,
! [X4079] : zero_zero_nat != hAPP_nat_nat(suc,X4079),
inference(variable_rename,[status(thm)],[fact_696_Zero__not__Suc]) ).
fof(i_0_2114,plain,
! [X4078] : zero_zero_nat != hAPP_nat_nat(suc,X4078),
inference(variable_rename,[status(thm)],[fact_695_nat_Osimps_I2_J]) ).
fof(i_0_2115,plain,
! [X4075] : zero_zero_nat != hAPP_nat_nat(suc,X4075),
inference(variable_rename,[status(thm)],[fact_692_Zero__neq__Suc]) ).
fof(i_0_2116,plain,
! [X4072] : hAPP_nat_nat(minus_minus_nat(X4072),zero_zero_nat) = X4072,
inference(variable_rename,[status(thm)],[fact_689_minus__nat_Odiff__0]) ).
fof(i_0_2117,plain,
! [X2219] :
( ~ is_fun1661590463l_bool(X2219)
| is_fun1661590463l_bool(collec1974731493e_bool(X2219)) ),
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_2118,plain,
! [X2207] :
( ~ is_bool(X2207)
| is_fun1661590463l_bool(cOMBK_1857069011e_bool(X2207)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J])]) ).
fof(i_0_2119,plain,
! [X2352] :
( ~ is_fun_a_bool(X2352)
| is_fun949378684l_bool(p(X2352)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_v_P])]) ).
fof(i_0_2120,plain,
! [X2218] :
( ~ is_fun949378684l_bool(X2218)
| is_fun949378684l_bool(collect_fun_a_bool(X2218)) ),
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_2121,plain,
! [X2206] :
( ~ is_bool(X2206)
| is_fun949378684l_bool(cOMBK_324466864a_bool(X2206)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J])]) ).
fof(i_0_2122,plain,
! [X2217] :
( ~ is_fun_pname_bool(X2217)
| is_fun_pname_bool(collect_pname(X2217)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000tc__Com__Opname])]) ).
fof(i_0_2123,plain,
! [X2205] :
( ~ is_bool(X2205)
| is_fun_pname_bool(cOMBK_bool_pname(X2205)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname])]) ).
fof(i_0_2124,plain,
! [X2216] :
( ~ is_fun_a_bool(X2216)
| is_fun_a_bool(collect_a(X2216)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000t__a])]) ).
fof(i_0_2125,plain,
! [X2204] :
( ~ is_bool(X2204)
| is_fun_a_bool(cOMBK_bool_a(X2204)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBK_000tc__HOL__Obool_000t__a])]) ).
fof(i_0_2126,plain,
! [X4073] : hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X4073) = zero_zero_nat,
inference(variable_rename,[status(thm)],[fact_690_diff__0__eq__0]) ).
fof(i_0_2127,plain,
! [X3532] : image_pname_a(X3532,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
inference(variable_rename,[status(thm)],[fact_468_image__empty]) ).
fof(i_0_2128,plain,
! [X3089] :
( ~ is_fun1661590463l_bool(X3089)
| collec1974731493e_bool(X3089) = X3089 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_293_Collect__def])]) ).
fof(i_0_2129,plain,
! [X3090] :
( ~ is_fun949378684l_bool(X3090)
| collect_fun_a_bool(X3090) = X3090 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_294_Collect__def])]) ).
fof(i_0_2130,plain,
! [X3087] :
( ~ is_fun_pname_bool(X3087)
| collect_pname(X3087) = X3087 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_291_Collect__def])]) ).
fof(i_0_2131,plain,
! [X3086] :
( ~ is_fun_a_bool(X3086)
| collect_a(X3086) = X3086 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_290_Collect__def])]) ).
fof(i_0_2132,plain,
! [X2353] : is_a(mgt(X2353)),
inference(variable_rename,[status(thm)],[gsy_v_mgt]) ).
fof(i_0_2133,plain,
! [X2354] : is_bool(wt(X2354)),
inference(variable_rename,[status(thm)],[gsy_v_wt]) ).
fof(i_0_2134,plain,
! [X4096] :
( ~ is_bool(X4096)
| X4096 = fTrue
| X4096 = fFalse ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T])]) ).
fof(i_0_2135,plain,
~ hBOOL(fFalse),
inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).
cnf(i_0_2136,plain,
bot_bo1701429464l_bool = collect_fun_nat_bool(cOMBK_1994329625t_bool(fFalse)),
inference(split_conjunct,[status(thm)],[fact_420_empty__def]) ).
cnf(i_0_2137,plain,
bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
inference(split_conjunct,[status(thm)],[fact_424_empty__def]) ).
cnf(i_0_2138,plain,
( hBOOL(hAPP_fun_a_bool_bool(p(X2),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,X1))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(p(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,X1))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),mgt(the_com(body(X1))))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1213,c_0_1214]),c_0_1214]),c_0_1214]),
[final] ).
cnf(i_0_2139,plain,
( hBOOL(hAPP_f1935102916l_bool(X1,X3))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),esk111_3(X1,X2,X3))),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),esk112_3(X1,X2,X3)))))) ),
inference(rw,[status(thm)],[i_0_1215,c_0_1216]),
[final] ).
cnf(i_0_2140,plain,
( hBOOL(hAPP_f621171935l_bool(X1,X3))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X2))
| ~ hBOOL(hAPP_f621171935l_bool(X1,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),esk113_3(X1,X2,X3))),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),esk114_3(X1,X2,X3)))))) ),
inference(rw,[status(thm)],[i_0_1217,c_0_1218]),
[final] ).
cnf(i_0_2141,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,bot_bo844097828e_bool))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),esk105_3(X1,X2,X3))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),esk106_3(X1,X2,X3)))))) ),
inference(rw,[status(thm)],[i_0_1219,c_0_1220]),
[final] ).
cnf(i_0_2142,plain,
( 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(finite_finite_a,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),esk107_3(X1,X2,X3))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),esk108_3(X1,X2,X3)))))) ),
inference(rw,[status(thm)],[i_0_1221,c_0_1214]),
[final] ).
cnf(i_0_2143,plain,
( X1 = X3
| 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),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X4)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool)))))) != collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool))))))
| ~ is_pname(X4)
| ~ is_pname(X3)
| ~ is_pname(X2)
| ~ is_pname(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1222,c_0_1220]),c_0_1220]),c_0_1220]),c_0_1220]),
[final] ).
cnf(i_0_2144,plain,
( X1 = X3
| X1 = X2
| collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool)))))) != collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X4)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),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),bot_bo844097828e_bool))))))
| ~ is_pname(X4)
| ~ is_pname(X3)
| ~ is_pname(X2)
| ~ is_pname(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1223,c_0_1220]),c_0_1220]),c_0_1220]),c_0_1220]),
[final] ).
cnf(i_0_2145,plain,
( X1 = X3
| 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),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X4)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))))) != collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool))))))
| ~ is_a(X4)
| ~ is_a(X3)
| ~ is_a(X2)
| ~ is_a(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1224,c_0_1214]),c_0_1214]),c_0_1214]),c_0_1214]),
[final] ).
cnf(i_0_2146,plain,
( X1 = X3
| X1 = X2
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))))) != collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X4)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),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),bot_bot_fun_a_bool))))))
| ~ is_a(X4)
| ~ is_a(X3)
| ~ is_a(X2)
| ~ is_a(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1225,c_0_1214]),c_0_1214]),c_0_1214]),c_0_1214]),
[final] ).
cnf(i_0_2147,plain,
( X2 = X3
| 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),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool)))))) != collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X4)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool))))))
| ~ is_pname(X4)
| ~ is_pname(X3)
| ~ is_pname(X2)
| ~ is_pname(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1226,c_0_1220]),c_0_1220]),c_0_1220]),c_0_1220]),
[final] ).
cnf(i_0_2148,plain,
( X2 = X3
| X1 = X2
| collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X4)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool)))))) != collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),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),bot_bo844097828e_bool))))))
| ~ is_pname(X4)
| ~ is_pname(X3)
| ~ is_pname(X2)
| ~ is_pname(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1227,c_0_1220]),c_0_1220]),c_0_1220]),c_0_1220]),
[final] ).
cnf(i_0_2149,plain,
( X2 = X3
| 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),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))))) != collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X4)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool))))))
| ~ is_a(X4)
| ~ is_a(X3)
| ~ is_a(X2)
| ~ is_a(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1228,c_0_1214]),c_0_1214]),c_0_1214]),c_0_1214]),
[final] ).
cnf(i_0_2150,plain,
( X2 = X3
| X1 = X2
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X4)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))))) != collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),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),bot_bot_fun_a_bool))))))
| ~ is_a(X4)
| ~ is_a(X3)
| ~ is_a(X2)
| ~ is_a(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1229,c_0_1214]),c_0_1214]),c_0_1214]),c_0_1214]),
[final] ).
cnf(i_0_2151,plain,
( hBOOL(hAPP_fun_a_bool_bool(p(X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),mgt(X2))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))))
| ~ hBOOL(wt(X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(p(X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,esk81_2(X1,X2)))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1230,c_0_1214]),c_0_1214]),
[final] ).
cnf(i_0_2152,negated_conjecture,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g)))),image_pname_a(mgt_call,u))),
inference(rw,[status(thm)],[i_0_1231,c_0_1214]),
[final] ).
cnf(i_0_2153,plain,
( hBOOL(hAPP_f1637334154l_bool(X1,X3))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),esk109_3(X1,X2,X3))),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),esk110_3(X1,X2,X3))))) ),
inference(rw,[status(thm)],[i_0_1232,c_0_1233]),
[final] ).
cnf(i_0_2154,plain,
( hBOOL(hAPP_f54304608l_bool(X1,X3))
| ~ hBOOL(hAPP_f54304608l_bool(X1,bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(X1,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),esk103_3(X1,X2,X3))),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),esk104_3(X1,X2,X3))))) ),
inference(rw,[status(thm)],[i_0_1234,c_0_1235]),
[final] ).
cnf(i_0_2155,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1)),hAPP_n850744903l_bool(cOMBC_1666426608t_bool(cOMBB_1896684278e_bool(fequal_nat,X2)),hAPP_f921600141ol_nat(X2,esk43_2(X2,X1)))))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1236]),
[final] ).
cnf(i_0_2156,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1)),hAPP_p338031245l_bool(cOMBC_1004116266e_bool(cOMBB_598082538e_bool(fequal_pname,X2)),hAPP_f1297739591_pname(X2,esk37_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1237]),
[final] ).
cnf(i_0_2157,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1)),hAPP_n1414589940l_bool(cOMBC_619334683t_bool(cOMBB_164527437a_bool(fequal_nat,X2)),hAPP_fun_a_bool_nat(X2,esk44_2(X2,X1)))))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1238]),
[final] ).
cnf(i_0_2158,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1)),hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(cOMBB_1693087065a_bool(fequal_pname,X2)),hAPP_f1128469712_pname(X2,esk38_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1239]),
[final] ).
cnf(i_0_2159,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_f654413245e_bool(cOMBC_267053842l_bool(cOMBB_928955006_pname(fequal_fun_nat_bool,X2)),hAPP_p1499970991t_bool(X2,esk49_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1240]),
[final] ).
cnf(i_0_2160,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_f759274231e_bool(cOMBC_1058051404l_bool(cOMBB_408569982_pname(fequal533582459e_bool,X2)),hAPP_p61793385e_bool(X2,esk50_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1241]),
[final] ).
cnf(i_0_2161,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_f1794073134e_bool(cOMBC_445755039l_bool(cOMBB_392435466_pname(fequal_fun_a_bool,X2)),hAPP_p1534023578a_bool(X2,esk51_2(X2,X1)))))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1242]),
[final] ).
cnf(i_0_2162,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_n1025906991e_bool(cOMBC_pname_nat_bool(cOMBB_523834888_pname(fequal_nat,X2)),hAPP_pname_nat(X2,esk41_2(X2,X1)))))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1243]),
[final] ).
cnf(i_0_2163,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_p61793385e_bool(cOMBC_1149511130e_bool(cOMBB_542850580_pname(fequal_pname,X2)),hAPP_pname_pname(X2,esk35_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1244]),
[final] ).
cnf(i_0_2164,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,esk56_2(X2,X1)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1245]),
[final] ).
cnf(i_0_2165,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)),hAPP_f1549043526a_bool(cOMBC_777206479l_bool(cOMBB_743407885bool_a(fequal_fun_nat_bool,X2)),hAPP_a_fun_nat_bool(X2,esk53_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1246]),
[final] ).
cnf(i_0_2166,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)),hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(cOMBB_1137537805bool_a(fequal533582459e_bool,X2)),hAPP_a93125764e_bool(X2,esk54_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1247]),
[final] ).
cnf(i_0_2167,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(cOMBB_472261505bool_a(fequal_fun_a_bool,X2)),hAPP_a_fun_a_bool(X2,esk55_2(X2,X1)))))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1248]),
[final] ).
cnf(i_0_2168,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)),hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(cOMBB_1321347587bool_a(fequal_nat,X2)),hAPP_a_nat(X2,esk40_2(X2,X1)))))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1249]),
[final] ).
cnf(i_0_2169,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)),hAPP_p1534023578a_bool(cOMBC_a_pname_bool(cOMBB_610033911bool_a(fequal_pname,X2)),hAPP_a_pname(X2,esk34_2(X2,X1)))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1250]),
[final] ).
cnf(i_0_2170,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)),hAPP_a_fun_a_bool(cOMBC_a_a_bool(cOMBB_a_fun_a_bool_a(fequal_a,X2)),hAPP_a_a(X2,esk52_2(X2,X1)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1251]),
[final] ).
cnf(i_0_2171,plain,
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),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X3)))))) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),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),X3)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1252,c_0_1220]),c_0_1220]),c_0_1220]),c_0_1220]),
[final] ).
cnf(i_0_2172,plain,
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),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))))) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),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),X3)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1253,c_0_1214]),c_0_1214]),c_0_1214]),c_0_1214]),
[final] ).
cnf(i_0_2173,plain,
( 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),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool)))))) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X4)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool))))))
| X3 != X4
| X1 != X2
| ~ is_pname(X4)
| ~ is_pname(X3)
| ~ is_pname(X2)
| ~ is_pname(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1254,c_0_1220]),c_0_1220]),c_0_1220]),c_0_1220]),
[final] ).
cnf(i_0_2174,plain,
( 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),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))))) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X4)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool))))))
| X3 != X4
| X1 != X2
| ~ is_a(X4)
| ~ is_a(X3)
| ~ is_a(X2)
| ~ is_a(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1255,c_0_1214]),c_0_1214]),c_0_1214]),c_0_1214]),
[final] ).
cnf(i_0_2175,plain,
( hBOOL(hAPP_f1935102916l_bool(X1,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),esk117_2(X1,X2))),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),esk118_2(X1,X2)))))) ),
inference(rw,[status(thm)],[i_0_1256,c_0_1216]),
[final] ).
cnf(i_0_2176,plain,
( hBOOL(hAPP_f621171935l_bool(X1,X2))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(X1,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),esk119_2(X1,X2))),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),esk120_2(X1,X2)))))) ),
inference(rw,[status(thm)],[i_0_1257,c_0_1218]),
[final] ).
cnf(i_0_2177,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))),X2)) ),
inference(rw,[status(thm)],[i_0_1258,c_0_1220]),
[final] ).
cnf(i_0_2178,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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),X3)))),X2)) ),
inference(rw,[status(thm)],[i_0_1259,c_0_1220]),
[final] ).
cnf(i_0_2179,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,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))),X2)) ),
inference(rw,[status(thm)],[i_0_1260,c_0_1214]),
[final] ).
cnf(i_0_2180,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,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),X3)))),X2)) ),
inference(rw,[status(thm)],[i_0_1261,c_0_1214]),
[final] ).
cnf(i_0_2181,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,esk30_3(X2,X3,X1))),hAPP_n1699378549t_bool(X1,hAPP_nat_nat(suc,esk30_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1262]),
[final] ).
cnf(i_0_2182,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,esk29_3(X2,X3,X1))),hAPP_n1025906991e_bool(X1,hAPP_nat_nat(suc,esk29_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1263]),
[final] ).
cnf(i_0_2183,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,esk31_3(X2,X3,X1))),hAPP_nat_fun_a_bool(X1,hAPP_nat_nat(suc,esk31_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1264]),
[final] ).
cnf(i_0_2184,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,esk32_3(X2,X3,X1))),hAPP_nat_nat(X1,hAPP_nat_nat(suc,esk32_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1265]),
[final] ).
cnf(i_0_2185,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,esk28_3(X2,X3,X1))),hAPP_nat_bool(X1,hAPP_nat_nat(suc,esk28_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1266]),
[final] ).
cnf(i_0_2186,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1267,c_0_1220]),c_0_1220]),
[final] ).
cnf(i_0_2187,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1268,c_0_1214]),c_0_1214]),
[final] ).
cnf(i_0_2188,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X1,X2)),X3)),hAPP_nat_nat(X1,hAPP_nat_nat(plus_plus_nat(X2),X3))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(X1,esk126_3(X2,X3,X1))),hAPP_nat_nat(X1,esk127_3(X2,X3,X1)))) ),
inference(split_conjunct,[status(thm)],[i_0_1269]),
[final] ).
cnf(i_0_2189,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,esk131_3(X2,X3,X1))),hAPP_nat_nat(X1,esk132_3(X2,X3,X1))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1270]),
[final] ).
cnf(i_0_2190,plain,
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),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)))))) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1271,c_0_1220]),c_0_1220]),c_0_1220]),
[final] ).
cnf(i_0_2191,plain,
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),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)))))) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1272,c_0_1214]),c_0_1214]),c_0_1214]),
[final] ).
cnf(i_0_2192,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X2,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)),hAPP_n215258509l_bool(cOMBC_385542954t_bool(cOMBB_1250273980t_bool(fequal_nat,X2)),hAPP_f22106695ol_nat(X2,esk42_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1273,c_0_968]),
[final] ).
cnf(i_0_2193,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X2,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)),hAPP_p130839763l_bool(cOMBC_615407716e_bool(cOMBB_141086128t_bool(fequal_pname,X2)),hAPP_f1291551745_pname(X2,esk36_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1274,c_0_968]),
[final] ).
cnf(i_0_2194,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,esk46_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1275,c_0_971]),
[final] ).
cnf(i_0_2195,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,esk47_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1276,c_0_971]),
[final] ).
cnf(i_0_2196,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,esk48_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1277,c_0_971]),
[final] ).
cnf(i_0_2197,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(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_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(fequal_nat,X2)),hAPP_nat_nat(X2,esk39_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1278,c_0_971]),
[final] ).
cnf(i_0_2198,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(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_p1499970991t_bool(cOMBC_nat_pname_bool(cOMBB_1212655066ol_nat(fequal_pname,X2)),hAPP_nat_pname(X2,esk33_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1279,c_0_971]),
[final] ).
cnf(i_0_2199,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(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_a_fun_nat_bool(cOMBC_nat_a_bool(cOMBB_1885489796ol_nat(fequal_a,X2)),hAPP_nat_a(X2,esk45_2(X2,X1)))))) ),
inference(rw,[status(thm)],[i_0_1280,c_0_971]),
[final] ).
cnf(i_0_2200,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,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),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(rw,[status(thm)],[i_0_1281,c_0_1220]),
[final] ).
cnf(i_0_2201,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,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),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(rw,[status(thm)],[i_0_1282,c_0_1214]),
[final] ).
cnf(i_0_2202,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)),hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X2)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1))))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(rw,[status(thm)],[i_0_1283,c_0_1218]),
[final] ).
cnf(i_0_2203,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1)),hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X2)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1))))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(rw,[status(thm)],[i_0_1284,c_0_1216]),
[final] ).
cnf(i_0_2204,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,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(rw,[status(thm)],[i_0_1285,c_0_1214]),
[final] ).
cnf(i_0_2205,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,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(rw,[status(thm)],[i_0_1286,c_0_1220]),
[final] ).
cnf(i_0_2206,plain,
( X1 = X3
| 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),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X4)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool)))) != cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1287,c_0_1235]),c_0_1235]),c_0_1235]),c_0_1235]),
[final] ).
cnf(i_0_2207,plain,
( X1 = X3
| X1 = X2
| cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool)))) != cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X4)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_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),bot_bot_fun_nat_bool)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1288,c_0_1235]),c_0_1235]),c_0_1235]),c_0_1235]),
[final] ).
cnf(i_0_2208,plain,
( X2 = X3
| 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),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool)))) != cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X4)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1289,c_0_1235]),c_0_1235]),c_0_1235]),c_0_1235]),
[final] ).
cnf(i_0_2209,plain,
( X2 = X3
| X1 = X2
| cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X4)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool)))) != cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_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),bot_bot_fun_nat_bool)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1290,c_0_1235]),c_0_1235]),c_0_1235]),c_0_1235]),
[final] ).
cnf(i_0_2210,plain,
( X1 = bot_bo844097828e_bool
| X1 = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool)))
| ~ is_fun_pname_bool(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1291,c_0_1220]),c_0_1220]),
[final] ).
cnf(i_0_2211,plain,
( X1 = bot_bot_fun_a_bool
| X1 = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1292,c_0_1214]),c_0_1214]),
[final] ).
cnf(i_0_2212,plain,
( hBOOL(hAPP_f1637334154l_bool(X1,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),esk115_2(X1,X2))),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),esk116_2(X1,X2))))) ),
inference(rw,[status(thm)],[i_0_1293,c_0_1233]),
[final] ).
cnf(i_0_2213,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X3))))) ),
inference(rw,[status(thm)],[i_0_1294,c_0_1220]),
[final] ).
cnf(i_0_2214,plain,
( 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),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3))))) ),
inference(rw,[status(thm)],[i_0_1295,c_0_1214]),
[final] ).
cnf(i_0_2215,plain,
( X1 = X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ is_pname(X2)
| ~ is_pname(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X3))))) ),
inference(rw,[status(thm)],[i_0_1296,c_0_1220]),
[final] ).
cnf(i_0_2216,plain,
( X1 = X2
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X3))
| ~ is_pname(X2)
| ~ is_pname(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X3))))) ),
inference(rw,[status(thm)],[i_0_1297,c_0_1220]),
[final] ).
cnf(i_0_2217,plain,
( X1 = X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ is_a(X2)
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3))))) ),
inference(rw,[status(thm)],[i_0_1298,c_0_1214]),
[final] ).
cnf(i_0_2218,plain,
( X1 = X2
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X3))
| ~ is_a(X2)
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3))))) ),
inference(rw,[status(thm)],[i_0_1299,c_0_1214]),
[final] ).
cnf(i_0_2219,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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),X3))),X2)) ),
inference(rw,[status(thm)],[i_0_1300,c_0_1235]),
[final] ).
cnf(i_0_2220,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))),X2)) ),
inference(rw,[status(thm)],[i_0_1301,c_0_1235]),
[final] ).
cnf(i_0_2221,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(X1,X3)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(X1,esk72_3(X1,X2,X3))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1302]),
[final] ).
cnf(i_0_2222,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(X1,X3)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(X1,esk74_3(X1,X2,X3))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2223,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_nat_pname(X1,X3)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(X1,esk76_3(X1,X2,X3))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1304]),
[final] ).
cnf(i_0_2224,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(X1,X3)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(X1,esk73_3(X1,X2,X3))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1305]),
[final] ).
cnf(i_0_2225,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(X1,X3)),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_a_pname(X1,esk75_3(X1,X2,X3))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1306]),
[final] ).
cnf(i_0_2226,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(X1,X3)),X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(X1,esk77_3(X1,X2,X3))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1307]),
[final] ).
cnf(i_0_2227,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,esk78_3(X1,X2,X3))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1308]),
[final] ).
cnf(i_0_2228,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1309,c_0_1235]),c_0_1235]),
[final] ).
cnf(i_0_2229,plain,
( X1 = X2
| ~ is_pname(X2)
| ~ is_pname(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool))))) ),
inference(rw,[status(thm)],[i_0_1310,c_0_1220]),
[final] ).
cnf(i_0_2230,plain,
( X1 = X2
| ~ is_pname(X2)
| ~ is_pname(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool))))) ),
inference(rw,[status(thm)],[i_0_1311,c_0_1220]),
[final] ).
cnf(i_0_2231,plain,
( X1 = X2
| ~ is_a(X2)
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool))))) ),
inference(rw,[status(thm)],[i_0_1312,c_0_1214]),
[final] ).
cnf(i_0_2232,plain,
( X1 = X2
| ~ is_a(X2)
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool))))) ),
inference(rw,[status(thm)],[i_0_1313,c_0_1214]),
[final] ).
cnf(i_0_2233,plain,
( X1 = X3
| hBOOL(hAPP_pname_bool(X2,X3))
| ~ is_pname(X3)
| ~ is_pname(X1)
| ~ hBOOL(hAPP_pname_bool(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))),X3)) ),
inference(rw,[status(thm)],[i_0_1314,c_0_1220]),
[final] ).
cnf(i_0_2234,plain,
( X1 = X3
| hBOOL(hAPP_a_bool(X2,X3))
| ~ is_a(X3)
| ~ is_a(X1)
| ~ hBOOL(hAPP_a_bool(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))),X3)) ),
inference(rw,[status(thm)],[i_0_1315,c_0_1214]),
[final] ).
cnf(i_0_2235,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X2))))) ),
inference(rw,[status(thm)],[i_0_1316,c_0_1216]),
[final] ).
cnf(i_0_2236,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X2))))) ),
inference(rw,[status(thm)],[i_0_1317,c_0_1218]),
[final] ).
cnf(i_0_2237,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,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(rw,[status(thm)],[i_0_1318,c_0_1220]),
[final] ).
cnf(i_0_2238,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,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(rw,[status(thm)],[i_0_1319,c_0_1214]),
[final] ).
cnf(i_0_2239,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk126_3(X1,X2,X3)),esk127_3(X1,X2,X3)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(X3,X1)),X2)),hAPP_nat_nat(X3,hAPP_nat_nat(plus_plus_nat(X1),X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1269]),
[final] ).
cnf(i_0_2240,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk81_2(X1,X2)),u))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),mgt(X2))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))))
| ~ hBOOL(wt(X2)) ),
inference(rw,[status(thm)],[i_0_1320,c_0_1214]),
[final] ).
cnf(i_0_2241,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,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),X3))),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1321,c_0_1235]),
[final] ).
cnf(i_0_2242,plain,
( hBOOL(hAPP_f1637334154l_bool(X1,X3))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,esk109_3(X1,X2,X3)),esk110_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_966]),
[final] ).
cnf(i_0_2243,plain,
( hBOOL(hAPP_f1935102916l_bool(X1,X3))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,esk111_3(X1,X2,X3)),esk112_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_955]),
[final] ).
cnf(i_0_2244,plain,
( hBOOL(hAPP_f621171935l_bool(X1,X3))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,esk113_3(X1,X2,X3)),esk114_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_957]),
[final] ).
cnf(i_0_2245,plain,
( hBOOL(hAPP_f54304608l_bool(X1,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk103_3(X1,X2,X3)),esk104_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_969]),
[final] ).
cnf(i_0_2246,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk105_3(X1,X2,X3)),esk106_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_959]),
[final] ).
cnf(i_0_2247,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk107_3(X1,X2,X3)),esk108_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_961]),
[final] ).
cnf(i_0_2248,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1322,c_0_1220]),
[final] ).
cnf(i_0_2249,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),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1323,c_0_1214]),
[final] ).
cnf(i_0_2250,plain,
( is_pname(esk81_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(p(X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),mgt(X2))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))))
| ~ hBOOL(wt(X2)) ),
inference(rw,[status(thm)],[i_0_1324,c_0_1214]),
[final] ).
cnf(i_0_2251,plain,
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),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X3)))) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_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),X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1325,c_0_1235]),c_0_1235]),c_0_1235]),c_0_1235]),
[final] ).
cnf(i_0_2252,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,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(rw,[status(thm)],[i_0_1326,c_0_1235]),
[final] ).
cnf(i_0_2253,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1)),hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X2)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1)))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(rw,[status(thm)],[i_0_1327,c_0_1233]),
[final] ).
cnf(i_0_2254,plain,
( 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),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool)))) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X4)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool))))
| X3 != X4
| X1 != X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1328,c_0_1235]),c_0_1235]),c_0_1235]),c_0_1235]),
[final] ).
cnf(i_0_2255,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ is_pname(X3)
| ~ is_pname(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1329,c_0_1220]),
[final] ).
cnf(i_0_2256,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ is_a(X3)
| ~ is_a(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1330,c_0_1214]),
[final] ).
cnf(i_0_2257,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1331,c_0_1220]),
[final] ).
cnf(i_0_2258,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1332,c_0_1220]),
[final] ).
cnf(i_0_2259,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X2)))))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1333,c_0_1220]),
[final] ).
cnf(i_0_2260,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1334,c_0_1214]),
[final] ).
cnf(i_0_2261,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1335,c_0_1214]),
[final] ).
cnf(i_0_2262,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X2)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1336,c_0_1214]),
[final] ).
cnf(i_0_2263,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X3)))))
| X1 != X2
| ~ is_pname(X2)
| ~ is_pname(X1) ),
inference(rw,[status(thm)],[i_0_1337,c_0_1220]),
[final] ).
cnf(i_0_2264,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))))
| X1 != X2
| ~ is_a(X2)
| ~ is_a(X1) ),
inference(rw,[status(thm)],[i_0_1338,c_0_1214]),
[final] ).
cnf(i_0_2265,plain,
( hBOOL(hAPP_pname_bool(collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X3)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))),X2))
| ~ is_pname(X3)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1339,c_0_1220]),
[final] ).
cnf(i_0_2266,plain,
( hBOOL(hAPP_a_bool(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))),X2))
| ~ is_a(X3)
| ~ is_a(X2)
| ~ hBOOL(hAPP_a_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1340,c_0_1214]),
[final] ).
cnf(i_0_2267,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X3)))))
| X1 != X2 ),
inference(rw,[status(thm)],[i_0_1341,c_0_1220]),
[final] ).
cnf(i_0_2268,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))))
| X1 != X2 ),
inference(rw,[status(thm)],[i_0_1342,c_0_1214]),
[final] ).
cnf(i_0_2269,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))))),
inference(rw,[status(thm)],[i_0_1343,c_0_1220]),
[final] ).
cnf(i_0_2270,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),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(rw,[status(thm)],[i_0_1344,c_0_1220]),
[final] ).
cnf(i_0_2271,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))))),
inference(rw,[status(thm)],[i_0_1345,c_0_1214]),
[final] ).
cnf(i_0_2272,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),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(rw,[status(thm)],[i_0_1346,c_0_1214]),
[final] ).
cnf(i_0_2273,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X2)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1)))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(rw,[status(thm)],[i_0_1347,c_0_1216]),
[final] ).
cnf(i_0_2274,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X2)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1)))))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(rw,[status(thm)],[i_0_1348,c_0_1216]),
[final] ).
cnf(i_0_2275,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X2)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1)))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(rw,[status(thm)],[i_0_1349,c_0_1218]),
[final] ).
cnf(i_0_2276,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X2)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1)))))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(rw,[status(thm)],[i_0_1350,c_0_1218]),
[final] ).
cnf(i_0_2277,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(rw,[status(thm)],[i_0_1351,c_0_1220]),
[final] ).
cnf(i_0_2278,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(rw,[status(thm)],[i_0_1352,c_0_1220]),
[final] ).
cnf(i_0_2279,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(rw,[status(thm)],[i_0_1353,c_0_1214]),
[final] ).
cnf(i_0_2280,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(rw,[status(thm)],[i_0_1354,c_0_1214]),
[final] ).
cnf(i_0_2281,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool)))))
| X1 != X2
| ~ is_pname(X2)
| ~ is_pname(X1) ),
inference(rw,[status(thm)],[i_0_1355,c_0_1220]),
[final] ).
cnf(i_0_2282,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))))
| X1 != X2
| ~ is_a(X2)
| ~ is_a(X1) ),
inference(rw,[status(thm)],[i_0_1356,c_0_1214]),
[final] ).
cnf(i_0_2283,plain,
image_pname_a(X1,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X3)))) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(X1,X2))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X1,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1357,c_0_1214]),c_0_1220]),
[final] ).
cnf(i_0_2284,plain,
image_a_pname(X1,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),hAPP_a_pname(X1,X2))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),image_a_pname(X1,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1358,c_0_1214]),c_0_1220]),
[final] ).
cnf(i_0_2285,plain,
( hBOOL(hAPP_pname_bool(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),X3))),X2))
| X1 != X2
| ~ is_pname(X2)
| ~ is_pname(X1) ),
inference(rw,[status(thm)],[i_0_1359,c_0_1220]),
[final] ).
cnf(i_0_2286,plain,
( hBOOL(hAPP_a_bool(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),X3))),X2))
| X1 != X2
| ~ is_a(X2)
| ~ is_a(X1) ),
inference(rw,[status(thm)],[i_0_1360,c_0_1214]),
[final] ).
cnf(i_0_2287,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),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X3)))) ),
inference(rw,[status(thm)],[i_0_1361,c_0_1235]),
[final] ).
cnf(i_0_2288,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk131_3(X1,X2,X3)),esk132_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_1270]),
[final] ).
cnf(i_0_2289,plain,
( X1 = bot_bot_fun_nat_bool
| X1 = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1362,c_0_1235]),c_0_1235]),
[final] ).
cnf(i_0_2290,plain,
( X1 = X2
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X3)))) ),
inference(rw,[status(thm)],[i_0_1363,c_0_1235]),
[final] ).
cnf(i_0_2291,plain,
( X1 = X2
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X3)))) ),
inference(rw,[status(thm)],[i_0_1364,c_0_1235]),
[final] ).
cnf(i_0_2292,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))
| 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))) != 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),X3)))
| ~ is_fun_pname_bool(X3)
| ~ is_fun_pname_bool(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1365,c_0_1220]),c_0_1220]),
[final] ).
cnf(i_0_2293,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))
| 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))) != 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),X3)))
| ~ is_fun_a_bool(X3)
| ~ is_fun_a_bool(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1366,c_0_1214]),c_0_1214]),
[final] ).
cnf(i_0_2294,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool)))) ),
inference(rw,[status(thm)],[i_0_1367,c_0_1235]),
[final] ).
cnf(i_0_2295,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool)))) ),
inference(rw,[status(thm)],[i_0_1368,c_0_1235]),
[final] ).
cnf(i_0_2296,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,esk83_2(X1,X2))),hAPP_nat_bool(X2,esk83_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1369]),
[final] ).
cnf(i_0_2297,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(X1,esk82_2(X1,X2))),hAPP_pname_bool(X2,esk82_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1370]),
[final] ).
cnf(i_0_2298,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,esk84_2(X1,X2))),hAPP_a_bool(X2,esk84_2(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[i_0_1371]),
[final] ).
cnf(i_0_2299,plain,
( X1 = X3
| hBOOL(hAPP_nat_bool(X2,X3))
| ~ hBOOL(hAPP_nat_bool(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)),X3)) ),
inference(rw,[status(thm)],[i_0_1372,c_0_1235]),
[final] ).
cnf(i_0_2300,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2)))) ),
inference(rw,[status(thm)],[i_0_1373,c_0_1233]),
[final] ).
cnf(i_0_2301,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_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(rw,[status(thm)],[i_0_1374,c_0_1235]),
[final] ).
cnf(i_0_2302,plain,
image_nat_a(X1,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X3))) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_nat_a(X1,X2))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_nat_a(X1,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1375,c_0_1214]),c_0_1235]),
[final] ).
cnf(i_0_2303,plain,
( 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),bot_bo844097828e_bool))) != collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool)))
| ~ is_pname(X2)
| ~ is_pname(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1376,c_0_1220]),c_0_1220]),
[final] ).
cnf(i_0_2304,plain,
( 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),bot_bot_fun_a_bool))) != collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))
| ~ is_a(X2)
| ~ is_a(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1377,c_0_1214]),c_0_1214]),
[final] ).
cnf(i_0_2305,plain,
image_a_nat(X1,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),hAPP_a_nat(X1,X2))),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),image_a_nat(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1378,c_0_1214]),c_0_1235]),
[final] ).
cnf(i_0_2306,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,esk121_2(X1,X2)),hAPP_nat_nat(X2,esk121_2(X1,X2)))) ),
inference(rw,[status(thm)],[i_0_1379,c_0_971]),
[final] ).
cnf(i_0_2307,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1380,c_0_1235]),
[final] ).
cnf(i_0_2308,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(minus_minus_nat(X1),X2)),hAPP_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_1381]),
[final] ).
cnf(i_0_2309,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(minus_minus_nat(X1),X2)),hAPP_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_1382]),
[final] ).
cnf(i_0_2310,plain,
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),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)))) = 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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1383,c_0_1235]),c_0_1235]),c_0_1235]),
[final] ).
cnf(i_0_2311,plain,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,esk9_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_1384]),
[final] ).
cnf(i_0_2312,plain,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,esk1_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_1385]),
[final] ).
cnf(i_0_2313,plain,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,esk10_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_1386]),
[final] ).
cnf(i_0_2314,plain,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,esk2_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_1387]),
[final] ).
cnf(i_0_2315,plain,
( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,esk11_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_1388]),
[final] ).
cnf(i_0_2316,plain,
( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,esk3_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_1389]),
[final] ).
cnf(i_0_2317,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk25_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_1390]),
[final] ).
cnf(i_0_2318,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk24_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_1391]),
[final] ).
cnf(i_0_2319,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk23_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_1392]),
[final] ).
cnf(i_0_2320,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk21_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_1393]),
[final] ).
cnf(i_0_2321,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk27_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_1394]),
[final] ).
cnf(i_0_2322,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk19_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_1395]),
[final] ).
cnf(i_0_2323,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk18_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_1396]),
[final] ).
cnf(i_0_2324,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk17_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_1397]),
[final] ).
cnf(i_0_2325,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk8_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_1398]),
[final] ).
cnf(i_0_2326,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk7_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_1399]),
[final] ).
cnf(i_0_2327,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk6_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_1400]),
[final] ).
cnf(i_0_2328,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk4_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_1401]),
[final] ).
cnf(i_0_2329,plain,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,esk13_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_1402]),
[final] ).
cnf(i_0_2330,plain,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,esk14_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_1403]),
[final] ).
cnf(i_0_2331,plain,
( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,esk15_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_1404]),
[final] ).
cnf(i_0_2332,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk26_3(X1,X2,X3)),X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_nat_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1405]),
[final] ).
cnf(i_0_2333,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk22_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_1406]),
[final] ).
cnf(i_0_2334,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_1407]),
[final] ).
cnf(i_0_2335,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk16_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_1408]),
[final] ).
cnf(i_0_2336,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk12_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_1409]),
[final] ).
cnf(i_0_2337,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk5_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_1410]),
[final] ).
cnf(i_0_2338,plain,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,esk109_3(X1,X2,X3)),X2))
| hBOOL(hAPP_f1637334154l_bool(X1,X3))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_966]),
[final] ).
cnf(i_0_2339,plain,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,esk111_3(X1,X2,X3)),X2))
| hBOOL(hAPP_f1935102916l_bool(X1,X3))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_955]),
[final] ).
cnf(i_0_2340,plain,
( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,esk113_3(X1,X2,X3)),X2))
| hBOOL(hAPP_f621171935l_bool(X1,X3))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_957]),
[final] ).
cnf(i_0_2341,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk103_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_969]),
[final] ).
cnf(i_0_2342,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk105_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_959]),
[final] ).
cnf(i_0_2343,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk107_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_961]),
[final] ).
cnf(i_0_2344,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1411,c_0_1235]),
[final] ).
cnf(i_0_2345,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1412,c_0_1235]),
[final] ).
cnf(i_0_2346,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1413,c_0_1235]),
[final] ).
cnf(i_0_2347,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X2))))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1414,c_0_1235]),
[final] ).
cnf(i_0_2348,plain,
( hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X2)))) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X2)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1415,c_0_1218]),
[final] ).
cnf(i_0_2349,plain,
( hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X2)))) = hAPP_f55526627ol_nat(finite1340463720e_bool,X2)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1416,c_0_1216]),
[final] ).
cnf(i_0_2350,plain,
( hAPP_fun_a_bool_nat(finite_card_a,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)))) = hAPP_fun_a_bool_nat(finite_card_a,X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1417,c_0_1214]),
[final] ).
cnf(i_0_2351,plain,
( hAPP_f921600141ol_nat(finite_card_pname,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)))) = hAPP_f921600141ol_nat(finite_card_pname,X2)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1418,c_0_1220]),
[final] ).
cnf(i_0_2352,plain,
collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),collec1974731493e_bool(X2)))) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1))),X2)),
inference(rw,[status(thm)],[i_0_1419,c_0_1216]),
[final] ).
cnf(i_0_2353,plain,
collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),collect_fun_a_bool(X2)))) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1))),X2)),
inference(rw,[status(thm)],[i_0_1420,c_0_1218]),
[final] ).
cnf(i_0_2354,plain,
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),collect_pname(X2)))) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1))),X2)),
inference(rw,[status(thm)],[i_0_1421,c_0_1220]),
[final] ).
cnf(i_0_2355,plain,
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),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(rw,[status(thm)],[i_0_1422,c_0_1214]),
[final] ).
cnf(i_0_2356,plain,
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),hAPP_pname_pname(X3,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),image_pname_pname(X3,X2)))) = image_pname_pname(X3,X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1423,c_0_1220]),
[final] ).
cnf(i_0_2357,plain,
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),hAPP_a_pname(X3,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),image_a_pname(X3,X2)))) = image_a_pname(X3,X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1424,c_0_1220]),
[final] ).
cnf(i_0_2358,plain,
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_nat_a(X3,X1))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_nat_a(X3,X2)))) = image_nat_a(X3,X2)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1425,c_0_1214]),
[final] ).
cnf(i_0_2359,plain,
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(X3,X1))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X3,X2)))) = image_pname_a(X3,X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1426,c_0_1214]),
[final] ).
cnf(i_0_2360,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk65_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_nat_a(X2,X3)))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1427]),
[final] ).
cnf(i_0_2361,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk64_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),image_nat_pname(X2,X3)))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1428]),
[final] ).
cnf(i_0_2362,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,esk60_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_nat_a(X2,X3)))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1429]),
[final] ).
cnf(i_0_2363,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk63_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_1430]),
[final] ).
cnf(i_0_2364,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk68_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_1431]),
[final] ).
cnf(i_0_2365,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk59_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_1432]),
[final] ).
cnf(i_0_2366,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk61_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),image_a_pname(X2,X3)))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1433]),
[final] ).
cnf(i_0_2367,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk66_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),image_pname_nat(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1434]),
[final] ).
cnf(i_0_2368,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,esk62_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),image_a_nat(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1435]),
[final] ).
cnf(i_0_2369,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk67_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),image_a_nat(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1436]),
[final] ).
cnf(i_0_2370,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk128_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_1437]),
[final] ).
cnf(i_0_2371,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,esk128_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_1437]),
[final] ).
cnf(i_0_2372,plain,
( hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X2)))) = hAPP_nat_nat(suc,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(rw,[status(thm)],[i_0_1438,c_0_1218]),
[final] ).
cnf(i_0_2373,plain,
( hAPP_f2009550088ol_nat(finite1306199131a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X2)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1)))) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X2),X1))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(rw,[status(thm)],[i_0_1439,c_0_1218]),
[final] ).
cnf(i_0_2374,plain,
( hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X2)))) = hAPP_nat_nat(suc,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(rw,[status(thm)],[i_0_1440,c_0_1216]),
[final] ).
cnf(i_0_2375,plain,
( hAPP_f55526627ol_nat(finite1340463720e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X2)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1)))) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X2),X1))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(rw,[status(thm)],[i_0_1441,c_0_1216]),
[final] ).
cnf(i_0_2376,plain,
( hAPP_fun_a_bool_nat(finite_card_a,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)))) = hAPP_nat_nat(suc,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(rw,[status(thm)],[i_0_1442,c_0_1214]),
[final] ).
cnf(i_0_2377,plain,
( hAPP_fun_a_bool_nat(finite_card_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1)))) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(rw,[status(thm)],[i_0_1443,c_0_1214]),
[final] ).
cnf(i_0_2378,plain,
( hAPP_f921600141ol_nat(finite_card_pname,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)))) = hAPP_nat_nat(suc,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(rw,[status(thm)],[i_0_1444,c_0_1220]),
[final] ).
cnf(i_0_2379,plain,
( hAPP_f921600141ol_nat(finite_card_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1)))) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(rw,[status(thm)],[i_0_1445,c_0_1220]),
[final] ).
cnf(i_0_2380,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk72_3(X1,X2,X3)),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1302]),
[final] ).
cnf(i_0_2381,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk74_3(X1,X2,X3)),X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2382,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk76_3(X1,X2,X3)),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_nat_pname(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1304]),
[final] ).
cnf(i_0_2383,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk73_3(X1,X2,X3)),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1305]),
[final] ).
cnf(i_0_2384,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk75_3(X1,X2,X3)),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1306]),
[final] ).
cnf(i_0_2385,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk77_3(X1,X2,X3)),X3))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1307]),
[final] ).
cnf(i_0_2386,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk78_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_1308]),
[final] ).
cnf(i_0_2387,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X1),X3)),hAPP_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_1381]),
[final] ).
cnf(i_0_2388,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X3)),hAPP_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_1382]),
[final] ).
cnf(i_0_2389,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,esk57_3(X2,X1,X3))))
| hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1446]),
[final] ).
cnf(i_0_2390,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(minus_minus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_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_1447]),
[final] ).
cnf(i_0_2391,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X3))))
| X1 != X2 ),
inference(rw,[status(thm)],[i_0_1448,c_0_1235]),
[final] ).
cnf(i_0_2392,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X3))))
| X1 != X2 ),
inference(rw,[status(thm)],[i_0_1449,c_0_1235]),
[final] ).
cnf(i_0_2393,plain,
( hBOOL(hAPP_nat_bool(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X3)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1450,c_0_1235]),
[final] ).
cnf(i_0_2394,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),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_1451,c_0_1235]),
[final] ).
cnf(i_0_2395,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1)))),
inference(rw,[status(thm)],[i_0_1452,c_0_1235]),
[final] ).
cnf(i_0_2396,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X2)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(rw,[status(thm)],[i_0_1453,c_0_1233]),
[final] ).
cnf(i_0_2397,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X2)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(rw,[status(thm)],[i_0_1454,c_0_1233]),
[final] ).
cnf(i_0_2398,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(rw,[status(thm)],[i_0_1455,c_0_1235]),
[final] ).
cnf(i_0_2399,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(rw,[status(thm)],[i_0_1456,c_0_1235]),
[final] ).
cnf(i_0_2400,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool))))
| X1 != X2 ),
inference(rw,[status(thm)],[i_0_1457,c_0_1235]),
[final] ).
cnf(i_0_2401,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_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_1447]),
[final] ).
cnf(i_0_2402,plain,
( hBOOL(hAPP_nat_bool(X1,X2))
| ~ hBOOL(hAPP_nat_bool(X1,esk128_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_1437]),
[final] ).
cnf(i_0_2403,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X3),hAPP_nat_nat(minus_minus_nat(hAPP_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_1458]),
[final] ).
cnf(i_0_2404,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))
| 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)) != 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),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1459,c_0_1235]),c_0_1235]),
[final] ).
cnf(i_0_2405,plain,
( hBOOL(hAPP_nat_bool(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),X3)),X2))
| X1 != X2 ),
inference(rw,[status(thm)],[i_0_1460,c_0_1235]),
[final] ).
cnf(i_0_2406,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(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1461]),
[final] ).
cnf(i_0_2407,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(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1462]),
[final] ).
cnf(i_0_2408,plain,
( is_fun1661590463l_bool(collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X2))))
| ~ is_fun_pname_bool(X1)
| ~ is_fun1661590463l_bool(X2) ),
inference(rw,[status(thm)],[i_0_1463,c_0_1216]),
[final] ).
cnf(i_0_2409,plain,
( is_fun949378684l_bool(collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X2))))
| ~ is_fun_a_bool(X1)
| ~ is_fun949378684l_bool(X2) ),
inference(rw,[status(thm)],[i_0_1464,c_0_1218]),
[final] ).
cnf(i_0_2410,plain,
( is_fun_pname_bool(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))))
| ~ is_fun_pname_bool(X2)
| ~ is_pname(X1) ),
inference(rw,[status(thm)],[i_0_1465,c_0_1220]),
[final] ).
cnf(i_0_2411,hypothesis,
( is_fun_a_bool(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))))
| ~ is_fun_a_bool(X2)
| ~ is_a(X1) ),
inference(rw,[status(thm)],[i_0_1466,c_0_1214]),
[final] ).
cnf(i_0_2412,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_1467]),
[final] ).
cnf(i_0_2413,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_1467]),
[final] ).
cnf(i_0_2414,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_1468]),
[final] ).
cnf(i_0_2415,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_1468]),
[final] ).
cnf(i_0_2416,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_1469]),
[final] ).
cnf(i_0_2417,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_1469]),
[final] ).
cnf(i_0_2418,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_1470]),
[final] ).
cnf(i_0_2419,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_1470]),
[final] ).
cnf(i_0_2420,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_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_1471]),
[final] ).
cnf(i_0_2421,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X1),X3)),hAPP_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_1472]),
[final] ).
cnf(i_0_2422,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X3),X2)),hAPP_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_1473]),
[final] ).
cnf(i_0_2423,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_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_1474]),
[final] ).
cnf(i_0_2424,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(X1,esk57_3(X2,X1,X3)))
| ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1446]),
[final] ).
cnf(i_0_2425,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_1475]),
[final] ).
cnf(i_0_2426,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_1476]),
[final] ).
cnf(i_0_2427,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_1477]),
[final] ).
cnf(i_0_2428,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_1478]),
[final] ).
cnf(i_0_2429,plain,
( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X2)),X1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X2)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),bot_bo1649642514l_bool)))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1479,c_0_1216]),
[final] ).
cnf(i_0_2430,plain,
( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X2)),X1)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X2)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),bot_bo1389914601l_bool)))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1480,c_0_1218]),
[final] ).
cnf(i_0_2431,plain,
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),X1)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool)))
| ~ hBOOL(hAPP_pname_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1481,c_0_1220]),
[final] ).
cnf(i_0_2432,plain,
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))
| ~ hBOOL(hAPP_a_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1482,c_0_1214]),
[final] ).
cnf(i_0_2433,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(minus_minus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1483]),
[final] ).
cnf(i_0_2434,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1484]),
[final] ).
cnf(i_0_2435,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_1485]),
[final] ).
cnf(i_0_2436,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_1486]),
[final] ).
cnf(i_0_2437,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk9_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_1384]),
[final] ).
cnf(i_0_2438,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk1_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_1385]),
[final] ).
cnf(i_0_2439,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk10_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_1386]),
[final] ).
cnf(i_0_2440,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk2_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_1387]),
[final] ).
cnf(i_0_2441,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk11_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_1388]),
[final] ).
cnf(i_0_2442,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk3_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_1389]),
[final] ).
cnf(i_0_2443,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk25_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_1390]),
[final] ).
cnf(i_0_2444,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk24_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_1391]),
[final] ).
cnf(i_0_2445,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk23_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_1392]),
[final] ).
cnf(i_0_2446,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk21_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_1393]),
[final] ).
cnf(i_0_2447,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk27_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_1394]),
[final] ).
cnf(i_0_2448,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk19_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_1395]),
[final] ).
cnf(i_0_2449,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk18_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_1396]),
[final] ).
cnf(i_0_2450,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk17_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_1397]),
[final] ).
cnf(i_0_2451,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk8_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_1398]),
[final] ).
cnf(i_0_2452,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk7_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_1399]),
[final] ).
cnf(i_0_2453,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk6_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_1400]),
[final] ).
cnf(i_0_2454,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk4_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_1401]),
[final] ).
cnf(i_0_2455,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk13_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_1402]),
[final] ).
cnf(i_0_2456,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk14_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_1403]),
[final] ).
cnf(i_0_2457,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk15_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_1404]),
[final] ).
cnf(i_0_2458,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk26_3(X1,X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_nat_nat(X1,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1405]),
[final] ).
cnf(i_0_2459,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk22_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_1406]),
[final] ).
cnf(i_0_2460,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_1407]),
[final] ).
cnf(i_0_2461,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk16_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_1408]),
[final] ).
cnf(i_0_2462,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk12_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_1409]),
[final] ).
cnf(i_0_2463,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk5_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_1410]),
[final] ).
cnf(i_0_2464,plain,
( hBOOL(hAPP_f1637334154l_bool(X1,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,esk115_2(X1,X2)),esk116_2(X1,X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1013]),
[final] ).
cnf(i_0_2465,plain,
( hBOOL(hAPP_f1935102916l_bool(X1,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,esk117_2(X1,X2)),esk118_2(X1,X2)))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_990]),
[final] ).
cnf(i_0_2466,plain,
( hBOOL(hAPP_f621171935l_bool(X1,X2))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,esk119_2(X1,X2)),esk120_2(X1,X2)))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_991]),
[final] ).
cnf(i_0_2467,plain,
( hBOOL(hAPP_f1637334154l_bool(X1,esk110_3(X1,X2,X3)))
| hBOOL(hAPP_f1637334154l_bool(X1,X3))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_966]),
[final] ).
cnf(i_0_2468,plain,
( hBOOL(hAPP_f1935102916l_bool(X1,esk112_3(X1,X2,X3)))
| hBOOL(hAPP_f1935102916l_bool(X1,X3))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_955]),
[final] ).
cnf(i_0_2469,plain,
( hBOOL(hAPP_f621171935l_bool(X1,esk114_3(X1,X2,X3)))
| hBOOL(hAPP_f621171935l_bool(X1,X3))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_957]),
[final] ).
cnf(i_0_2470,plain,
( hBOOL(hAPP_f54304608l_bool(X1,esk104_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_969]),
[final] ).
cnf(i_0_2471,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,esk106_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_959]),
[final] ).
cnf(i_0_2472,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,esk108_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_961]),
[final] ).
cnf(i_0_2473,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk110_3(X1,X2,X3)))
| hBOOL(hAPP_f1637334154l_bool(X1,X3))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X3),X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_966]),
[final] ).
cnf(i_0_2474,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk112_3(X1,X2,X3)))
| hBOOL(hAPP_f1935102916l_bool(X1,X3))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_955]),
[final] ).
cnf(i_0_2475,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk114_3(X1,X2,X3)))
| hBOOL(hAPP_f621171935l_bool(X1,X3))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_957]),
[final] ).
cnf(i_0_2476,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,esk104_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_969]),
[final] ).
cnf(i_0_2477,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk106_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_959]),
[final] ).
cnf(i_0_2478,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,esk108_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_961]),
[final] ).
cnf(i_0_2479,plain,
( collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,X2)),X1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X2)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),bot_bo1649642514l_bool)))
| ~ hBOOL(hAPP_f1664156314l_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1487,c_0_1216]),
[final] ).
cnf(i_0_2480,plain,
( collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,X2)),X1)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X2)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),bot_bo1389914601l_bool)))
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1488,c_0_1218]),
[final] ).
cnf(i_0_2481,plain,
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,X2)),X1)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),bot_bo844097828e_bool)))
| ~ hBOOL(hAPP_pname_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1489,c_0_1220]),
[final] ).
cnf(i_0_2482,plain,
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,X2)),X1)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))
| ~ hBOOL(hAPP_a_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1490,c_0_1214]),
[final] ).
cnf(i_0_2483,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(minus_minus_nat(X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1483]),
[final] ).
cnf(i_0_2484,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X3)),X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1484]),
[final] ).
cnf(i_0_2485,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_1491]),
[final] ).
cnf(i_0_2486,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_1492]),
[final] ).
cnf(i_0_2487,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_1493]),
[final] ).
cnf(i_0_2488,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_1494]),
[final] ).
cnf(i_0_2489,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_1495]),
[final] ).
cnf(i_0_2490,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_1496]),
[final] ).
cnf(i_0_2491,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_1497]),
[final] ).
cnf(i_0_2492,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_1498]),
[final] ).
cnf(i_0_2493,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_1499]),
[final] ).
cnf(i_0_2494,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_1500]),
[final] ).
cnf(i_0_2495,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_1501]),
[final] ).
cnf(i_0_2496,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_1502]),
[final] ).
cnf(i_0_2497,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_1503]),
[final] ).
cnf(i_0_2498,plain,
( hAPP_f22106695ol_nat(finite_card_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))) = hAPP_f22106695ol_nat(finite_card_nat,X2)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1504,c_0_1235]),
[final] ).
cnf(i_0_2499,plain,
( hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2))) = hAPP_f696928925ol_nat(finite346522414t_bool,X2)
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1505,c_0_1233]),
[final] ).
cnf(i_0_2500,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_1467]),
[final] ).
cnf(i_0_2501,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_1468]),
[final] ).
cnf(i_0_2502,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_1469]),
[final] ).
cnf(i_0_2503,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_1470]),
[final] ).
cnf(i_0_2504,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X2),X1))),X3) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2)),hAPP_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_1506]),
[final] ).
cnf(i_0_2505,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(plus_plus_nat(X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1507]),
[final] ).
cnf(i_0_2506,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(plus_plus_nat(X1),X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_2507,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(plus_plus_nat(X3),X1)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1508]),
[final] ).
cnf(i_0_2508,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(plus_plus_nat(X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1509]),
[final] ).
cnf(i_0_2509,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(plus_plus_nat(X1),X2)),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1510]),
[final] ).
cnf(i_0_2510,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_1511]),
[final] ).
cnf(i_0_2511,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_1511]),
[final] ).
cnf(i_0_2512,plain,
( hAPP_f22106695ol_nat(finite_card_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))) = hAPP_nat_nat(suc,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(rw,[status(thm)],[i_0_1512,c_0_1235]),
[final] ).
cnf(i_0_2513,plain,
( hAPP_f22106695ol_nat(finite_card_nat,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1))) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(rw,[status(thm)],[i_0_1513,c_0_1235]),
[final] ).
cnf(i_0_2514,plain,
( hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2))) = hAPP_nat_nat(suc,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(rw,[status(thm)],[i_0_1514,c_0_1233]),
[final] ).
cnf(i_0_2515,plain,
( hAPP_f696928925ol_nat(finite346522414t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X2)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1))) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X2),X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(rw,[status(thm)],[i_0_1515,c_0_1233]),
[final] ).
cnf(i_0_2516,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_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_1516]),
[final] ).
cnf(i_0_2517,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_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_1461]),
[final] ).
cnf(i_0_2518,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),X3)),hAPP_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_1517]),
[final] ).
cnf(i_0_2519,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_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_1462]),
[final] ).
cnf(i_0_2520,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X3)),hAPP_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_1518]),
[final] ).
cnf(i_0_2521,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X3),X2)),hAPP_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_1519]),
[final] ).
cnf(i_0_2522,plain,
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),hAPP_pname_nat(X3,X1))),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),image_pname_nat(X3,X2))) = image_pname_nat(X3,X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1520,c_0_1235]),
[final] ).
cnf(i_0_2523,plain,
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),hAPP_a_nat(X3,X1))),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),image_a_nat(X3,X2))) = image_a_nat(X3,X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1521,c_0_1235]),
[final] ).
cnf(i_0_2524,plain,
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))) != bot_bo844097828e_bool,
inference(rw,[status(thm)],[i_0_1522,c_0_1220]),
[final] ).
cnf(i_0_2525,plain,
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))) != bot_bot_fun_a_bool,
inference(rw,[status(thm)],[i_0_1523,c_0_1214]),
[final] ).
cnf(i_0_2526,plain,
bot_bo844097828e_bool != 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(rw,[status(thm)],[i_0_1524,c_0_1220]),
[final] ).
cnf(i_0_2527,plain,
bot_bot_fun_a_bool != 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(rw,[status(thm)],[i_0_1525,c_0_1214]),
[final] ).
cnf(i_0_2528,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_1526]),
[final] ).
cnf(i_0_2529,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_1527]),
[final] ).
cnf(i_0_2530,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_1528]),
[final] ).
cnf(i_0_2531,plain,
( 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),bot_bot_fun_nat_bool)) != cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1529,c_0_1235]),c_0_1235]),
[final] ).
cnf(i_0_2532,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_1530]),
[final] ).
cnf(i_0_2533,plain,
( image_pname_a(cOMBK_a_pname(X3),X2) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1531,c_0_1214]),
[final] ).
cnf(i_0_2534,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X2)),hAPP_nat_nat(suc,X3)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X3),
inference(split_conjunct,[status(thm)],[i_0_1532]),
[final] ).
cnf(i_0_2535,plain,
( collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1))) = X1
| ~ is_fun_pname_bool(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(rw,[status(thm)],[i_0_1533,c_0_1220]),
[final] ).
cnf(i_0_2536,plain,
( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1))) = X1
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X1)) ),
inference(rw,[status(thm)],[i_0_1534,c_0_1214]),
[final] ).
cnf(i_0_2537,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),hAPP_nat_nat(minus_minus_nat(X3),X1)) = hAPP_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_1535]),
[final] ).
cnf(i_0_2538,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),esk133_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_1536]),
[final] ).
cnf(i_0_2539,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_1537]),
[final] ).
cnf(i_0_2540,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_1537]),
[final] ).
cnf(i_0_2541,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_1538]),
[final] ).
cnf(i_0_2542,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_1538]),
[final] ).
cnf(i_0_2543,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_1539]),
[final] ).
cnf(i_0_2544,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_1539]),
[final] ).
cnf(i_0_2545,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_1540]),
[final] ).
cnf(i_0_2546,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_1540]),
[final] ).
cnf(i_0_2547,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_1541]),
[final] ).
cnf(i_0_2548,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_1542]),
[final] ).
cnf(i_0_2549,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_1543]),
[final] ).
cnf(i_0_2550,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_1544]),
[final] ).
cnf(i_0_2551,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_1545]),
[final] ).
cnf(i_0_2552,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_1546]),
[final] ).
cnf(i_0_2553,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_1547]),
[final] ).
cnf(i_0_2554,plain,
( X1 = image_1921560913_pname(X2,esk9_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_1384]),
[final] ).
cnf(i_0_2555,plain,
( X1 = image_fun_nat_bool_a(X2,esk1_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_1385]),
[final] ).
cnf(i_0_2556,plain,
( X1 = image_1283814551_pname(X2,esk10_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_1386]),
[final] ).
cnf(i_0_2557,plain,
( X1 = image_876012084bool_a(X2,esk2_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_1387]),
[final] ).
cnf(i_0_2558,plain,
( X1 = image_1854862208_pname(X2,esk11_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_1388]),
[final] ).
cnf(i_0_2559,plain,
( X1 = image_fun_a_bool_a(X2,esk3_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_1389]),
[final] ).
cnf(i_0_2560,plain,
( X1 = image_1655916159e_bool(X2,esk23_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_1392]),
[final] ).
cnf(i_0_2561,plain,
( X1 = image_nat_fun_a_bool(X2,esk24_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_1391]),
[final] ).
cnf(i_0_2562,plain,
( X1 = image_nat_pname(X2,esk25_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_1390]),
[final] ).
cnf(i_0_2563,plain,
( X1 = image_nat_a(X2,esk21_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_1393]),
[final] ).
cnf(i_0_2564,plain,
( X1 = image_47868345e_bool(X2,esk17_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_1397]),
[final] ).
cnf(i_0_2565,plain,
( X1 = image_112932426a_bool(X2,esk18_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_1396]),
[final] ).
cnf(i_0_2566,plain,
( X1 = image_pname_pname(X2,esk19_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_1395]),
[final] ).
cnf(i_0_2567,plain,
( X1 = image_pname_a(X2,esk27_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_1394]),
[final] ).
cnf(i_0_2568,plain,
( X1 = image_819518260e_bool(X2,esk6_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_1400]),
[final] ).
cnf(i_0_2569,plain,
( X1 = image_a_fun_a_bool(X2,esk7_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_1399]),
[final] ).
cnf(i_0_2570,plain,
( X1 = image_a_pname(X2,esk8_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_1398]),
[final] ).
cnf(i_0_2571,plain,
( X1 = image_a_a(X2,esk4_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_1401]),
[final] ).
cnf(i_0_2572,plain,
( X1 = image_a_fun_nat_bool(X2,esk5_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_1410]),
[final] ).
cnf(i_0_2573,plain,
( X1 = image_nat_nat(X2,esk26_3(X2,X3,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),image_nat_nat(X2,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1405]),
[final] ).
cnf(i_0_2574,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_1407]),
[final] ).
cnf(i_0_2575,plain,
( X1 = image_fun_a_bool_nat(X2,esk15_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_1404]),
[final] ).
cnf(i_0_2576,plain,
( X1 = image_1551609309ol_nat(X2,esk14_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_1403]),
[final] ).
cnf(i_0_2577,plain,
( X1 = image_496248727ol_nat(X2,esk13_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_1402]),
[final] ).
cnf(i_0_2578,plain,
( X1 = image_a_nat(X2,esk12_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_1409]),
[final] ).
cnf(i_0_2579,plain,
( X1 = image_26036933t_bool(X2,esk22_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_1406]),
[final] ).
cnf(i_0_2580,plain,
( X1 = image_2129980159t_bool(X2,esk16_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_1408]),
[final] ).
cnf(i_0_2581,plain,
( is_fun1661590463l_bool(esk10_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_1386]),
[final] ).
cnf(i_0_2582,plain,
( is_fun1661590463l_bool(esk2_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_1387]),
[final] ).
cnf(i_0_2583,plain,
( is_fun949378684l_bool(esk11_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_1388]),
[final] ).
cnf(i_0_2584,plain,
( is_fun949378684l_bool(esk3_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_1389]),
[final] ).
cnf(i_0_2585,plain,
( is_fun_pname_bool(esk27_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_1394]),
[final] ).
cnf(i_0_2586,plain,
( is_fun_pname_bool(esk19_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_1395]),
[final] ).
cnf(i_0_2587,plain,
( is_fun_pname_bool(esk18_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_1396]),
[final] ).
cnf(i_0_2588,plain,
( is_fun_pname_bool(esk17_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_1397]),
[final] ).
cnf(i_0_2589,plain,
( is_fun_a_bool(esk8_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_1398]),
[final] ).
cnf(i_0_2590,plain,
( is_fun_a_bool(esk7_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_1399]),
[final] ).
cnf(i_0_2591,plain,
( is_fun_a_bool(esk6_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_1400]),
[final] ).
cnf(i_0_2592,plain,
( is_fun_a_bool(esk4_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_1401]),
[final] ).
cnf(i_0_2593,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[i_0_1548]),
[final] ).
cnf(i_0_2594,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X2)),
inference(split_conjunct,[status(thm)],[i_0_1549]),
[final] ).
cnf(i_0_2595,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk69_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1550]),
[final] ).
cnf(i_0_2596,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk70_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1551]),
[final] ).
cnf(i_0_2597,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,esk71_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1552]),
[final] ).
cnf(i_0_2598,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(X1,X3)),hAPP_pname_bool(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ is_pname(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1370]),
[final] ).
cnf(i_0_2599,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_1371]),
[final] ).
cnf(i_0_2600,plain,
( hAPP_nat_nat(minus_minus_nat(X3),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X2),X1))) = hAPP_nat_nat(minus_minus_nat(hAPP_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_1553]),
[final] ).
cnf(i_0_2601,plain,
( is_fun1661590463l_bool(esk14_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_1403]),
[final] ).
cnf(i_0_2602,plain,
( is_fun949378684l_bool(esk15_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_1404]),
[final] ).
cnf(i_0_2603,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_1407]),
[final] ).
cnf(i_0_2604,plain,
( is_fun_pname_bool(esk16_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_1408]),
[final] ).
cnf(i_0_2605,plain,
( is_fun_a_bool(esk12_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_1409]),
[final] ).
cnf(i_0_2606,plain,
( is_fun_a_bool(esk5_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_1410]),
[final] ).
cnf(i_0_2607,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(X3,X1)),image_pname_nat(X3,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1554]),
[final] ).
cnf(i_0_2608,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(X3,X1)),image_a_nat(X3,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1555]),
[final] ).
cnf(i_0_2609,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(X3,X1)),image_a_nat(X3,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1556]),
[final] ).
cnf(i_0_2610,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(X3,X1)),image_a_pname(X3,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1557]),
[final] ).
cnf(i_0_2611,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(X3,X1)),image_nat_pname(X3,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1558]),
[final] ).
cnf(i_0_2612,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(X3,X1)),image_nat_a(X3,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1559]),
[final] ).
cnf(i_0_2613,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_1560]),
[final] ).
cnf(i_0_2614,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(X3,X1)),image_nat_a(X3,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1561]),
[final] ).
cnf(i_0_2615,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_1562]),
[final] ).
cnf(i_0_2616,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_1563]),
[final] ).
cnf(i_0_2617,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_1564]),
[final] ).
cnf(i_0_2618,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_1369]),
[final] ).
cnf(i_0_2619,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(X1,X3)),hAPP_pname_bool(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1565]),
[final] ).
cnf(i_0_2620,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(X1,X3)),hAPP_pname_bool(X2,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1566]),
[final] ).
cnf(i_0_2621,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_1567]),
[final] ).
cnf(i_0_2622,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_1568]),
[final] ).
cnf(i_0_2623,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_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_1569]),
[final] ).
cnf(i_0_2624,plain,
( is_fun1661590463l_bool(esk112_3(X1,X2,X3))
| hBOOL(hAPP_f1935102916l_bool(X1,X3))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_955]),
[final] ).
cnf(i_0_2625,plain,
( is_fun_pname_bool(esk111_3(X1,X2,X3))
| hBOOL(hAPP_f1935102916l_bool(X1,X3))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X3),X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_955]),
[final] ).
cnf(i_0_2626,plain,
( is_fun949378684l_bool(esk114_3(X1,X2,X3))
| hBOOL(hAPP_f621171935l_bool(X1,X3))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_957]),
[final] ).
cnf(i_0_2627,plain,
( is_fun_a_bool(esk113_3(X1,X2,X3))
| hBOOL(hAPP_f621171935l_bool(X1,X3))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X3),X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_957]),
[final] ).
cnf(i_0_2628,plain,
( is_pname(esk105_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_959]),
[final] ).
cnf(i_0_2629,plain,
( is_fun_pname_bool(esk106_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_959]),
[final] ).
cnf(i_0_2630,plain,
( is_a(esk107_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_961]),
[final] ).
cnf(i_0_2631,plain,
( is_fun_a_bool(esk108_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_961]),
[final] ).
cnf(i_0_2632,plain,
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)) = 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)],[inference(rw,[status(thm)],[i_0_1570,c_0_971]),c_0_971]),c_0_1235]),
[final] ).
cnf(i_0_2633,plain,
cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X2)) = cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1))),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1571,c_0_968]),c_0_968]),c_0_1233]),
[final] ).
cnf(i_0_2634,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_1572]),
[final] ).
cnf(i_0_2635,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_1573]),
[final] ).
cnf(i_0_2636,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_1574]),
[final] ).
cnf(i_0_2637,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_1575]),
[final] ).
cnf(i_0_2638,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_1576]),
[final] ).
cnf(i_0_2639,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_1526]),
[final] ).
cnf(i_0_2640,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_1577]),
[final] ).
cnf(i_0_2641,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_1528]),
[final] ).
cnf(i_0_2642,plain,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,esk42_2(X1,X2)),X2))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_998]),
[final] ).
cnf(i_0_2643,plain,
( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,esk36_2(X1,X2)),X2))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_999]),
[final] ).
cnf(i_0_2644,plain,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,esk43_2(X1,X2)),X2))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1236]),
[final] ).
cnf(i_0_2645,plain,
( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,esk37_2(X1,X2)),X2))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1237]),
[final] ).
cnf(i_0_2646,plain,
( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,esk44_2(X1,X2)),X2))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1238]),
[final] ).
cnf(i_0_2647,plain,
( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,esk38_2(X1,X2)),X2))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1239]),
[final] ).
cnf(i_0_2648,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk48_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_1002]),
[final] ).
cnf(i_0_2649,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk47_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_1001]),
[final] ).
cnf(i_0_2650,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk46_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_1000]),
[final] ).
cnf(i_0_2651,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk45_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1005]),
[final] ).
cnf(i_0_2652,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk39_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_nat_nat(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1003]),
[final] ).
cnf(i_0_2653,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk33_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1004]),
[final] ).
cnf(i_0_2654,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk56_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_1245]),
[final] ).
cnf(i_0_2655,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk51_2(X1,X2)),X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1242]),
[final] ).
cnf(i_0_2656,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk50_2(X1,X2)),X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1241]),
[final] ).
cnf(i_0_2657,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk49_2(X1,X2)),X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1240]),
[final] ).
cnf(i_0_2658,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk41_2(X1,X2)),X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1243]),
[final] ).
cnf(i_0_2659,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk35_2(X1,X2)),X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1244]),
[final] ).
cnf(i_0_2660,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk55_2(X1,X2)),X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1248]),
[final] ).
cnf(i_0_2661,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk54_2(X1,X2)),X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1247]),
[final] ).
cnf(i_0_2662,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk53_2(X1,X2)),X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1246]),
[final] ).
cnf(i_0_2663,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk52_2(X1,X2)),X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1251]),
[final] ).
cnf(i_0_2664,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk40_2(X1,X2)),X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1249]),
[final] ).
cnf(i_0_2665,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk34_2(X1,X2)),X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1250]),
[final] ).
cnf(i_0_2666,plain,
( X1 = hAPP_nat_pname(X2,esk64_3(X1,X2,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),image_nat_pname(X2,X3)))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1428]),
[final] ).
cnf(i_0_2667,plain,
( X1 = hAPP_nat_a(X2,esk65_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_nat_a(X2,X3)))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1427]),
[final] ).
cnf(i_0_2668,plain,
( X1 = hAPP_pname_a(X2,esk68_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_1431]),
[final] ).
cnf(i_0_2669,plain,
( X1 = hAPP_pname_a(X2,esk59_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_1432]),
[final] ).
cnf(i_0_2670,plain,
( X1 = image_nat_a(X2,esk60_3(X1,X2,X3))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),image_nat_a(X2,X3)))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1429]),
[final] ).
cnf(i_0_2671,plain,
( X1 = image_pname_a(X2,esk63_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_1430]),
[final] ).
cnf(i_0_2672,plain,
( X1 = image_a_pname(X2,esk61_3(X1,X2,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),image_a_pname(X2,X3)))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1433]),
[final] ).
cnf(i_0_2673,plain,
( X1 = hAPP_pname_nat(X2,esk66_3(X1,X2,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),image_pname_nat(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1434]),
[final] ).
cnf(i_0_2674,plain,
( X1 = hAPP_a_nat(X2,esk67_3(X1,X2,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),image_a_nat(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1436]),
[final] ).
cnf(i_0_2675,plain,
( X1 = image_a_nat(X2,esk62_3(X1,X2,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),image_a_nat(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1435]),
[final] ).
cnf(i_0_2676,plain,
( is_pname(esk68_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_1431]),
[final] ).
cnf(i_0_2677,plain,
( is_pname(esk59_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_1432]),
[final] ).
cnf(i_0_2678,plain,
( is_fun_pname_bool(esk63_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_1430]),
[final] ).
cnf(i_0_2679,plain,
( is_fun_a_bool(esk61_3(X1,X2,X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),image_a_pname(X2,X3)))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1433]),
[final] ).
cnf(i_0_2680,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_1578]),
[final] ).
cnf(i_0_2681,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_1579]),
[final] ).
cnf(i_0_2682,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_1580]),
[final] ).
cnf(i_0_2683,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_1581]),
[final] ).
cnf(i_0_2684,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_1582]),
[final] ).
cnf(i_0_2685,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_1583]),
[final] ).
cnf(i_0_2686,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_1584]),
[final] ).
cnf(i_0_2687,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1585]),
[final] ).
cnf(i_0_2688,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X3))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1586]),
[final] ).
cnf(i_0_2689,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1587]),
[final] ).
cnf(i_0_2690,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_1588]),
[final] ).
cnf(i_0_2691,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_1589]),
[final] ).
cnf(i_0_2692,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_1590]),
[final] ).
cnf(i_0_2693,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_1591]),
[final] ).
cnf(i_0_2694,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_1592]),
[final] ).
cnf(i_0_2695,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_1593]),
[final] ).
cnf(i_0_2696,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_1594]),
[final] ).
cnf(i_0_2697,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_1595]),
[final] ).
cnf(i_0_2698,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_1596]),
[final] ).
cnf(i_0_2699,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_1597]),
[final] ).
cnf(i_0_2700,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_1598]),
[final] ).
cnf(i_0_2701,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_1599]),
[final] ).
cnf(i_0_2702,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_1600]),
[final] ).
cnf(i_0_2703,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_1601]),
[final] ).
cnf(i_0_2704,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1602]),
[final] ).
cnf(i_0_2705,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1603]),
[final] ).
cnf(i_0_2706,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_1604]),
[final] ).
cnf(i_0_2707,plain,
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),X3) = hAPP_nat_nat(minus_minus_nat(hAPP_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_1605]),
[final] ).
cnf(i_0_2708,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X2),X3)),X1) = hAPP_nat_nat(plus_plus_nat(hAPP_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_1606]),
[final] ).
cnf(i_0_2709,plain,
( is_pname(esk66_3(X1,X2,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),image_pname_nat(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1434]),
[final] ).
cnf(i_0_2710,plain,
( is_a(esk67_3(X1,X2,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),image_a_nat(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1436]),
[final] ).
cnf(i_0_2711,plain,
( is_fun_a_bool(esk62_3(X1,X2,X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),image_a_nat(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1435]),
[final] ).
cnf(i_0_2712,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_1607]),
[final] ).
cnf(i_0_2713,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk124_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1608]),
[final] ).
cnf(i_0_2714,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk80_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1609]),
[final] ).
cnf(i_0_2715,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,esk130_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1610]),
[final] ).
cnf(i_0_2716,plain,
( X1 = X3
| hAPP_nat_nat(minus_minus_nat(X1),X2) != hAPP_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_1611]),
[final] ).
cnf(i_0_2717,plain,
( X1 = hAPP_nat_nat(suc,esk133_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_1536]),
[final] ).
cnf(i_0_2718,plain,
( X2 = hAPP_nat_nat(suc,esk58_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_1612]),
[final] ).
cnf(i_0_2719,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_1613]),
[final] ).
cnf(i_0_2720,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_1614,c_0_971]),
[final] ).
cnf(i_0_2721,plain,
collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),bot_bo1649642514l_bool))),
inference(rw,[status(thm)],[i_0_1615,c_0_1216]),
[final] ).
cnf(i_0_2722,plain,
collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),bot_bo1389914601l_bool))),
inference(rw,[status(thm)],[i_0_1616,c_0_1218]),
[final] ).
cnf(i_0_2723,plain,
collect_pname(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1)) = 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),bot_bo844097828e_bool))),
inference(rw,[status(thm)],[i_0_1617,c_0_1220]),
[final] ).
cnf(i_0_2724,plain,
collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1)) = 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),bot_bot_fun_a_bool))),
inference(rw,[status(thm)],[i_0_1618,c_0_1214]),
[final] ).
cnf(i_0_2725,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1619,c_0_968]),c_0_968]),
[final] ).
cnf(i_0_2726,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X2),X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1620,c_0_968]),c_0_968]),
[final] ).
cnf(i_0_2727,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_1621,c_0_971]),c_0_971]),
[final] ).
cnf(i_0_2728,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_1622,c_0_971]),c_0_971]),
[final] ).
cnf(i_0_2729,plain,
( is_pname(esk78_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_1308]),
[final] ).
cnf(i_0_2730,plain,
( is_pname(esk73_3(X1,X2,X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_pname_pname(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1305]),
[final] ).
cnf(i_0_2731,plain,
( is_pname(esk72_3(X1,X2,X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1302]),
[final] ).
cnf(i_0_2732,plain,
( is_a(esk75_3(X1,X2,X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1306]),
[final] ).
cnf(i_0_2733,plain,
( is_a(esk74_3(X1,X2,X3))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(X1,X3)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1303]),
[final] ).
cnf(i_0_2734,plain,
( X1 = bot_bo844097828e_bool
| image_pname_a(cOMBK_a_pname(X2),X1) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool)))
| ~ is_fun_pname_bool(X1) ),
inference(rw,[status(thm)],[i_0_1623,c_0_1214]),
[final] ).
cnf(i_0_2735,plain,
collec1974731493e_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),bot_bo1649642514l_bool))),
inference(rw,[status(thm)],[i_0_1624,c_0_1216]),
[final] ).
cnf(i_0_2736,plain,
collect_fun_a_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),bot_bo1389914601l_bool))),
inference(rw,[status(thm)],[i_0_1625,c_0_1218]),
[final] ).
cnf(i_0_2737,plain,
collect_pname(hAPP_p61793385e_bool(fequal_pname,X1)) = 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),bot_bo844097828e_bool))),
inference(rw,[status(thm)],[i_0_1626,c_0_1220]),
[final] ).
cnf(i_0_2738,plain,
collect_a(hAPP_a_fun_a_bool(fequal_a,X1)) = 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),bot_bot_fun_a_bool))),
inference(rw,[status(thm)],[i_0_1627,c_0_1214]),
[final] ).
cnf(i_0_2739,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_1628]),
[final] ).
cnf(i_0_2740,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_1574]),
[final] ).
cnf(i_0_2741,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_1575]),
[final] ).
cnf(i_0_2742,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X3),image_a_pname(X4,X2)))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X3 != image_a_pname(X4,X1)
| ~ is_fun_pname_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1433]),
[final] ).
cnf(i_0_2743,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_1430]),
[final] ).
cnf(i_0_2744,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_1432]),
[final] ).
cnf(i_0_2745,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_1629]),
[final] ).
cnf(i_0_2746,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_1630]),
[final] ).
cnf(i_0_2747,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_2748,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X3),image_a_nat(X4,X2)))
| ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X3 != image_a_nat(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1435]),
[final] ).
cnf(i_0_2749,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X3),image_nat_a(X4,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X3 != image_nat_a(X4,X1)
| ~ is_fun_a_bool(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1429]),
[final] ).
cnf(i_0_2750,plain,
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),X1) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1631,c_0_971]),c_0_1235]),
[final] ).
cnf(i_0_2751,plain,
( cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X2)),X1) = cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X2)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f54304608l_bool(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1632,c_0_968]),c_0_1233]),
[final] ).
cnf(i_0_2752,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3),X2)),X1) = hAPP_nat_nat(plus_plus_nat(X3),hAPP_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_1633]),
[final] ).
cnf(i_0_2753,plain,
( hAPP_nat_nat(plus_plus_nat(X3),hAPP_nat_nat(minus_minus_nat(X2),X1)) = hAPP_nat_nat(minus_minus_nat(hAPP_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_1634]),
[final] ).
cnf(i_0_2754,plain,
( hAPP_nat_nat(minus_minus_nat(X3),hAPP_nat_nat(minus_minus_nat(X2),X1)) = hAPP_nat_nat(minus_minus_nat(hAPP_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_1635]),
[final] ).
cnf(i_0_2755,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(suc,X1))),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2756,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),X2)))),
inference(split_conjunct,[status(thm)],[i_0_1637]),
[final] ).
cnf(i_0_2757,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X2),X1)))),
inference(split_conjunct,[status(thm)],[i_0_1638]),
[final] ).
cnf(i_0_2758,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_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_1639]),
[final] ).
cnf(i_0_2759,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_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_1640]),
[final] ).
cnf(i_0_2760,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_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_1641]),
[final] ).
cnf(i_0_2761,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_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_1642]),
[final] ).
cnf(i_0_2762,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_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_1643]),
[final] ).
cnf(i_0_2763,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_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_1644]),
[final] ).
cnf(i_0_2764,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_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_1645]),
[final] ).
cnf(i_0_2765,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_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_1646]),
[final] ).
cnf(i_0_2766,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_1647]),
[final] ).
cnf(i_0_2767,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_1648]),
[final] ).
cnf(i_0_2768,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_1649]),
[final] ).
cnf(i_0_2769,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_1650]),
[final] ).
cnf(i_0_2770,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_1651]),
[final] ).
cnf(i_0_2771,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_1652]),
[final] ).
cnf(i_0_2772,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_1653]),
[final] ).
cnf(i_0_2773,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_1654]),
[final] ).
cnf(i_0_2774,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_1655]),
[final] ).
cnf(i_0_2775,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),image_nat_nat(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1656]),
[final] ).
cnf(i_0_2776,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),image_pname_nat(X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1657]),
[final] ).
cnf(i_0_2777,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_1658]),
[final] ).
cnf(i_0_2778,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_1659]),
[final] ).
cnf(i_0_2779,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_1660]),
[final] ).
cnf(i_0_2780,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_1661]),
[final] ).
cnf(i_0_2781,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_1662]),
[final] ).
cnf(i_0_2782,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_1663]),
[final] ).
cnf(i_0_2783,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_1664]),
[final] ).
cnf(i_0_2784,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_1665]),
[final] ).
cnf(i_0_2785,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_1666]),
[final] ).
cnf(i_0_2786,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_1667]),
[final] ).
cnf(i_0_2787,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_1668]),
[final] ).
cnf(i_0_2788,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_1669]),
[final] ).
cnf(i_0_2789,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_1670]),
[final] ).
cnf(i_0_2790,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),image_pname_nat(X2,X4)))
| X1 != hAPP_pname_nat(X2,X3)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2791,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),image_a_nat(X2,X4)))
| X1 != hAPP_a_nat(X2,X3)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_2792,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),image_pname_nat(X4,X2)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| X3 != hAPP_pname_nat(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2793,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),image_a_nat(X4,X2)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| X3 != hAPP_a_nat(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1674]),
[final] ).
cnf(i_0_2794,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),image_nat_pname(X2,X4)))
| X1 != hAPP_nat_pname(X2,X3)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1675]),
[final] ).
cnf(i_0_2795,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X3),image_nat_pname(X4,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| X3 != hAPP_nat_pname(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1676]),
[final] ).
cnf(i_0_2796,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),image_nat_a(X2,X4)))
| X1 != hAPP_nat_a(X2,X3)
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X3),X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1677]),
[final] ).
cnf(i_0_2797,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_1678]),
[final] ).
cnf(i_0_2798,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X3),image_nat_a(X4,X2)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| X3 != hAPP_nat_a(X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1679]),
[final] ).
cnf(i_0_2799,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_1680]),
[final] ).
cnf(i_0_2800,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_1681]),
[final] ).
cnf(i_0_2801,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_1682]),
[final] ).
cnf(i_0_2802,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_1683]),
[final] ).
cnf(i_0_2803,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_1684]),
[final] ).
cnf(i_0_2804,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_1685]),
[final] ).
cnf(i_0_2805,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_1686]),
[final] ).
cnf(i_0_2806,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),esk134_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_1687]),
[final] ).
cnf(i_0_2807,plain,
( cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,X2)),X1) = cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),bot_bot_fun_nat_bool))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1688,c_0_971]),c_0_1235]),
[final] ).
cnf(i_0_2808,plain,
( cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,X2)),X1) = cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X2)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f54304608l_bool(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1689,c_0_968]),c_0_1233]),
[final] ).
cnf(i_0_2809,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(plus_plus_nat(X3),X2) != hAPP_nat_nat(plus_plus_nat(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1690]),
[final] ).
cnf(i_0_2810,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1),X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1691,c_0_968]),c_0_968]),c_0_968]),
[final] ).
cnf(i_0_2811,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_1692,c_0_971]),c_0_971]),c_0_971]),
[final] ).
cnf(i_0_2812,plain,
( X1 = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1693]),
[final] ).
cnf(i_0_2813,plain,
( X1 = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1694]),
[final] ).
cnf(i_0_2814,plain,
( X1 = X2
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1695]),
[final] ).
cnf(i_0_2815,plain,
( X2 = X1
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1696]),
[final] ).
cnf(i_0_2816,plain,
( X1 = X2
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1697]),
[final] ).
cnf(i_0_2817,plain,
( X1 = X2
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1698]),
[final] ).
cnf(i_0_2818,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_1699]),
[final] ).
cnf(i_0_2819,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_1700]),
[final] ).
cnf(i_0_2820,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_1701]),
[final] ).
cnf(i_0_2821,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_1702]),
[final] ).
cnf(i_0_2822,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_1703]),
[final] ).
cnf(i_0_2823,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_1704]),
[final] ).
cnf(i_0_2824,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk69_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1550]),
[final] ).
cnf(i_0_2825,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk70_2(X1,X2)),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1551]),
[final] ).
cnf(i_0_2826,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk71_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_1552]),
[final] ).
cnf(i_0_2827,plain,
( 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)) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(rw,[status(thm)],[i_0_1705,c_0_1235]),
[final] ).
cnf(i_0_2828,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1706]),
[final] ).
cnf(i_0_2829,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1706]),
[final] ).
cnf(i_0_2830,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1707]),
[final] ).
cnf(i_0_2831,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1707]),
[final] ).
cnf(i_0_2832,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1708]),
[final] ).
cnf(i_0_2833,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1708]),
[final] ).
cnf(i_0_2834,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1709]),
[final] ).
cnf(i_0_2835,plain,
( hBOOL(X2)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1709]),
[final] ).
cnf(i_0_2836,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),esk123_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_1608]),
[final] ).
cnf(i_0_2837,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),esk79_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_1609]),
[final] ).
cnf(i_0_2838,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_1604]),
[final] ).
cnf(i_0_2839,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_1541]),
[final] ).
cnf(i_0_2840,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_1710]),
[final] ).
cnf(i_0_2841,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_1711]),
[final] ).
cnf(i_0_2842,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_1712]),
[final] ).
cnf(i_0_2843,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_1713]),
[final] ).
cnf(i_0_2844,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_1714]),
[final] ).
cnf(i_0_2845,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_1715]),
[final] ).
cnf(i_0_2846,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_1716]),
[final] ).
cnf(i_0_2847,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_1717]),
[final] ).
cnf(i_0_2848,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_1718]),
[final] ).
cnf(i_0_2849,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_1719]),
[final] ).
cnf(i_0_2850,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_1720]),
[final] ).
cnf(i_0_2851,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_1681]),
[final] ).
cnf(i_0_2852,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_1721]),
[final] ).
cnf(i_0_2853,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_1722]),
[final] ).
cnf(i_0_2854,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_1685]),
[final] ).
cnf(i_0_2855,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_1629]),
[final] ).
cnf(i_0_2856,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_1723]),
[final] ).
cnf(i_0_2857,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_1724]),
[final] ).
cnf(i_0_2858,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_1725]),
[final] ).
cnf(i_0_2859,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2)),X1) = hAPP_nat_nat(suc,hAPP_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_1726]),
[final] ).
cnf(i_0_2860,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X2))
| collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X2)),X1)) = bot_bo1649642514l_bool ),
inference(split_conjunct,[status(thm)],[i_0_1101]),
[final] ).
cnf(i_0_2861,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X2)),X1)) = bot_bo1389914601l_bool ),
inference(split_conjunct,[status(thm)],[i_0_1102]),
[final] ).
cnf(i_0_2862,plain,
( hBOOL(hAPP_pname_bool(X1,X2))
| collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X2)),X1)) = bot_bo844097828e_bool ),
inference(split_conjunct,[status(thm)],[i_0_1103]),
[final] ).
cnf(i_0_2863,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_1104]),
[final] ).
cnf(i_0_2864,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),X1)),
inference(split_conjunct,[status(thm)],[i_0_1727]),
[final] ).
cnf(i_0_2865,plain,
( X2 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),esk129_2(X1,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1728]),
[final] ).
cnf(i_0_2866,plain,
( X2 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),esk125_2(X1,X2)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1729]),
[final] ).
cnf(i_0_2867,plain,
( hAPP_nat_nat(plus_plus_nat(hAPP_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_1730]),
[final] ).
cnf(i_0_2868,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1),X2)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1731,c_0_968]),c_0_968]),
[final] ).
cnf(i_0_2869,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X2),X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1732,c_0_968]),c_0_968]),
[final] ).
cnf(i_0_2870,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_1733,c_0_971]),c_0_971]),
[final] ).
cnf(i_0_2871,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_1734,c_0_971]),c_0_971]),
[final] ).
cnf(i_0_2872,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_1735]),
[final] ).
cnf(i_0_2873,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_1736]),
[final] ).
cnf(i_0_2874,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_1737]),
[final] ).
cnf(i_0_2875,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_1738]),
[final] ).
cnf(i_0_2876,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_1739]),
[final] ).
cnf(i_0_2877,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1707]),
[final] ).
cnf(i_0_2878,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_2879,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X3))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1741]),
[final] ).
cnf(i_0_2880,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X1))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_2881,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1743]),
[final] ).
cnf(i_0_2882,plain,
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)) != bot_bot_fun_nat_bool,
inference(rw,[status(thm)],[i_0_1744,c_0_1235]),
[final] ).
cnf(i_0_2883,plain,
bot_bot_fun_nat_bool != 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_1745,c_0_1235]),
[final] ).
cnf(i_0_2884,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk124_2(X1,X2)),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1608]),
[final] ).
cnf(i_0_2885,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk80_2(X1,X2)),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1609]),
[final] ).
cnf(i_0_2886,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk130_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1610]),
[final] ).
cnf(i_0_2887,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1707]),
[final] ).
cnf(i_0_2888,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_2889,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X2),X3))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1741]),
[final] ).
cnf(i_0_2890,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X1))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_2891,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X2))
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X3),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1743]),
[final] ).
cnf(i_0_2892,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_1682]),
[final] ).
cnf(i_0_2893,plain,
( hBOOL(hAPP_f1637334154l_bool(X1,esk116_2(X1,X2)))
| hBOOL(hAPP_f1637334154l_bool(X1,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1013]),
[final] ).
cnf(i_0_2894,plain,
( hBOOL(hAPP_f1935102916l_bool(X1,esk118_2(X1,X2)))
| hBOOL(hAPP_f1935102916l_bool(X1,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_990]),
[final] ).
cnf(i_0_2895,plain,
( hBOOL(hAPP_f621171935l_bool(X1,esk120_2(X1,X2)))
| hBOOL(hAPP_f621171935l_bool(X1,X2))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_991]),
[final] ).
cnf(i_0_2896,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_1746]),
[final] ).
cnf(i_0_2897,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_1747]),
[final] ).
cnf(i_0_2898,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_1748]),
[final] ).
cnf(i_0_2899,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_1607]),
[final] ).
cnf(i_0_2900,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,X2))
| collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,hAPP_f434788991l_bool(fequal533582459e_bool,X2)),X1)) = bot_bo1649642514l_bool ),
inference(split_conjunct,[status(thm)],[i_0_1105]),
[final] ).
cnf(i_0_2901,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,X2))
| collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,hAPP_f1631501043l_bool(fequal_fun_a_bool,X2)),X1)) = bot_bo1389914601l_bool ),
inference(split_conjunct,[status(thm)],[i_0_1106]),
[final] ).
cnf(i_0_2902,plain,
( hBOOL(hAPP_pname_bool(X1,X2))
| collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_p61793385e_bool(fequal_pname,X2)),X1)) = bot_bo844097828e_bool ),
inference(split_conjunct,[status(thm)],[i_0_1107]),
[final] ).
cnf(i_0_2903,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_1108]),
[final] ).
cnf(i_0_2904,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,esk116_2(X1,X2)))
| hBOOL(hAPP_f1637334154l_bool(X1,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(X1,bot_bo1701429464l_bool))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1013]),
[final] ).
cnf(i_0_2905,plain,
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,esk118_2(X1,X2)))
| hBOOL(hAPP_f1935102916l_bool(X1,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_990]),
[final] ).
cnf(i_0_2906,plain,
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,esk120_2(X1,X2)))
| hBOOL(hAPP_f621171935l_bool(X1,X2))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_991]),
[final] ).
cnf(i_0_2907,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_1749]),
[final] ).
cnf(i_0_2908,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_1746]),
[final] ).
cnf(i_0_2909,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_1747]),
[final] ).
cnf(i_0_2910,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_1750]),
[final] ).
cnf(i_0_2911,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_1751]),
[final] ).
cnf(i_0_2912,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X3) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X3)),X2),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_2913,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_1753]),
[final] ).
cnf(i_0_2914,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_1754]),
[final] ).
cnf(i_0_2915,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_1755]),
[final] ).
cnf(i_0_2916,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_1756]),
[final] ).
cnf(i_0_2917,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_1757]),
[final] ).
cnf(i_0_2918,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_1758]),
[final] ).
cnf(i_0_2919,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_1759]),
[final] ).
cnf(i_0_2920,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_1760]),
[final] ).
cnf(i_0_2921,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_1761]),
[final] ).
cnf(i_0_2922,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_1762]),
[final] ).
cnf(i_0_2923,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_1763]),
[final] ).
cnf(i_0_2924,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_1764]),
[final] ).
cnf(i_0_2925,plain,
( is_pname(esk56_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_1245]),
[final] ).
cnf(i_0_2926,plain,
( is_pname(esk51_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1242]),
[final] ).
cnf(i_0_2927,plain,
( is_pname(esk50_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1241]),
[final] ).
cnf(i_0_2928,plain,
( is_pname(esk49_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1240]),
[final] ).
cnf(i_0_2929,plain,
( is_pname(esk41_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1243]),
[final] ).
cnf(i_0_2930,plain,
( is_pname(esk35_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1244]),
[final] ).
cnf(i_0_2931,plain,
( is_a(esk55_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_a_fun_a_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1248]),
[final] ).
cnf(i_0_2932,plain,
( is_a(esk54_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_819518260e_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1247]),
[final] ).
cnf(i_0_2933,plain,
( is_a(esk53_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_a_fun_nat_bool(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1246]),
[final] ).
cnf(i_0_2934,plain,
( is_a(esk52_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1251]),
[final] ).
cnf(i_0_2935,plain,
( is_a(esk40_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1249]),
[final] ).
cnf(i_0_2936,plain,
( is_a(esk34_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1250]),
[final] ).
cnf(i_0_2937,plain,
( is_fun_pname_bool(esk43_2(X1,X2))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1236]),
[final] ).
cnf(i_0_2938,plain,
( is_fun_pname_bool(esk37_2(X1,X2))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1237]),
[final] ).
cnf(i_0_2939,plain,
( is_fun_a_bool(esk44_2(X1,X2))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1238]),
[final] ).
cnf(i_0_2940,plain,
( is_fun_a_bool(esk38_2(X1,X2))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1239]),
[final] ).
cnf(i_0_2941,plain,
( hAPP_nat_nat(plus_plus_nat(X1),hAPP_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_1765]),
[final] ).
cnf(i_0_2942,plain,
( hAPP_nat_nat(minus_minus_nat(X2),hAPP_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_1766]),
[final] ).
cnf(i_0_2943,hypothesis,
hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_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_2944,plain,
( hAPP_nat_nat(minus_minus_nat(X1),X3) = X2
| X1 != hAPP_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_1767]),
[final] ).
cnf(i_0_2945,plain,
( X1 = hAPP_nat_nat(plus_plus_nat(X3),X2)
| hAPP_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_1767]),
[final] ).
cnf(i_0_2946,plain,
( X1 = hAPP_nat_nat(suc,esk134_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_1687]),
[final] ).
cnf(i_0_2947,plain,
( X2 = hAPP_nat_nat(plus_plus_nat(X1),esk122_2(X1,X2))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1768]),
[final] ).
cnf(i_0_2948,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_1769]),
[final] ).
cnf(i_0_2949,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_1770]),
[final] ).
cnf(i_0_2950,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X2),X1))
| X1 != hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1729]),
[final] ).
cnf(i_0_2951,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_1771]),
[final] ).
cnf(i_0_2952,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_1772]),
[final] ).
cnf(i_0_2953,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X1),X3)) = hAPP_nat_nat(minus_minus_nat(X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_2954,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(plus_plus_nat(X3),X2)) = hAPP_nat_nat(minus_minus_nat(X1),X3),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_2955,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1775]),
[final] ).
cnf(i_0_2956,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X3) = hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)),
inference(split_conjunct,[status(thm)],[i_0_1776]),
[final] ).
cnf(i_0_2957,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_1777]),
[final] ).
cnf(i_0_2958,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_1778]),
[final] ).
cnf(i_0_2959,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_1779]),
[final] ).
cnf(i_0_2960,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X1),X2))),
inference(split_conjunct,[status(thm)],[i_0_1780]),
[final] ).
cnf(i_0_2961,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X1))),
inference(split_conjunct,[status(thm)],[i_0_1781]),
[final] ).
cnf(i_0_2962,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_1782]),
[final] ).
cnf(i_0_2963,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_1783]),
[final] ).
cnf(i_0_2964,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_1784]),
[final] ).
cnf(i_0_2965,plain,
( is_fun1661590463l_bool(esk118_2(X1,X2))
| hBOOL(hAPP_f1935102916l_bool(X1,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_990]),
[final] ).
cnf(i_0_2966,plain,
( is_fun949378684l_bool(esk120_2(X1,X2))
| hBOOL(hAPP_f621171935l_bool(X1,X2))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_991]),
[final] ).
cnf(i_0_2967,plain,
( is_fun_pname_bool(esk117_2(X1,X2))
| hBOOL(hAPP_f1935102916l_bool(X1,X2))
| ~ hBOOL(hAPP_f1935102916l_bool(X1,bot_bo1649642514l_bool))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_990]),
[final] ).
cnf(i_0_2968,plain,
( is_fun_a_bool(esk119_2(X1,X2))
| hBOOL(hAPP_f621171935l_bool(X1,X2))
| ~ hBOOL(hAPP_f621171935l_bool(X1,bot_bo1389914601l_bool))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_991]),
[final] ).
cnf(i_0_2969,plain,
hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1) = 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),bot_bot_fun_nat_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1785,c_0_971]),c_0_1235]),
[final] ).
cnf(i_0_2970,plain,
hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1) = cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),bot_bo1701429464l_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1786,c_0_968]),c_0_1233]),
[final] ).
cnf(i_0_2971,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_1629]),
[final] ).
cnf(i_0_2972,plain,
hAPP_n1699378549t_bool(fequal_nat,X1) = 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),bot_bot_fun_nat_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1787,c_0_971]),c_0_1235]),
[final] ).
cnf(i_0_2973,plain,
hAPP_f103356543l_bool(fequal_fun_nat_bool,X1) = cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),bot_bo1701429464l_bool)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1788,c_0_968]),c_0_1233]),
[final] ).
cnf(i_0_2974,plain,
( hAPP_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_1789]),
[final] ).
cnf(i_0_2975,plain,
( hAPP_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_1790]),
[final] ).
cnf(i_0_2976,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_1791]),
[final] ).
cnf(i_0_2977,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_1792]),
[final] ).
cnf(i_0_2978,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_1793]),
[final] ).
cnf(i_0_2979,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_1794]),
[final] ).
cnf(i_0_2980,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_1795]),
[final] ).
cnf(i_0_2981,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_1796]),
[final] ).
cnf(i_0_2982,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_1797]),
[final] ).
cnf(i_0_2983,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_1798]),
[final] ).
cnf(i_0_2984,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(minus_minus_nat(X1),X2)) = X1 ),
inference(split_conjunct,[status(thm)],[i_0_1799]),
[final] ).
cnf(i_0_2985,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_2986,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_2987,plain,
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(rw,[status(thm)],[i_0_1800,c_0_968]),
[final] ).
cnf(i_0_2988,plain,
hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(suc,X2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1),one_one_nat)),X2),
inference(split_conjunct,[status(thm)],[i_0_1801]),
[final] ).
cnf(i_0_2989,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_1802,c_0_971]),
[final] ).
cnf(i_0_2990,plain,
( cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X2)),X1) = bot_bo1701429464l_bool
| hBOOL(hAPP_f54304608l_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1803,c_0_968]),
[final] ).
cnf(i_0_2991,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1804]),
[final] ).
cnf(i_0_2992,plain,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1805]),
[final] ).
cnf(i_0_2993,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_1681]),
[final] ).
cnf(i_0_2994,plain,
( hBOOL(bot_bot_bool)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),bot_bot_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1806]),
[final] ).
cnf(i_0_2995,plain,
( hBOOL(bot_bot_bool)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),bot_bot_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1807]),
[final] ).
cnf(i_0_2996,plain,
( hBOOL(X1)
| ~ hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),bot_bot_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1806]),
[final] ).
cnf(i_0_2997,plain,
( hBOOL(X1)
| ~ hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),bot_bot_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1807]),
[final] ).
cnf(i_0_2998,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1808]),
[final] ).
cnf(i_0_2999,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1809]),
[final] ).
cnf(i_0_3000,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_1782]),
[final] ).
cnf(i_0_3001,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_1783]),
[final] ).
cnf(i_0_3002,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_1784]),
[final] ).
cnf(i_0_3003,plain,
( X1 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),bot_bo844097828e_bool))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1810]),
[final] ).
cnf(i_0_3004,plain,
( X1 = bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),bot_bo844097828e_bool))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1811]),
[final] ).
cnf(i_0_3005,plain,
( X1 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),bot_bo844097828e_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1812]),
[final] ).
cnf(i_0_3006,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_1813]),
[final] ).
cnf(i_0_3007,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_1814]),
[final] ).
cnf(i_0_3008,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_1815]),
[final] ).
cnf(i_0_3009,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1816]),
[final] ).
cnf(i_0_3010,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1817]),
[final] ).
cnf(i_0_3011,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1772]),
[final] ).
cnf(i_0_3012,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1772]),
[final] ).
cnf(i_0_3013,plain,
( X1 != X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1746]),
[final] ).
cnf(i_0_3014,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_1818]),
[final] ).
cnf(i_0_3015,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_1819]),
[final] ).
cnf(i_0_3016,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_1820]),
[final] ).
cnf(i_0_3017,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_1821]),
[final] ).
cnf(i_0_3018,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_1822]),
[final] ).
cnf(i_0_3019,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_1823]),
[final] ).
cnf(i_0_3020,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_1824]),
[final] ).
cnf(i_0_3021,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_1825]),
[final] ).
cnf(i_0_3022,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_1826]),
[final] ).
cnf(i_0_3023,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_1827]),
[final] ).
cnf(i_0_3024,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_1828]),
[final] ).
cnf(i_0_3025,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_1829]),
[final] ).
cnf(i_0_3026,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_1830]),
[final] ).
cnf(i_0_3027,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_1831]),
[final] ).
cnf(i_0_3028,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_1832]),
[final] ).
cnf(i_0_3029,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_1833]),
[final] ).
cnf(i_0_3030,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_1834]),
[final] ).
cnf(i_0_3031,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_1835]),
[final] ).
cnf(i_0_3032,plain,
( X1 != bot_bo844097828e_bool
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1836]),
[final] ).
cnf(i_0_3033,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_1837]),
[final] ).
cnf(i_0_3034,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_1838]),
[final] ).
cnf(i_0_3035,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1839]),
[final] ).
cnf(i_0_3036,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1840]),
[final] ).
cnf(i_0_3037,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X1))),
inference(split_conjunct,[status(thm)],[i_0_1841]),
[final] ).
cnf(i_0_3038,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1842]),
[final] ).
cnf(i_0_3039,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1843]),
[final] ).
cnf(i_0_3040,plain,
hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3)) = hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(plus_plus_nat(X1),X3)),
inference(split_conjunct,[status(thm)],[i_0_1844]),
[final] ).
cnf(i_0_3041,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,X1)),X2) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1845]),
[final] ).
cnf(i_0_3042,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_1846]),
[final] ).
cnf(i_0_3043,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_1847]),
[final] ).
cnf(i_0_3044,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_1848]),
[final] ).
cnf(i_0_3045,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_1849]),
[final] ).
cnf(i_0_3046,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_1850]),
[final] ).
cnf(i_0_3047,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_1851]),
[final] ).
cnf(i_0_3048,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_1852]),
[final] ).
cnf(i_0_3049,plain,
~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),bot_bot_fun_nat_bool)),
inference(split_conjunct,[status(thm)],[i_0_1853]),
[final] ).
cnf(i_0_3050,plain,
~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),bot_bot_fun_nat_bool)),
inference(split_conjunct,[status(thm)],[i_0_1854]),
[final] ).
cnf(i_0_3051,plain,
~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),bot_bo844097828e_bool)),
inference(split_conjunct,[status(thm)],[i_0_1855]),
[final] ).
cnf(i_0_3052,plain,
~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),bot_bo844097828e_bool)),
inference(split_conjunct,[status(thm)],[i_0_1856]),
[final] ).
cnf(i_0_3053,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_1857]),
[final] ).
cnf(i_0_3054,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_1858]),
[final] ).
cnf(i_0_3055,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),zero_zero_nat)),
inference(split_conjunct,[status(thm)],[i_0_1859]),
[final] ).
cnf(i_0_3056,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_1860,c_0_971]),
[final] ).
cnf(i_0_3057,plain,
( cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,hAPP_f103356543l_bool(fequal_fun_nat_bool,X2)),X1) = bot_bo1701429464l_bool
| hBOOL(hAPP_f54304608l_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1861,c_0_968]),
[final] ).
cnf(i_0_3058,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1))
| X1 != hAPP_nat_nat(plus_plus_nat(X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1768]),
[final] ).
cnf(i_0_3059,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_3060,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk101_1(X1)),X1))
| X1 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1791]),
[final] ).
cnf(i_0_3061,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk98_1(X1)),X1))
| X1 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1793]),
[final] ).
cnf(i_0_3062,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk102_1(X1)),X1))
| X1 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1792]),
[final] ).
cnf(i_0_3063,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_1794]),
[final] ).
cnf(i_0_3064,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),hAPP_nat_nat(suc,X2)) = hAPP_nat_nat(minus_minus_nat(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_1862]),
[final] ).
cnf(i_0_3065,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,X1)),X2) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(suc,X2)),
inference(split_conjunct,[status(thm)],[i_0_1863]),
[final] ).
cnf(i_0_3066,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(minus_minus_nat(X1),X2) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_1789]),
[final] ).
cnf(i_0_3067,plain,
( is_pname(esk82_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1370]),
[final] ).
cnf(i_0_3068,plain,
( is_pname(esk70_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1551]),
[final] ).
cnf(i_0_3069,plain,
( is_a(esk84_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1371]),
[final] ).
cnf(i_0_3070,plain,
( is_a(esk71_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1552]),
[final] ).
cnf(i_0_3071,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_1864]),
[final] ).
cnf(i_0_3072,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_1865]),
[final] ).
cnf(i_0_3073,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_1866]),
[final] ).
cnf(i_0_3074,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_1867]),
[final] ).
cnf(i_0_3075,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_1868]),
[final] ).
cnf(i_0_3076,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_1869]),
[final] ).
cnf(i_0_3077,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk100_1(X1)),X1))
| X1 = bot_bot_fun_nat_bool ),
inference(split_conjunct,[status(thm)],[i_0_1834]),
[final] ).
cnf(i_0_3078,plain,
( X1 = bot_bot_fun_nat_bool
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk97_1(X1)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1838]),
[final] ).
cnf(i_0_3079,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X1) = X2,
inference(split_conjunct,[status(thm)],[i_0_1870]),
[final] ).
cnf(i_0_3080,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X2) = X1,
inference(split_conjunct,[status(thm)],[i_0_1871]),
[final] ).
cnf(i_0_3081,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X1 != X2
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1693]),
[final] ).
cnf(i_0_3082,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X2 != X1
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1693]),
[final] ).
cnf(i_0_3083,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X1 != X2
| ~ is_fun_pname_bool(X1)
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1697]),
[final] ).
cnf(i_0_3084,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X2 != X1
| ~ is_fun_pname_bool(X2)
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1697]),
[final] ).
cnf(i_0_3085,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_1699]),
[final] ).
cnf(i_0_3086,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_1699]),
[final] ).
cnf(i_0_3087,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_1703]),
[final] ).
cnf(i_0_3088,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_1703]),
[final] ).
cnf(i_0_3089,plain,
hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(suc,X2)) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1872]),
[final] ).
cnf(i_0_3090,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_1873]),
[final] ).
cnf(i_0_3091,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_1874]),
[final] ).
cnf(i_0_3092,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_1875]),
[final] ).
cnf(i_0_3093,plain,
hAPP_f54304608l_bool(hAPP_p130839763l_bool(cOMBC_615407716e_bool(X1),X2),X3) = hAPP_pname_bool(hAPP_f654413245e_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1876]),
[final] ).
cnf(i_0_3094,plain,
hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X1),X2),X3) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1877]),
[final] ).
cnf(i_0_3095,plain,
hAPP_f54304608l_bool(hAPP_n215258509l_bool(cOMBC_385542954t_bool(X1),X2),X3) = hAPP_nat_bool(hAPP_f800510211t_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1878]),
[final] ).
cnf(i_0_3096,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_1879]),
[final] ).
cnf(i_0_3097,plain,
hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X1),X2),X3) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1880]),
[final] ).
cnf(i_0_3098,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_1881]),
[final] ).
cnf(i_0_3099,plain,
hAPP_f1664156314l_bool(hAPP_n850744903l_bool(cOMBC_1666426608t_bool(X1),X2),X3) = hAPP_nat_bool(hAPP_f1066163005t_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1882]),
[final] ).
cnf(i_0_3100,plain,
hAPP_f1664156314l_bool(hAPP_p338031245l_bool(cOMBC_1004116266e_bool(X1),X2),X3) = hAPP_pname_bool(hAPP_f759274231e_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1883]),
[final] ).
cnf(i_0_3101,plain,
hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X1),X2),X3) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1884]),
[final] ).
cnf(i_0_3102,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_1885]),
[final] ).
cnf(i_0_3103,plain,
hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(cOMBC_619334683t_bool(X1),X2),X3) = hAPP_nat_bool(hAPP_f282463732t_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1886]),
[final] ).
cnf(i_0_3104,plain,
hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(cOMBC_1738168533e_bool(X1),X2),X3) = hAPP_pname_bool(hAPP_f1794073134e_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1887]),
[final] ).
cnf(i_0_3105,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_1888]),
[final] ).
cnf(i_0_3106,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_1889]),
[final] ).
cnf(i_0_3107,plain,
hAPP_nat_bool(hAPP_a_fun_nat_bool(cOMBC_nat_a_bool(X1),X2),X3) = hAPP_a_bool(hAPP_nat_fun_a_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1890]),
[final] ).
cnf(i_0_3108,plain,
hAPP_nat_bool(hAPP_p1499970991t_bool(cOMBC_nat_pname_bool(X1),X2),X3) = hAPP_pname_bool(hAPP_n1025906991e_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_3109,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_1892]),
[final] ).
cnf(i_0_3110,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_1893]),
[final] ).
cnf(i_0_3111,plain,
hAPP_pname_bool(hAPP_f654413245e_bool(cOMBC_267053842l_bool(X1),X2),X3) = hAPP_f54304608l_bool(hAPP_p130839763l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1894]),
[final] ).
cnf(i_0_3112,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_1895]),
[final] ).
cnf(i_0_3113,plain,
hAPP_pname_bool(hAPP_f1794073134e_bool(cOMBC_445755039l_bool(X1),X2),X3) = hAPP_fun_a_bool_bool(hAPP_p1824510254l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_3114,plain,
hAPP_pname_bool(hAPP_n1025906991e_bool(cOMBC_pname_nat_bool(X1),X2),X3) = hAPP_nat_bool(hAPP_p1499970991t_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1897]),
[final] ).
cnf(i_0_3115,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_1898]),
[final] ).
cnf(i_0_3116,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_1899]),
[final] ).
cnf(i_0_3117,plain,
hAPP_a_bool(hAPP_f1549043526a_bool(cOMBC_777206479l_bool(X1),X2),X3) = hAPP_f54304608l_bool(hAPP_a1392362872l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1900]),
[final] ).
cnf(i_0_3118,plain,
hAPP_a_bool(hAPP_f1051908748a_bool(cOMBC_1834145417l_bool(X1),X2),X3) = hAPP_f1664156314l_bool(hAPP_a217006258l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1901]),
[final] ).
cnf(i_0_3119,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_1902]),
[final] ).
cnf(i_0_3120,plain,
hAPP_a_bool(hAPP_nat_fun_a_bool(cOMBC_a_nat_bool(X1),X2),X3) = hAPP_nat_bool(hAPP_a_fun_nat_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1903]),
[final] ).
cnf(i_0_3121,plain,
hAPP_a_bool(hAPP_p1534023578a_bool(cOMBC_a_pname_bool(X1),X2),X3) = hAPP_pname_bool(hAPP_a93125764e_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1904]),
[final] ).
cnf(i_0_3122,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_1905]),
[final] ).
cnf(i_0_3123,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_1906,c_0_971]),
[final] ).
cnf(i_0_3124,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_1907,c_0_971]),
[final] ).
cnf(i_0_3125,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1706]),
[final] ).
cnf(i_0_3126,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
| ~ hBOOL(X2)
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1706]),
[final] ).
cnf(i_0_3127,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1908]),
[final] ).
cnf(i_0_3128,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1909]),
[final] ).
cnf(i_0_3129,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
| hBOOL(X1)
| hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1706]),
[final] ).
cnf(i_0_3130,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2))
| hBOOL(X2)
| hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1706]),
[final] ).
cnf(i_0_3131,plain,
( hBOOL(X1)
| hBOOL(X2)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1908]),
[final] ).
cnf(i_0_3132,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),bot_bot_bool))
| ~ hBOOL(X1)
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[i_0_1806]),
[final] ).
cnf(i_0_3133,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1910]),
[final] ).
cnf(i_0_3134,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1911]),
[final] ).
cnf(i_0_3135,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1912]),
[final] ).
cnf(i_0_3136,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),bot_bo844097828e_bool))
| X1 != bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1810]),
[final] ).
cnf(i_0_3137,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),bot_bo844097828e_bool))
| X1 != bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1811]),
[final] ).
cnf(i_0_3138,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_1813]),
[final] ).
cnf(i_0_3139,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_1814]),
[final] ).
cnf(i_0_3140,plain,
( hBOOL(X1)
| hBOOL(bot_bot_bool)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),bot_bot_bool)) ),
inference(split_conjunct,[status(thm)],[i_0_1806]),
[final] ).
cnf(i_0_3141,plain,
( hBOOL(X1)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1913]),
[final] ).
cnf(i_0_3142,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_1914]),
[final] ).
cnf(i_0_3143,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_1915]),
[final] ).
cnf(i_0_3144,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_1916]),
[final] ).
cnf(i_0_3145,plain,
hAPP_a1392362872l_bool(cOMBB_743407885bool_a(X1,X2),X3) = hAPP_f103356543l_bool(X1,hAPP_a_fun_nat_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1917]),
[final] ).
cnf(i_0_3146,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_1918]),
[final] ).
cnf(i_0_3147,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_1919]),
[final] ).
cnf(i_0_3148,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_1920]),
[final] ).
cnf(i_0_3149,plain,
hAPP_f282463732t_bool(cOMBB_164527437a_bool(X1,X2),X3) = hAPP_n1699378549t_bool(X1,hAPP_fun_a_bool_nat(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1921]),
[final] ).
cnf(i_0_3150,plain,
hAPP_f1066163005t_bool(cOMBB_1896684278e_bool(X1,X2),X3) = hAPP_n1699378549t_bool(X1,hAPP_f921600141ol_nat(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1922]),
[final] ).
cnf(i_0_3151,plain,
hAPP_a_fun_nat_bool(cOMBB_1321347587bool_a(X1,X2),X3) = hAPP_n1699378549t_bool(X1,hAPP_a_nat(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1923]),
[final] ).
cnf(i_0_3152,plain,
hAPP_p130839763l_bool(cOMBB_928955006_pname(X1,X2),X3) = hAPP_f103356543l_bool(X1,hAPP_p1499970991t_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1924]),
[final] ).
cnf(i_0_3153,plain,
hAPP_p1499970991t_bool(cOMBB_523834888_pname(X1,X2),X3) = hAPP_n1699378549t_bool(X1,hAPP_pname_nat(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1925]),
[final] ).
cnf(i_0_3154,plain,
hAPP_f800510211t_bool(cOMBB_1250273980t_bool(X1,X2),X3) = hAPP_n1699378549t_bool(X1,hAPP_f22106695ol_nat(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1926]),
[final] ).
cnf(i_0_3155,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_1927]),
[final] ).
cnf(i_0_3156,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_1928]),
[final] ).
cnf(i_0_3157,plain,
hAPP_f654413245e_bool(cOMBB_141086128t_bool(X1,X2),X3) = hAPP_p61793385e_bool(X1,hAPP_f1291551745_pname(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1929]),
[final] ).
cnf(i_0_3158,plain,
hAPP_f54304608l_bool(cOMBB_238756964t_bool(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_f54304608l_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1930]),
[final] ).
cnf(i_0_3159,plain,
hAPP_f759274231e_bool(cOMBB_598082538e_bool(X1,X2),X3) = hAPP_p61793385e_bool(X1,hAPP_f1297739591_pname(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1931]),
[final] ).
cnf(i_0_3160,plain,
hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_f1664156314l_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1932]),
[final] ).
cnf(i_0_3161,plain,
hAPP_f1794073134e_bool(cOMBB_1693087065a_bool(X1,X2),X3) = hAPP_p61793385e_bool(X1,hAPP_f1128469712_pname(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1933]),
[final] ).
cnf(i_0_3162,plain,
hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X1,X2),X3) = hAPP_bool_bool(X1,hAPP_fun_a_bool_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1934]),
[final] ).
cnf(i_0_3163,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_1935]),
[final] ).
cnf(i_0_3164,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_1936]),
[final] ).
cnf(i_0_3165,plain,
hAPP_n1025906991e_bool(cOMBB_1212655066ol_nat(X1,X2),X3) = hAPP_p61793385e_bool(X1,hAPP_nat_pname(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1937]),
[final] ).
cnf(i_0_3166,plain,
hAPP_nat_fun_a_bool(cOMBB_1885489796ol_nat(X1,X2),X3) = hAPP_a_fun_a_bool(X1,hAPP_nat_a(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3167,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_1939]),
[final] ).
cnf(i_0_3168,plain,
hAPP_p338031245l_bool(cOMBB_408569982_pname(X1,X2),X3) = hAPP_f434788991l_bool(X1,hAPP_p61793385e_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1940]),
[final] ).
cnf(i_0_3169,plain,
hAPP_p1824510254l_bool(cOMBB_392435466_pname(X1,X2),X3) = hAPP_f1631501043l_bool(X1,hAPP_p1534023578a_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1941]),
[final] ).
cnf(i_0_3170,plain,
hAPP_p61793385e_bool(cOMBB_542850580_pname(X1,X2),X3) = hAPP_p61793385e_bool(X1,hAPP_pname_pname(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1942]),
[final] ).
cnf(i_0_3171,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_1943]),
[final] ).
cnf(i_0_3172,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_1944]),
[final] ).
cnf(i_0_3173,plain,
hAPP_a217006258l_bool(cOMBB_1137537805bool_a(X1,X2),X3) = hAPP_f434788991l_bool(X1,hAPP_a93125764e_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1945]),
[final] ).
cnf(i_0_3174,plain,
hAPP_a85458249l_bool(cOMBB_472261505bool_a(X1,X2),X3) = hAPP_f1631501043l_bool(X1,hAPP_a_fun_a_bool(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1946]),
[final] ).
cnf(i_0_3175,plain,
hAPP_a93125764e_bool(cOMBB_610033911bool_a(X1,X2),X3) = hAPP_p61793385e_bool(X1,hAPP_a_pname(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1947]),
[final] ).
cnf(i_0_3176,plain,
hAPP_a_fun_a_bool(cOMBB_a_fun_a_bool_a(X1,X2),X3) = hAPP_a_fun_a_bool(X1,hAPP_a_a(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1948]),
[final] ).
cnf(i_0_3177,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_1949]),
[final] ).
cnf(i_0_3178,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1950]),
[final] ).
cnf(i_0_3179,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1710]),
[final] ).
cnf(i_0_3180,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1710]),
[final] ).
cnf(i_0_3181,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1951]),
[final] ).
cnf(i_0_3182,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1952]),
[final] ).
cnf(i_0_3183,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1952]),
[final] ).
cnf(i_0_3184,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1953]),
[final] ).
cnf(i_0_3185,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1714]),
[final] ).
cnf(i_0_3186,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1714]),
[final] ).
cnf(i_0_3187,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1954]),
[final] ).
cnf(i_0_3188,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1955]),
[final] ).
cnf(i_0_3189,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1956]),
[final] ).
cnf(i_0_3190,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1957]),
[final] ).
cnf(i_0_3191,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1957]),
[final] ).
cnf(i_0_3192,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1958]),
[final] ).
cnf(i_0_3193,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1959]),
[final] ).
cnf(i_0_3194,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_1960]),
[final] ).
cnf(i_0_3195,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1961]),
[final] ).
cnf(i_0_3196,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1962]),
[final] ).
cnf(i_0_3197,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1962]),
[final] ).
cnf(i_0_3198,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1963]),
[final] ).
cnf(i_0_3199,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1964]),
[final] ).
cnf(i_0_3200,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3201,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1747]),
[final] ).
cnf(i_0_3202,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1751]),
[final] ).
cnf(i_0_3203,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_3204,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_3205,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1966]),
[final] ).
cnf(i_0_3206,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1967]),
[final] ).
cnf(i_0_3207,plain,
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1968]),
[final] ).
cnf(i_0_3208,plain,
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1969]),
[final] ).
cnf(i_0_3209,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1970]),
[final] ).
cnf(i_0_3210,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1971]),
[final] ).
cnf(i_0_3211,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_3212,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1973]),
[final] ).
cnf(i_0_3213,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1974]),
[final] ).
cnf(i_0_3214,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1975]),
[final] ).
cnf(i_0_3215,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1976]),
[final] ).
cnf(i_0_3216,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1977]),
[final] ).
cnf(i_0_3217,plain,
hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_1978]),
[final] ).
cnf(i_0_3218,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_1849]),
[final] ).
cnf(i_0_3219,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_1850]),
[final] ).
cnf(i_0_3220,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_1846]),
[final] ).
cnf(i_0_3221,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_1847]),
[final] ).
cnf(i_0_3222,plain,
( X1 = hAPP_nat_nat(suc,zero_zero_nat)
| X2 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(plus_plus_nat(X2),X1) != hAPP_nat_nat(suc,zero_zero_nat) ),
inference(split_conjunct,[status(thm)],[i_0_1979]),
[final] ).
cnf(i_0_3223,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(plus_plus_nat(X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1980]),
[final] ).
cnf(i_0_3224,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X1)),
inference(split_conjunct,[status(thm)],[i_0_1981]),
[final] ).
cnf(i_0_3225,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),X1)),
inference(split_conjunct,[status(thm)],[i_0_1982]),
[final] ).
cnf(i_0_3226,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),X1)),
inference(split_conjunct,[status(thm)],[i_0_1983]),
[final] ).
cnf(i_0_3227,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,bot_bo844097828e_bool),X1)),
inference(split_conjunct,[status(thm)],[i_0_1984]),
[final] ).
cnf(i_0_3228,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_1985]),
[final] ).
cnf(i_0_3229,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_1986]),
[final] ).
cnf(i_0_3230,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)),
inference(split_conjunct,[status(thm)],[i_0_1987]),
[final] ).
cnf(i_0_3231,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)),
inference(split_conjunct,[status(thm)],[i_0_1988]),
[final] ).
cnf(i_0_3232,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),X1)),
inference(split_conjunct,[status(thm)],[i_0_1989]),
[final] ).
cnf(i_0_3233,plain,
hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,bot_bot_bool),X1)),
inference(split_conjunct,[status(thm)],[i_0_1990]),
[final] ).
cnf(i_0_3234,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(split_conjunct,[status(thm)],[conj_4]),
[final] ).
cnf(i_0_3235,plain,
( X1 = X2
| hAPP_nat_nat(minus_minus_nat(X1),X2) != zero_zero_nat
| hAPP_nat_nat(minus_minus_nat(X2),X1) != zero_zero_nat ),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_3236,plain,
( X1 = X3
| hAPP_nat_nat(plus_plus_nat(X1),X2) != hAPP_nat_nat(plus_plus_nat(X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1992]),
[final] ).
cnf(i_0_3237,plain,
( X2 = X3
| hAPP_nat_nat(plus_plus_nat(X1),X2) != hAPP_nat_nat(plus_plus_nat(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1993]),
[final] ).
cnf(i_0_3238,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),one_one_nat) = X1,
inference(split_conjunct,[status(thm)],[i_0_1994]),
[final] ).
cnf(i_0_3239,plain,
( X1 = zero_zero_nat
| X1 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(plus_plus_nat(X1),X2) != hAPP_nat_nat(suc,zero_zero_nat) ),
inference(split_conjunct,[status(thm)],[i_0_1979]),
[final] ).
cnf(i_0_3240,plain,
( X1 = hAPP_nat_nat(suc,zero_zero_nat)
| X1 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X2),X1) != hAPP_nat_nat(suc,zero_zero_nat) ),
inference(split_conjunct,[status(thm)],[i_0_1979]),
[final] ).
cnf(i_0_3241,plain,
( X1 = zero_zero_nat
| X1 = hAPP_nat_nat(suc,zero_zero_nat)
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(plus_plus_nat(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1980]),
[final] ).
cnf(i_0_3242,plain,
( X1 = hAPP_nat_nat(suc,zero_zero_nat)
| X1 = zero_zero_nat
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(plus_plus_nat(X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1980]),
[final] ).
cnf(i_0_3243,plain,
( collec1974731493e_bool(X1) != bot_bo1649642514l_bool
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1995]),
[final] ).
cnf(i_0_3244,plain,
( collect_fun_a_bool(X1) != bot_bo1389914601l_bool
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1996]),
[final] ).
cnf(i_0_3245,plain,
( collect_pname(X1) != bot_bo844097828e_bool
| ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1997]),
[final] ).
cnf(i_0_3246,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_1998]),
[final] ).
cnf(i_0_3247,plain,
( bot_bo1649642514l_bool != collec1974731493e_bool(X1)
| ~ is_fun_pname_bool(X2)
| ~ hBOOL(hAPP_f1664156314l_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3248,plain,
( bot_bo1389914601l_bool != collect_fun_a_bool(X1)
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2000]),
[final] ).
cnf(i_0_3249,plain,
( bot_bo844097828e_bool != collect_pname(X1)
| ~ is_pname(X2)
| ~ hBOOL(hAPP_pname_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_3250,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_2002]),
[final] ).
cnf(i_0_3251,plain,
hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(plus_plus_nat(X1),X2)) = zero_zero_nat,
inference(split_conjunct,[status(thm)],[i_0_2003]),
[final] ).
cnf(i_0_3252,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_2004,c_0_971]),
[final] ).
cnf(i_0_3253,plain,
( hAPP_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_1979]),
[final] ).
cnf(i_0_3254,plain,
( hAPP_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_1979]),
[final] ).
cnf(i_0_3255,plain,
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_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_1980]),
[final] ).
cnf(i_0_3256,plain,
( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_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_1980]),
[final] ).
cnf(i_0_3257,plain,
( X1 = zero_zero_nat
| X2 = zero_zero_nat
| hAPP_nat_nat(plus_plus_nat(X1),X2) != hAPP_nat_nat(suc,zero_zero_nat) ),
inference(split_conjunct,[status(thm)],[i_0_1979]),
[final] ).
cnf(i_0_3258,plain,
( X1 = zero_zero_nat
| X2 = zero_zero_nat
| hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(plus_plus_nat(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1980]),
[final] ).
cnf(i_0_3259,plain,
( ~ hBOOL(hAPP_bool_bool(fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2005]),
[final] ).
cnf(i_0_3260,plain,
( bot_bo1701429464l_bool != X1
| ~ hBOOL(hAPP_f54304608l_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2006,c_0_968]),
[final] ).
cnf(i_0_3261,plain,
( bot_bot_fun_nat_bool != X1
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2007,c_0_971]),
[final] ).
cnf(i_0_3262,plain,
( X1 != bot_bo1701429464l_bool
| ~ hBOOL(hAPP_f54304608l_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2008,c_0_968]),
[final] ).
cnf(i_0_3263,plain,
( X1 != bot_bot_fun_nat_bool
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2009,c_0_971]),
[final] ).
cnf(i_0_3264,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_3265,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_3266,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_2010]),
[final] ).
cnf(i_0_3267,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,esk87_1(X1)))
| collec1974731493e_bool(X1) = bot_bo1649642514l_bool ),
inference(split_conjunct,[status(thm)],[i_0_1995]),
[final] ).
cnf(i_0_3268,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,esk88_1(X1)))
| collect_fun_a_bool(X1) = bot_bo1389914601l_bool ),
inference(split_conjunct,[status(thm)],[i_0_1996]),
[final] ).
cnf(i_0_3269,plain,
( hBOOL(hAPP_pname_bool(X1,esk85_1(X1)))
| collect_pname(X1) = bot_bo844097828e_bool ),
inference(split_conjunct,[status(thm)],[i_0_1997]),
[final] ).
cnf(i_0_3270,plain,
( hBOOL(hAPP_a_bool(X1,esk89_1(X1)))
| collect_a(X1) = bot_bot_fun_a_bool ),
inference(split_conjunct,[status(thm)],[i_0_1998]),
[final] ).
cnf(i_0_3271,plain,
( hBOOL(hAPP_f1664156314l_bool(X1,esk93_1(X1)))
| bot_bo1649642514l_bool = collec1974731493e_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3272,plain,
( hBOOL(hAPP_fun_a_bool_bool(X1,esk94_1(X1)))
| bot_bo1389914601l_bool = collect_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2000]),
[final] ).
cnf(i_0_3273,plain,
( hBOOL(hAPP_pname_bool(X1,esk91_1(X1)))
| bot_bo844097828e_bool = collect_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_3274,plain,
( hBOOL(hAPP_a_bool(X1,esk95_1(X1)))
| bot_bot_fun_a_bool = collect_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2002]),
[final] ).
cnf(i_0_3275,plain,
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2011]),
[final] ).
cnf(i_0_3276,plain,
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2012]),
[final] ).
cnf(i_0_3277,plain,
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2013]),
[final] ).
cnf(i_0_3278,plain,
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2014]),
[final] ).
cnf(i_0_3279,plain,
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2015]),
[final] ).
cnf(i_0_3280,plain,
( hBOOL(bot_bot_bool)
| ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2016]),
[final] ).
cnf(i_0_3281,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_2017,c_0_971]),
[final] ).
cnf(i_0_3282,hypothesis,
( is_bool(hAPP_f1664156314l_bool(X1,X2))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2018]),
[final] ).
cnf(i_0_3283,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_2019]),
[final] ).
cnf(i_0_3284,plain,
( is_bool(hAPP_pname_bool(X1,X2))
| ~ is_fun_pname_bool(X1)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2020]),
[final] ).
cnf(i_0_3285,plain,
( is_bool(hAPP_a_bool(X1,X2))
| ~ is_fun_a_bool(X1)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2021]),
[final] ).
cnf(i_0_3286,plain,
( bot_bo1701429464l_bool = X1
| hBOOL(hAPP_f54304608l_bool(X1,esk92_1(X1))) ),
inference(rw,[status(thm)],[i_0_2022,c_0_968]),
[final] ).
cnf(i_0_3287,plain,
( bot_bot_fun_nat_bool = X1
| hBOOL(hAPP_nat_bool(X1,esk96_1(X1))) ),
inference(rw,[status(thm)],[i_0_2023,c_0_971]),
[final] ).
cnf(i_0_3288,plain,
( X1 = bot_bo1701429464l_bool
| hBOOL(hAPP_f54304608l_bool(X1,esk86_1(X1))) ),
inference(rw,[status(thm)],[i_0_2024,c_0_968]),
[final] ).
cnf(i_0_3289,plain,
( X1 = bot_bot_fun_nat_bool
| hBOOL(hAPP_nat_bool(X1,esk90_1(X1))) ),
inference(rw,[status(thm)],[i_0_2025,c_0_971]),
[final] ).
cnf(i_0_3290,plain,
( X1 = X2
| hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2026]),
[final] ).
cnf(i_0_3291,plain,
( X1 = X2
| hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2027]),
[final] ).
cnf(i_0_3292,plain,
hAPP_nat_nat(plus_plus_nat(X1),X2) = hAPP_nat_nat(plus_plus_nat(X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2028]),
[final] ).
cnf(i_0_3293,plain,
( is_pname(hAPP_f1297739591_pname(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2029]),
[final] ).
cnf(i_0_3294,plain,
( is_pname(hAPP_f1128469712_pname(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2030]),
[final] ).
cnf(i_0_3295,plain,
( is_pname(hAPP_pname_pname(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2031]),
[final] ).
cnf(i_0_3296,plain,
( is_pname(hAPP_a_pname(X2,X1))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2032]),
[final] ).
cnf(i_0_3297,hypothesis,
( is_a(hAPP_pname_a(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2033]),
[final] ).
cnf(i_0_3298,plain,
( is_a(hAPP_a_a(X2,X1))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2034]),
[final] ).
cnf(i_0_3299,plain,
( is_bool(hAPP_f1935102916l_bool(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2035]),
[final] ).
cnf(i_0_3300,plain,
( is_bool(hAPP_f621171935l_bool(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2036]),
[final] ).
cnf(i_0_3301,plain,
( is_bool(hAPP_bool_bool(X2,X1))
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2037]),
[final] ).
cnf(i_0_3302,plain,
( is_fun1661590463l_bool(hAPP_f559147733l_bool(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2038]),
[final] ).
cnf(i_0_3303,plain,
( is_fun1661590463l_bool(hAPP_f434788991l_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2039]),
[final] ).
cnf(i_0_3304,hypothesis,
( is_fun1661590463l_bool(hAPP_p338031245l_bool(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2040]),
[final] ).
cnf(i_0_3305,plain,
( is_fun1661590463l_bool(hAPP_a217006258l_bool(X2,X1))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2041]),
[final] ).
cnf(i_0_3306,plain,
( is_fun1661590463l_bool(image_47868345e_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2042]),
[final] ).
cnf(i_0_3307,plain,
( is_fun1661590463l_bool(image_819518260e_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2043]),
[final] ).
cnf(i_0_3308,plain,
( is_fun1661590463l_bool(cOMBS_350070575l_bool(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2044]),
[final] ).
cnf(i_0_3309,plain,
( is_fun1661590463l_bool(cOMBB_307249310e_bool(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2045]),
[final] ).
cnf(i_0_3310,plain,
( is_fun949378684l_bool(hAPP_f2117159681l_bool(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2046]),
[final] ).
cnf(i_0_3311,hypothesis,
( is_fun949378684l_bool(hAPP_f1631501043l_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2047]),
[final] ).
cnf(i_0_3312,plain,
( is_fun949378684l_bool(hAPP_p1824510254l_bool(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2048]),
[final] ).
cnf(i_0_3313,hypothesis,
( is_fun949378684l_bool(hAPP_a85458249l_bool(X2,X1))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2049]),
[final] ).
cnf(i_0_3314,plain,
( is_fun949378684l_bool(image_112932426a_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2050]),
[final] ).
cnf(i_0_3315,plain,
( is_fun949378684l_bool(image_a_fun_a_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2051]),
[final] ).
cnf(i_0_3316,plain,
( is_fun949378684l_bool(cOMBS_1035972772l_bool(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2052]),
[final] ).
cnf(i_0_3317,plain,
( is_fun949378684l_bool(cOMBB_2140588453a_bool(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2053]),
[final] ).
cnf(i_0_3318,plain,
( is_fun_pname_bool(hAPP_f759274231e_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_3319,plain,
( is_fun_pname_bool(hAPP_f1794073134e_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2055]),
[final] ).
cnf(i_0_3320,plain,
( is_fun_pname_bool(hAPP_p61793385e_bool(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2056]),
[final] ).
cnf(i_0_3321,plain,
( is_fun_pname_bool(hAPP_a93125764e_bool(X2,X1))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2057]),
[final] ).
cnf(i_0_3322,plain,
( is_fun_pname_bool(image_1283814551_pname(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2058]),
[final] ).
cnf(i_0_3323,plain,
( is_fun_pname_bool(image_1854862208_pname(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2059]),
[final] ).
cnf(i_0_3324,plain,
( is_fun_pname_bool(image_pname_pname(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2060]),
[final] ).
cnf(i_0_3325,plain,
( is_fun_pname_bool(image_a_pname(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2061]),
[final] ).
cnf(i_0_3326,plain,
( is_fun_pname_bool(cOMBS_568398431l_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2062]),
[final] ).
cnf(i_0_3327,plain,
( is_fun_pname_bool(cOMBB_647938656_pname(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2063]),
[final] ).
cnf(i_0_3328,plain,
( is_fun_a_bool(hAPP_f1051908748a_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2064]),
[final] ).
cnf(i_0_3329,plain,
( is_fun_a_bool(hAPP_f2050579477a_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2065]),
[final] ).
cnf(i_0_3330,plain,
( is_fun_a_bool(hAPP_p1534023578a_bool(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2066]),
[final] ).
cnf(i_0_3331,plain,
( is_fun_a_bool(hAPP_a_fun_a_bool(X2,X1))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2067]),
[final] ).
cnf(i_0_3332,plain,
( is_fun_a_bool(image_876012084bool_a(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2068]),
[final] ).
cnf(i_0_3333,plain,
( is_fun_a_bool(image_fun_a_bool_a(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2069]),
[final] ).
cnf(i_0_3334,hypothesis,
( is_fun_a_bool(image_pname_a(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2070]),
[final] ).
cnf(i_0_3335,plain,
( is_fun_a_bool(image_a_a(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2071]),
[final] ).
cnf(i_0_3336,plain,
( is_fun_a_bool(cOMBS_a_bool_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2072]),
[final] ).
cnf(i_0_3337,plain,
( is_fun_a_bool(cOMBB_bool_bool_a(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2073]),
[final] ).
cnf(i_0_3338,plain,
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1))
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2011]),
[final] ).
cnf(i_0_3339,plain,
( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1))
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2012]),
[final] ).
cnf(i_0_3340,plain,
( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X1))
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2013]),
[final] ).
cnf(i_0_3341,plain,
( hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X1))
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2014]),
[final] ).
cnf(i_0_3342,plain,
( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X1))
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2015]),
[final] ).
cnf(i_0_3343,plain,
( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X1))
| ~ hBOOL(bot_bot_bool) ),
inference(split_conjunct,[status(thm)],[i_0_2016]),
[final] ).
cnf(i_0_3344,plain,
( hBOOL(X1)
| hBOOL(hAPP_bool_bool(fNot,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2074]),
[final] ).
cnf(i_0_3345,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_2075]),
[final] ).
cnf(i_0_3346,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_2076]),
[final] ).
cnf(i_0_3347,plain,
hAPP_nat_nat(suc,X1) = hAPP_nat_nat(plus_plus_nat(X1),one_one_nat),
inference(split_conjunct,[status(thm)],[i_0_2077]),
[final] ).
cnf(i_0_3348,plain,
is_pname(hAPP_f1291551745_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2078]),
[final] ).
cnf(i_0_3349,plain,
is_pname(hAPP_nat_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2079]),
[final] ).
cnf(i_0_3350,plain,
is_a(hAPP_nat_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2080]),
[final] ).
cnf(i_0_3351,plain,
is_bool(hAPP_f937997336l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2081]),
[final] ).
cnf(i_0_3352,plain,
is_bool(hAPP_f389811538l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2082]),
[final] ).
cnf(i_0_3353,plain,
is_bool(hAPP_f292226953l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2083]),
[final] ).
cnf(i_0_3354,plain,
is_bool(hAPP_f1637334154l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2084]),
[final] ).
cnf(i_0_3355,plain,
is_bool(hAPP_f54304608l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2085]),
[final] ).
cnf(i_0_3356,hypothesis,
is_bool(hAPP_nat_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2086]),
[final] ).
cnf(i_0_3357,plain,
is_fun1661590463l_bool(hAPP_n850744903l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2087]),
[final] ).
cnf(i_0_3358,plain,
is_fun1661590463l_bool(image_1655916159e_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2088]),
[final] ).
cnf(i_0_3359,plain,
is_fun949378684l_bool(hAPP_n1414589940l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_3360,plain,
is_fun949378684l_bool(image_nat_fun_a_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2090]),
[final] ).
cnf(i_0_3361,plain,
is_fun_pname_bool(hAPP_f654413245e_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2091]),
[final] ).
cnf(i_0_3362,plain,
is_fun_pname_bool(hAPP_n1025906991e_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2092]),
[final] ).
cnf(i_0_3363,plain,
is_fun_pname_bool(image_1921560913_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2093]),
[final] ).
cnf(i_0_3364,plain,
is_fun_pname_bool(image_nat_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2094]),
[final] ).
cnf(i_0_3365,plain,
is_fun_a_bool(hAPP_f1549043526a_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2095]),
[final] ).
cnf(i_0_3366,plain,
is_fun_a_bool(hAPP_nat_fun_a_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2096]),
[final] ).
cnf(i_0_3367,plain,
is_fun_a_bool(image_fun_nat_bool_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2097]),
[final] ).
cnf(i_0_3368,plain,
is_fun_a_bool(image_nat_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_3369,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_1137]),
[final] ).
cnf(i_0_3370,plain,
hAPP_nat_nat(suc,X1) = hAPP_nat_nat(plus_plus_nat(one_one_nat),X1),
inference(split_conjunct,[status(thm)],[i_0_2099]),
[final] ).
cnf(i_0_3371,plain,
( hAPP_f54304608l_bool(cOMBK_1994329625t_bool(X1),X2) = X1
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2100]),
[final] ).
cnf(i_0_3372,plain,
( hAPP_f1664156314l_bool(cOMBK_1857069011e_bool(X1),X2) = X1
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2101]),
[final] ).
cnf(i_0_3373,plain,
( hAPP_fun_a_bool_bool(cOMBK_324466864a_bool(X1),X2) = X1
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2102]),
[final] ).
cnf(i_0_3374,plain,
( hAPP_nat_bool(cOMBK_bool_nat(X1),X2) = X1
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2103]),
[final] ).
cnf(i_0_3375,plain,
( hAPP_pname_bool(cOMBK_bool_pname(X1),X2) = X1
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_3376,plain,
( hAPP_pname_a(cOMBK_a_pname(X1),X2) = X1
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2105]),
[final] ).
cnf(i_0_3377,plain,
( hAPP_a_bool(cOMBK_bool_a(X1),X2) = X1
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2106]),
[final] ).
cnf(i_0_3378,plain,
hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,bot_bo1701429464l_bool)),
inference(split_conjunct,[status(thm)],[fact_386_finite_OemptyI]),
[final] ).
cnf(i_0_3379,plain,
hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,bot_bo1649642514l_bool)),
inference(split_conjunct,[status(thm)],[fact_387_finite_OemptyI]),
[final] ).
cnf(i_0_3380,plain,
hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,bot_bo1389914601l_bool)),
inference(split_conjunct,[status(thm)],[fact_388_finite_OemptyI]),
[final] ).
cnf(i_0_3381,plain,
hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
inference(split_conjunct,[status(thm)],[fact_391_finite_OemptyI]),
[final] ).
cnf(i_0_3382,hypothesis,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
inference(split_conjunct,[status(thm)],[conj_0]),
[final] ).
cnf(i_0_3383,plain,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
inference(split_conjunct,[status(thm)],[fact_390_finite_OemptyI]),
[final] ).
cnf(i_0_3384,plain,
hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
inference(split_conjunct,[status(thm)],[fact_389_finite_OemptyI]),
[final] ).
cnf(i_0_3385,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_2075]),
[final] ).
cnf(i_0_3386,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_2076]),
[final] ).
cnf(i_0_3387,plain,
hAPP_nat_nat(suc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_2107]),
[final] ).
cnf(i_0_3388,plain,
X1 != hAPP_nat_nat(suc,X1),
inference(split_conjunct,[status(thm)],[i_0_2108]),
[final] ).
cnf(i_0_3389,plain,
hAPP_nat_nat(minus_minus_nat(X1),X1) = zero_zero_nat,
inference(split_conjunct,[status(thm)],[i_0_2109]),
[final] ).
cnf(i_0_3390,plain,
hAPP_nat_nat(suc,X1) != zero_zero_nat,
inference(split_conjunct,[status(thm)],[i_0_2110]),
[final] ).
cnf(i_0_3391,plain,
hAPP_nat_nat(suc,X1) != zero_zero_nat,
inference(split_conjunct,[status(thm)],[i_0_2111]),
[final] ).
cnf(i_0_3392,plain,
hAPP_nat_nat(suc,X1) != zero_zero_nat,
inference(split_conjunct,[status(thm)],[i_0_2112]),
[final] ).
cnf(i_0_3393,plain,
zero_zero_nat != hAPP_nat_nat(suc,X1),
inference(split_conjunct,[status(thm)],[i_0_2113]),
[final] ).
cnf(i_0_3394,plain,
zero_zero_nat != hAPP_nat_nat(suc,X1),
inference(split_conjunct,[status(thm)],[i_0_2114]),
[final] ).
cnf(i_0_3395,plain,
zero_zero_nat != hAPP_nat_nat(suc,X1),
inference(split_conjunct,[status(thm)],[i_0_2115]),
[final] ).
cnf(i_0_3396,plain,
hAPP_nat_nat(minus_minus_nat(X1),zero_zero_nat) = X1,
inference(split_conjunct,[status(thm)],[i_0_2116]),
[final] ).
cnf(i_0_3397,plain,
( is_pname(esk101_1(X1))
| X1 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1791]),
[final] ).
cnf(i_0_3398,plain,
( is_pname(esk98_1(X1))
| X1 = bot_bo844097828e_bool
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1793]),
[final] ).
cnf(i_0_3399,plain,
( is_a(esk102_1(X1))
| X1 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1792]),
[final] ).
cnf(i_0_3400,plain,
( is_a(esk99_1(X1))
| X1 = bot_bot_fun_a_bool
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1794]),
[final] ).
cnf(i_0_3401,plain,
( is_fun1661590463l_bool(collec1974731493e_bool(X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2117]),
[final] ).
cnf(i_0_3402,plain,
( is_fun1661590463l_bool(cOMBK_1857069011e_bool(X1))
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2118]),
[final] ).
cnf(i_0_3403,plain,
( is_fun949378684l_bool(p(X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2119]),
[final] ).
cnf(i_0_3404,plain,
( is_fun949378684l_bool(collect_fun_a_bool(X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2120]),
[final] ).
cnf(i_0_3405,plain,
( is_fun949378684l_bool(cOMBK_324466864a_bool(X1))
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2121]),
[final] ).
cnf(i_0_3406,plain,
( is_fun_pname_bool(collect_pname(X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2122]),
[final] ).
cnf(i_0_3407,plain,
( is_fun_pname_bool(cOMBK_bool_pname(X1))
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2123]),
[final] ).
cnf(i_0_3408,plain,
( is_fun_a_bool(collect_a(X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2124]),
[final] ).
cnf(i_0_3409,plain,
( is_fun_a_bool(cOMBK_bool_a(X1))
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2125]),
[final] ).
cnf(i_0_3410,plain,
hAPP_nat_nat(minus_minus_nat(zero_zero_nat),X1) = zero_zero_nat,
inference(split_conjunct,[status(thm)],[i_0_2126]),
[final] ).
cnf(i_0_3411,plain,
( is_fun_pname_bool(esk87_1(X1))
| collec1974731493e_bool(X1) = bot_bo1649642514l_bool ),
inference(split_conjunct,[status(thm)],[i_0_1995]),
[final] ).
cnf(i_0_3412,plain,
( is_fun_a_bool(esk88_1(X1))
| collect_fun_a_bool(X1) = bot_bo1389914601l_bool ),
inference(split_conjunct,[status(thm)],[i_0_1996]),
[final] ).
cnf(i_0_3413,plain,
( is_pname(esk85_1(X1))
| collect_pname(X1) = bot_bo844097828e_bool ),
inference(split_conjunct,[status(thm)],[i_0_1997]),
[final] ).
cnf(i_0_3414,plain,
( is_a(esk89_1(X1))
| collect_a(X1) = bot_bot_fun_a_bool ),
inference(split_conjunct,[status(thm)],[i_0_1998]),
[final] ).
cnf(i_0_3415,plain,
( is_fun_pname_bool(esk93_1(X1))
| bot_bo1649642514l_bool = collec1974731493e_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3416,plain,
( is_fun_a_bool(esk94_1(X1))
| bot_bo1389914601l_bool = collect_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2000]),
[final] ).
cnf(i_0_3417,plain,
( is_pname(esk91_1(X1))
| bot_bo844097828e_bool = collect_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_3418,plain,
( is_a(esk95_1(X1))
| bot_bot_fun_a_bool = collect_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2002]),
[final] ).
cnf(i_0_3419,plain,
image_pname_a(X1,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
inference(split_conjunct,[status(thm)],[i_0_2127]),
[final] ).
cnf(i_0_3420,plain,
( collec1974731493e_bool(X1) = X1
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2128]),
[final] ).
cnf(i_0_3421,plain,
( collect_fun_a_bool(X1) = X1
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2129]),
[final] ).
cnf(i_0_3422,plain,
( collect_pname(X1) = X1
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_3423,plain,
( collect_a(X1) = X1
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2131]),
[final] ).
cnf(i_0_3424,plain,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
inference(split_conjunct,[status(thm)],[fact_686_One__nat__def]),
[final] ).
cnf(i_0_3425,plain,
is_a(mgt(X1)),
inference(split_conjunct,[status(thm)],[i_0_2132]),
[final] ).
cnf(i_0_3426,plain,
is_bool(wt(X1)),
inference(split_conjunct,[status(thm)],[i_0_2133]),
[final] ).
cnf(i_0_3427,plain,
( X1 = fTrue
| X1 = fFalse
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2134]),
[final] ).
cnf(i_0_3428,plain,
is_pname(undefined_pname(pname)),
inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Com__Opname]),
[final] ).
cnf(i_0_3429,plain,
is_a(undefined_a(x_a)),
inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000t__a]),
[final] ).
cnf(i_0_3430,plain,
bot_bo1649642514l_bool = collec1974731493e_bool(cOMBK_1857069011e_bool(fFalse)),
inference(split_conjunct,[status(thm)],[fact_421_empty__def]),
[final] ).
cnf(i_0_3431,plain,
bot_bo1389914601l_bool = collect_fun_a_bool(cOMBK_324466864a_bool(fFalse)),
inference(split_conjunct,[status(thm)],[fact_422_empty__def]),
[final] ).
cnf(i_0_3432,plain,
bot_bo844097828e_bool = collect_pname(cOMBK_bool_pname(fFalse)),
inference(split_conjunct,[status(thm)],[fact_419_empty__def]),
[final] ).
cnf(i_0_3433,plain,
bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
inference(split_conjunct,[status(thm)],[fact_423_empty__def]),
[final] ).
cnf(i_0_3434,plain,
~ hBOOL(fFalse),
inference(split_conjunct,[status(thm)],[i_0_2135]),
[final] ).
cnf(i_0_3435,hypothesis,
is_pname(pn),
inference(split_conjunct,[status(thm)],[gsy_v_pn]),
[final] ).
cnf(i_0_3436,plain,
is_bool(fTrue),
inference(split_conjunct,[status(thm)],[gsy_c_fTrue]),
[final] ).
cnf(i_0_3437,plain,
is_bool(fFalse),
inference(split_conjunct,[status(thm)],[gsy_c_fFalse]),
[final] ).
cnf(i_0_3438,plain,
is_bool(bot_bot_bool),
inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool]),
[final] ).
cnf(i_0_3439,plain,
is_fun1661590463l_bool(bot_bo1649642514l_bool),
inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__]),
[final] ).
cnf(i_0_3440,hypothesis,
is_fun1661590463l_bool(finite_finite_pname),
inference(split_conjunct,[status(thm)],[gsy_c_Finite__Set_Ofinite_000tc__Com__Opname]),
[final] ).
cnf(i_0_3441,plain,
is_fun949378684l_bool(bot_bo1389914601l_bool),
inference(split_conjunct,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc]),
[final] ).
cnf(i_0_3442,plain,
is_fun949378684l_bool(finite_finite_a),
inference(split_conjunct,[status(thm)],[gsy_c_Finite__Set_Ofinite_000t__a]),
[final] ).
cnf(i_0_3443,hypothesis,
is_fun_pname_bool(u),
inference(split_conjunct,[status(thm)],[gsy_v_U]),
[final] ).
cnf(i_0_3444,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_3445,hypothesis,
is_fun_a_bool(g),
inference(split_conjunct,[status(thm)],[gsy_v_G]),
[final] ).
cnf(i_0_3446,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_3447,plain,
bot_bo1701429464l_bool = cOMBK_1994329625t_bool(fFalse),
inference(rw,[status(thm)],[i_0_2136,c_0_968]),
[final] ).
cnf(i_0_3448,plain,
bot_bot_fun_nat_bool = cOMBK_bool_nat(fFalse),
inference(rw,[status(thm)],[i_0_2137,c_0_971]),
[final] ).
cnf(i_0_3449,plain,
bot_bot_nat = zero_zero_nat,
inference(split_conjunct,[status(thm)],[fact_697_bot__nat__def]),
[final] ).
cnf(i_0_3450,axiom,
X1 = X1 ).
cnf(i_0_3451,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_3452,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_3453,axiom,
( X1 != X2
| hAPP_fun_a_bool_bool(X1,X3) = hAPP_fun_a_bool_bool(X2,X3) ) ).
cnf(i_0_3454,axiom,
( X1 != X2
| hAPP_fun_a_bool_bool(X3,X1) = hAPP_fun_a_bool_bool(X3,X2) ) ).
cnf(i_0_3455,axiom,
( X1 != X2
| image_47868345e_bool(X1,X3) = image_47868345e_bool(X2,X3) ) ).
cnf(i_0_3456,axiom,
( X1 != X2
| image_47868345e_bool(X3,X1) = image_47868345e_bool(X3,X2) ) ).
cnf(i_0_3457,axiom,
( X1 != X2
| hAPP_f1794073134e_bool(X1,X3) = hAPP_f1794073134e_bool(X2,X3) ) ).
cnf(i_0_3458,axiom,
( X1 != X2
| hAPP_f1794073134e_bool(X3,X1) = hAPP_f1794073134e_bool(X3,X2) ) ).
cnf(i_0_3459,axiom,
( X1 != X2
| hAPP_p1534023578a_bool(X1,X3) = hAPP_p1534023578a_bool(X2,X3) ) ).
cnf(i_0_3460,axiom,
( X1 != X2
| hAPP_p1534023578a_bool(X3,X1) = hAPP_p1534023578a_bool(X3,X2) ) ).
cnf(i_0_3461,axiom,
( X1 != X2
| image_112932426a_bool(X1,X3) = image_112932426a_bool(X2,X3) ) ).
cnf(i_0_3462,axiom,
( X1 != X2
| image_112932426a_bool(X3,X1) = image_112932426a_bool(X3,X2) ) ).
cnf(i_0_3463,axiom,
( X1 != X2
| hAPP_n1025906991e_bool(X1,X3) = hAPP_n1025906991e_bool(X2,X3) ) ).
cnf(i_0_3464,axiom,
( X1 != X2
| hAPP_n1025906991e_bool(X3,X1) = hAPP_n1025906991e_bool(X3,X2) ) ).
cnf(i_0_3465,axiom,
( X1 != X2
| hAPP_pname_nat(X1,X3) = hAPP_pname_nat(X2,X3) ) ).
cnf(i_0_3466,axiom,
( X1 != X2
| hAPP_pname_nat(X3,X1) = hAPP_pname_nat(X3,X2) ) ).
cnf(i_0_3467,axiom,
( X1 != X2
| image_pname_nat(X1,X3) = image_pname_nat(X2,X3) ) ).
cnf(i_0_3468,axiom,
( X1 != X2
| image_pname_nat(X3,X1) = image_pname_nat(X3,X2) ) ).
cnf(i_0_3469,axiom,
( X1 != X2
| image_pname_pname(X1,X3) = image_pname_pname(X2,X3) ) ).
cnf(i_0_3470,axiom,
( X1 != X2
| image_pname_pname(X3,X1) = image_pname_pname(X3,X2) ) ).
cnf(i_0_3471,axiom,
( X1 != X2
| hAPP_a93125764e_bool(X1,X3) = hAPP_a93125764e_bool(X2,X3) ) ).
cnf(i_0_3472,axiom,
( X1 != X2
| hAPP_a93125764e_bool(X3,X1) = hAPP_a93125764e_bool(X3,X2) ) ).
cnf(i_0_3473,axiom,
( X1 != X2
| hAPP_a_fun_nat_bool(X1,X3) = hAPP_a_fun_nat_bool(X2,X3) ) ).
cnf(i_0_3474,axiom,
( X1 != X2
| hAPP_a_fun_nat_bool(X3,X1) = hAPP_a_fun_nat_bool(X3,X2) ) ).
cnf(i_0_3475,axiom,
( X1 != X2
| image_a_fun_nat_bool(X1,X3) = image_a_fun_nat_bool(X2,X3) ) ).
cnf(i_0_3476,axiom,
( X1 != X2
| image_a_fun_nat_bool(X3,X1) = image_a_fun_nat_bool(X3,X2) ) ).
cnf(i_0_3477,axiom,
( X1 != X2
| image_819518260e_bool(X1,X3) = image_819518260e_bool(X2,X3) ) ).
cnf(i_0_3478,axiom,
( X1 != X2
| image_819518260e_bool(X3,X1) = image_819518260e_bool(X3,X2) ) ).
cnf(i_0_3479,axiom,
( X1 != X2
| image_a_fun_a_bool(X1,X3) = image_a_fun_a_bool(X2,X3) ) ).
cnf(i_0_3480,axiom,
( X1 != X2
| image_a_fun_a_bool(X3,X1) = image_a_fun_a_bool(X3,X2) ) ).
cnf(i_0_3481,axiom,
( X1 != X2
| hAPP_nat_fun_a_bool(X1,X3) = hAPP_nat_fun_a_bool(X2,X3) ) ).
cnf(i_0_3482,axiom,
( X1 != X2
| hAPP_nat_fun_a_bool(X3,X1) = hAPP_nat_fun_a_bool(X3,X2) ) ).
cnf(i_0_3483,axiom,
( X1 != X2
| hAPP_f1935102916l_bool(X1,X3) = hAPP_f1935102916l_bool(X2,X3) ) ).
cnf(i_0_3484,axiom,
( X1 != X2
| hAPP_f1935102916l_bool(X3,X1) = hAPP_f1935102916l_bool(X3,X2) ) ).
cnf(i_0_3485,axiom,
( X1 != X2
| hAPP_a_nat(X1,X3) = hAPP_a_nat(X2,X3) ) ).
cnf(i_0_3486,axiom,
( X1 != X2
| hAPP_a_nat(X3,X1) = hAPP_a_nat(X3,X2) ) ).
cnf(i_0_3487,axiom,
( X1 != X2
| image_a_nat(X1,X3) = image_a_nat(X2,X3) ) ).
cnf(i_0_3488,axiom,
( X1 != X2
| image_a_nat(X3,X1) = image_a_nat(X3,X2) ) ).
cnf(i_0_3489,axiom,
( X1 != X2
| image_a_pname(X1,X3) = image_a_pname(X2,X3) ) ).
cnf(i_0_3490,axiom,
( X1 != X2
| image_a_pname(X3,X1) = image_a_pname(X3,X2) ) ).
cnf(i_0_3491,axiom,
( X1 != X2
| image_a_a(X1,X3) = image_a_a(X2,X3) ) ).
cnf(i_0_3492,axiom,
( X1 != X2
| image_a_a(X3,X1) = image_a_a(X3,X2) ) ).
cnf(i_0_3493,axiom,
( X1 != X2
| hAPP_a85458249l_bool(X1,X3) = hAPP_a85458249l_bool(X2,X3) ) ).
cnf(i_0_3494,axiom,
( X1 != X2
| hAPP_a85458249l_bool(X3,X1) = hAPP_a85458249l_bool(X3,X2) ) ).
cnf(i_0_3495,axiom,
( X1 != X2
| hAPP_nat_nat(X1,X3) = hAPP_nat_nat(X2,X3) ) ).
cnf(i_0_3496,axiom,
( X1 != X2
| hAPP_nat_nat(X3,X1) = hAPP_nat_nat(X3,X2) ) ).
cnf(i_0_3497,axiom,
( X1 != X2
| hAPP_nat_bool(X1,X3) = hAPP_nat_bool(X2,X3) ) ).
cnf(i_0_3498,axiom,
( X1 != X2
| hAPP_nat_bool(X3,X1) = hAPP_nat_bool(X3,X2) ) ).
cnf(i_0_3499,axiom,
( X1 != X2
| collec1974731493e_bool(X1) = collec1974731493e_bool(X2) ) ).
cnf(i_0_3500,axiom,
( X1 != X2
| hAPP_bool_bool(X1,X3) = hAPP_bool_bool(X2,X3) ) ).
cnf(i_0_3501,axiom,
( X1 != X2
| hAPP_bool_bool(X3,X1) = hAPP_bool_bool(X3,X2) ) ).
cnf(i_0_3502,axiom,
( X1 != X2
| hAPP_b589554111l_bool(X1,X3) = hAPP_b589554111l_bool(X2,X3) ) ).
cnf(i_0_3503,axiom,
( X1 != X2
| hAPP_b589554111l_bool(X3,X1) = hAPP_b589554111l_bool(X3,X2) ) ).
cnf(i_0_3504,axiom,
( X1 != X2
| image_496248727ol_nat(X1,X3) = image_496248727ol_nat(X2,X3) ) ).
cnf(i_0_3505,axiom,
( X1 != X2
| image_496248727ol_nat(X3,X1) = image_496248727ol_nat(X3,X2) ) ).
cnf(i_0_3506,axiom,
( X1 != X2
| hAPP_n215258509l_bool(X1,X3) = hAPP_n215258509l_bool(X2,X3) ) ).
cnf(i_0_3507,axiom,
( X1 != X2
| hAPP_n215258509l_bool(X3,X1) = hAPP_n215258509l_bool(X3,X2) ) ).
cnf(i_0_3508,axiom,
( X1 != X2
| hAPP_f22106695ol_nat(X1,X3) = hAPP_f22106695ol_nat(X2,X3) ) ).
cnf(i_0_3509,axiom,
( X1 != X2
| hAPP_f22106695ol_nat(X3,X1) = hAPP_f22106695ol_nat(X3,X2) ) ).
cnf(i_0_3510,axiom,
( X1 != X2
| image_1921560913_pname(X1,X3) = image_1921560913_pname(X2,X3) ) ).
cnf(i_0_3511,axiom,
( X1 != X2
| image_1921560913_pname(X3,X1) = image_1921560913_pname(X3,X2) ) ).
cnf(i_0_3512,axiom,
( X1 != X2
| hAPP_p130839763l_bool(X1,X3) = hAPP_p130839763l_bool(X2,X3) ) ).
cnf(i_0_3513,axiom,
( X1 != X2
| hAPP_p130839763l_bool(X3,X1) = hAPP_p130839763l_bool(X3,X2) ) ).
cnf(i_0_3514,axiom,
( X1 != X2
| image_26036933t_bool(X1,X3) = image_26036933t_bool(X2,X3) ) ).
cnf(i_0_3515,axiom,
( X1 != X2
| image_26036933t_bool(X3,X1) = image_26036933t_bool(X3,X2) ) ).
cnf(i_0_3516,axiom,
( X1 != X2
| image_1655916159e_bool(X1,X3) = image_1655916159e_bool(X2,X3) ) ).
cnf(i_0_3517,axiom,
( X1 != X2
| image_1655916159e_bool(X3,X1) = image_1655916159e_bool(X3,X2) ) ).
cnf(i_0_3518,axiom,
( X1 != X2
| hAPP_f1066163005t_bool(X1,X3) = hAPP_f1066163005t_bool(X2,X3) ) ).
cnf(i_0_3519,axiom,
( X1 != X2
| hAPP_f1066163005t_bool(X3,X1) = hAPP_f1066163005t_bool(X3,X2) ) ).
cnf(i_0_3520,axiom,
( X1 != X2
| hAPP_f434788991l_bool(X1,X3) = hAPP_f434788991l_bool(X2,X3) ) ).
cnf(i_0_3521,axiom,
( X1 != X2
| hAPP_f434788991l_bool(X3,X1) = hAPP_f434788991l_bool(X3,X2) ) ).
cnf(i_0_3522,axiom,
( X1 != X2
| image_nat_fun_a_bool(X1,X3) = image_nat_fun_a_bool(X2,X3) ) ).
cnf(i_0_3523,axiom,
( X1 != X2
| image_nat_fun_a_bool(X3,X1) = image_nat_fun_a_bool(X3,X2) ) ).
cnf(i_0_3524,axiom,
( X1 != X2
| hAPP_f282463732t_bool(X1,X3) = hAPP_f282463732t_bool(X2,X3) ) ).
cnf(i_0_3525,axiom,
( X1 != X2
| hAPP_f282463732t_bool(X3,X1) = hAPP_f282463732t_bool(X3,X2) ) ).
cnf(i_0_3526,axiom,
( X1 != X2
| image_nat_nat(X1,X3) = image_nat_nat(X2,X3) ) ).
cnf(i_0_3527,axiom,
( X1 != X2
| image_nat_nat(X3,X1) = image_nat_nat(X3,X2) ) ).
cnf(i_0_3528,axiom,
( X1 != X2
| image_nat_pname(X1,X3) = image_nat_pname(X2,X3) ) ).
cnf(i_0_3529,axiom,
( X1 != X2
| image_nat_pname(X3,X1) = image_nat_pname(X3,X2) ) ).
cnf(i_0_3530,axiom,
( X1 != X2
| hAPP_nat_pname(X1,X3) = hAPP_nat_pname(X2,X3) ) ).
cnf(i_0_3531,axiom,
( X1 != X2
| hAPP_nat_pname(X3,X1) = hAPP_nat_pname(X3,X2) ) ).
cnf(i_0_3532,axiom,
( X1 != X2
| image_nat_a(X1,X3) = image_nat_a(X2,X3) ) ).
cnf(i_0_3533,axiom,
( X1 != X2
| image_nat_a(X3,X1) = image_nat_a(X3,X2) ) ).
cnf(i_0_3534,axiom,
( X1 != X2
| hAPP_nat_a(X1,X3) = hAPP_nat_a(X2,X3) ) ).
cnf(i_0_3535,axiom,
( X1 != X2
| hAPP_nat_a(X3,X1) = hAPP_nat_a(X3,X2) ) ).
cnf(i_0_3536,axiom,
( X1 != X2
| hAPP_f2009550088ol_nat(X1,X3) = hAPP_f2009550088ol_nat(X2,X3) ) ).
cnf(i_0_3537,axiom,
( X1 != X2
| hAPP_f2009550088ol_nat(X3,X1) = hAPP_f2009550088ol_nat(X3,X2) ) ).
cnf(i_0_3538,axiom,
( X1 != X2
| hAPP_f55526627ol_nat(X1,X3) = hAPP_f55526627ol_nat(X2,X3) ) ).
cnf(i_0_3539,axiom,
( X1 != X2
| hAPP_f55526627ol_nat(X3,X1) = hAPP_f55526627ol_nat(X3,X2) ) ).
cnf(i_0_3540,axiom,
( X1 != X2
| hAPP_pname_bool(X1,X3) = hAPP_pname_bool(X2,X3) ) ).
cnf(i_0_3541,axiom,
( X1 != X2
| hAPP_pname_bool(X3,X1) = hAPP_pname_bool(X3,X2) ) ).
cnf(i_0_3542,axiom,
( X1 != X2
| hAPP_a_bool(X1,X3) = hAPP_a_bool(X2,X3) ) ).
cnf(i_0_3543,axiom,
( X1 != X2
| hAPP_a_bool(X3,X1) = hAPP_a_bool(X3,X2) ) ).
cnf(i_0_3544,axiom,
( X1 != X2
| hAPP_f696928925ol_nat(X1,X3) = hAPP_f696928925ol_nat(X2,X3) ) ).
cnf(i_0_3545,axiom,
( X1 != X2
| hAPP_f696928925ol_nat(X3,X1) = hAPP_f696928925ol_nat(X3,X2) ) ).
cnf(i_0_3546,axiom,
( X1 != X2
| image_fun_nat_bool_a(X1,X3) = image_fun_nat_bool_a(X2,X3) ) ).
cnf(i_0_3547,axiom,
( X1 != X2
| image_fun_nat_bool_a(X3,X1) = image_fun_nat_bool_a(X3,X2) ) ).
cnf(i_0_3548,axiom,
( X1 != X2
| image_876012084bool_a(X1,X3) = image_876012084bool_a(X2,X3) ) ).
cnf(i_0_3549,axiom,
( X1 != X2
| image_876012084bool_a(X3,X1) = image_876012084bool_a(X3,X2) ) ).
cnf(i_0_3550,axiom,
( X1 != X2
| image_fun_a_bool_a(X1,X3) = image_fun_a_bool_a(X2,X3) ) ).
cnf(i_0_3551,axiom,
( X1 != X2
| image_fun_a_bool_a(X3,X1) = image_fun_a_bool_a(X3,X2) ) ).
cnf(i_0_3552,axiom,
( X1 != X2
| hAPP_f621171935l_bool(X1,X3) = hAPP_f621171935l_bool(X2,X3) ) ).
cnf(i_0_3553,axiom,
( X1 != X2
| hAPP_f621171935l_bool(X3,X1) = hAPP_f621171935l_bool(X3,X2) ) ).
cnf(i_0_3554,axiom,
( X1 != X2
| collect_fun_a_bool(X1) = collect_fun_a_bool(X2) ) ).
cnf(i_0_3555,axiom,
( X1 != X2
| collect_a(X1) = collect_a(X2) ) ).
cnf(i_0_3556,axiom,
( X1 != X2
| hAPP_f1631501043l_bool(X1,X3) = hAPP_f1631501043l_bool(X2,X3) ) ).
cnf(i_0_3557,axiom,
( X1 != X2
| hAPP_f1631501043l_bool(X3,X1) = hAPP_f1631501043l_bool(X3,X2) ) ).
cnf(i_0_3558,axiom,
( X1 != X2
| hAPP_f1748468828l_bool(X1,X3) = hAPP_f1748468828l_bool(X2,X3) ) ).
cnf(i_0_3559,axiom,
( X1 != X2
| hAPP_f1748468828l_bool(X3,X1) = hAPP_f1748468828l_bool(X3,X2) ) ).
cnf(i_0_3560,axiom,
( X1 != X2
| hAPP_f1476298914l_bool(X1,X3) = hAPP_f1476298914l_bool(X2,X3) ) ).
cnf(i_0_3561,axiom,
( X1 != X2
| hAPP_f1476298914l_bool(X3,X1) = hAPP_f1476298914l_bool(X3,X2) ) ).
cnf(i_0_3562,axiom,
( X1 != X2
| hAPP_f198738859l_bool(X1,X3) = hAPP_f198738859l_bool(X2,X3) ) ).
cnf(i_0_3563,axiom,
( X1 != X2
| hAPP_f198738859l_bool(X3,X1) = hAPP_f198738859l_bool(X3,X2) ) ).
cnf(i_0_3564,axiom,
( X1 != X2
| hAPP_n1006566506l_bool(X1,X3) = hAPP_n1006566506l_bool(X2,X3) ) ).
cnf(i_0_3565,axiom,
( X1 != X2
| hAPP_n1006566506l_bool(X3,X1) = hAPP_n1006566506l_bool(X3,X2) ) ).
cnf(i_0_3566,axiom,
( X1 != X2
| hAPP_p393069232l_bool(X1,X3) = hAPP_p393069232l_bool(X2,X3) ) ).
cnf(i_0_3567,axiom,
( X1 != X2
| hAPP_p393069232l_bool(X3,X1) = hAPP_p393069232l_bool(X3,X2) ) ).
cnf(i_0_3568,axiom,
( X1 != X2
| hAPP_a_fun_bool_bool(X1,X3) = hAPP_a_fun_bool_bool(X2,X3) ) ).
cnf(i_0_3569,axiom,
( X1 != X2
| hAPP_a_fun_bool_bool(X3,X1) = hAPP_a_fun_bool_bool(X3,X2) ) ).
cnf(i_0_3570,axiom,
( X1 != X2
| hAPP_a1392362872l_bool(X1,X3) = hAPP_a1392362872l_bool(X2,X3) ) ).
cnf(i_0_3571,axiom,
( X1 != X2
| hAPP_a1392362872l_bool(X3,X1) = hAPP_a1392362872l_bool(X3,X2) ) ).
cnf(i_0_3572,axiom,
( X1 != X2
| hAPP_a217006258l_bool(X1,X3) = hAPP_a217006258l_bool(X2,X3) ) ).
cnf(i_0_3573,axiom,
( X1 != X2
| hAPP_a217006258l_bool(X3,X1) = hAPP_a217006258l_bool(X3,X2) ) ).
cnf(i_0_3574,axiom,
( X1 != X2
| cOMBK_1994329625t_bool(X1) = cOMBK_1994329625t_bool(X2) ) ).
cnf(i_0_3575,axiom,
( X1 != X2
| cOMBK_bool_nat(X1) = cOMBK_bool_nat(X2) ) ).
cnf(i_0_3576,axiom,
( X1 != X2
| hAPP_f1664156314l_bool(X1,X3) = hAPP_f1664156314l_bool(X2,X3) ) ).
cnf(i_0_3577,axiom,
( X1 != X2
| hAPP_f1664156314l_bool(X3,X1) = hAPP_f1664156314l_bool(X3,X2) ) ).
cnf(i_0_3578,axiom,
( X1 != X2
| collect_pname(X1) = collect_pname(X2) ) ).
cnf(i_0_3579,axiom,
( X1 != X2
| hAPP_p61793385e_bool(X1,X3) = hAPP_p61793385e_bool(X2,X3) ) ).
cnf(i_0_3580,axiom,
( X1 != X2
| hAPP_p61793385e_bool(X3,X1) = hAPP_p61793385e_bool(X3,X2) ) ).
cnf(i_0_3581,axiom,
( X1 != X2
| hAPP_f759274231e_bool(X1,X3) = hAPP_f759274231e_bool(X2,X3) ) ).
cnf(i_0_3582,axiom,
( X1 != X2
| hAPP_f759274231e_bool(X3,X1) = hAPP_f759274231e_bool(X3,X2) ) ).
cnf(i_0_3583,axiom,
( X1 != X2
| image_pname_a(X1,X3) = image_pname_a(X2,X3) ) ).
cnf(i_0_3584,axiom,
( X1 != X2
| image_pname_a(X3,X1) = image_pname_a(X3,X2) ) ).
cnf(i_0_3585,axiom,
( X1 != X2
| hAPP_f1637334154l_bool(X1,X3) = hAPP_f1637334154l_bool(X2,X3) ) ).
cnf(i_0_3586,axiom,
( X1 != X2
| hAPP_f1637334154l_bool(X3,X1) = hAPP_f1637334154l_bool(X3,X2) ) ).
cnf(i_0_3587,axiom,
( X1 != X2
| cOMBS_1187019125l_bool(X1,X3) = cOMBS_1187019125l_bool(X2,X3) ) ).
cnf(i_0_3588,axiom,
( X1 != X2
| cOMBS_1187019125l_bool(X3,X1) = cOMBS_1187019125l_bool(X3,X2) ) ).
cnf(i_0_3589,axiom,
( X1 != X2
| hAPP_f103356543l_bool(X1,X3) = hAPP_f103356543l_bool(X2,X3) ) ).
cnf(i_0_3590,axiom,
( X1 != X2
| hAPP_f103356543l_bool(X3,X1) = hAPP_f103356543l_bool(X3,X2) ) ).
cnf(i_0_3591,axiom,
( X1 != X2
| hAPP_a_fun_a_bool(X1,X3) = hAPP_a_fun_a_bool(X2,X3) ) ).
cnf(i_0_3592,axiom,
( X1 != X2
| hAPP_a_fun_a_bool(X3,X1) = hAPP_a_fun_a_bool(X3,X2) ) ).
cnf(i_0_3593,axiom,
( X1 != X2
| hAPP_f54304608l_bool(X1,X3) = hAPP_f54304608l_bool(X2,X3) ) ).
cnf(i_0_3594,axiom,
( X1 != X2
| hAPP_f54304608l_bool(X3,X1) = hAPP_f54304608l_bool(X3,X2) ) ).
cnf(i_0_3595,axiom,
( X1 != X2
| cOMBS_nat_bool_bool(X1,X3) = cOMBS_nat_bool_bool(X2,X3) ) ).
cnf(i_0_3596,axiom,
( X1 != X2
| cOMBS_nat_bool_bool(X3,X1) = cOMBS_nat_bool_bool(X3,X2) ) ).
cnf(i_0_3597,axiom,
( X1 != X2
| hAPP_n1699378549t_bool(X1,X3) = hAPP_n1699378549t_bool(X2,X3) ) ).
cnf(i_0_3598,axiom,
( X1 != X2
| hAPP_n1699378549t_bool(X3,X1) = hAPP_n1699378549t_bool(X3,X2) ) ).
cnf(i_0_3599,axiom,
( X1 != X2
| hAPP_f800510211t_bool(X1,X3) = hAPP_f800510211t_bool(X2,X3) ) ).
cnf(i_0_3600,axiom,
( X1 != X2
| hAPP_f800510211t_bool(X3,X1) = hAPP_f800510211t_bool(X3,X2) ) ).
cnf(i_0_3601,axiom,
( X1 != X2
| hAPP_n850744903l_bool(X1,X3) = hAPP_n850744903l_bool(X2,X3) ) ).
cnf(i_0_3602,axiom,
( X1 != X2
| hAPP_n850744903l_bool(X3,X1) = hAPP_n850744903l_bool(X3,X2) ) ).
cnf(i_0_3603,axiom,
( X1 != X2
| hAPP_f921600141ol_nat(X1,X3) = hAPP_f921600141ol_nat(X2,X3) ) ).
cnf(i_0_3604,axiom,
( X1 != X2
| hAPP_f921600141ol_nat(X3,X1) = hAPP_f921600141ol_nat(X3,X2) ) ).
cnf(i_0_3605,axiom,
( X1 != X2
| image_1551609309ol_nat(X1,X3) = image_1551609309ol_nat(X2,X3) ) ).
cnf(i_0_3606,axiom,
( X1 != X2
| image_1551609309ol_nat(X3,X1) = image_1551609309ol_nat(X3,X2) ) ).
cnf(i_0_3607,axiom,
( X1 != X2
| hAPP_p338031245l_bool(X1,X3) = hAPP_p338031245l_bool(X2,X3) ) ).
cnf(i_0_3608,axiom,
( X1 != X2
| hAPP_p338031245l_bool(X3,X1) = hAPP_p338031245l_bool(X3,X2) ) ).
cnf(i_0_3609,axiom,
( X1 != X2
| hAPP_pname_a(X1,X3) = hAPP_pname_a(X2,X3) ) ).
cnf(i_0_3610,axiom,
( X1 != X2
| hAPP_pname_a(X3,X1) = hAPP_pname_a(X3,X2) ) ).
cnf(i_0_3611,axiom,
( X1 != X2
| image_1283814551_pname(X1,X3) = image_1283814551_pname(X2,X3) ) ).
cnf(i_0_3612,axiom,
( X1 != X2
| image_1283814551_pname(X3,X1) = image_1283814551_pname(X3,X2) ) ).
cnf(i_0_3613,axiom,
( X1 != X2
| hAPP_n1414589940l_bool(X1,X3) = hAPP_n1414589940l_bool(X2,X3) ) ).
cnf(i_0_3614,axiom,
( X1 != X2
| hAPP_n1414589940l_bool(X3,X1) = hAPP_n1414589940l_bool(X3,X2) ) ).
cnf(i_0_3615,axiom,
( X1 != X2
| hAPP_fun_a_bool_nat(X1,X3) = hAPP_fun_a_bool_nat(X2,X3) ) ).
cnf(i_0_3616,axiom,
( X1 != X2
| hAPP_fun_a_bool_nat(X3,X1) = hAPP_fun_a_bool_nat(X3,X2) ) ).
cnf(i_0_3617,axiom,
( X1 != X2
| image_fun_a_bool_nat(X1,X3) = image_fun_a_bool_nat(X2,X3) ) ).
cnf(i_0_3618,axiom,
( X1 != X2
| image_fun_a_bool_nat(X3,X1) = image_fun_a_bool_nat(X3,X2) ) ).
cnf(i_0_3619,axiom,
( X1 != X2
| hAPP_p1824510254l_bool(X1,X3) = hAPP_p1824510254l_bool(X2,X3) ) ).
cnf(i_0_3620,axiom,
( X1 != X2
| hAPP_p1824510254l_bool(X3,X1) = hAPP_p1824510254l_bool(X3,X2) ) ).
cnf(i_0_3621,axiom,
( X1 != X2
| image_1854862208_pname(X1,X3) = image_1854862208_pname(X2,X3) ) ).
cnf(i_0_3622,axiom,
( X1 != X2
| image_1854862208_pname(X3,X1) = image_1854862208_pname(X3,X2) ) ).
cnf(i_0_3623,axiom,
( X1 != X2
| hAPP_f654413245e_bool(X1,X3) = hAPP_f654413245e_bool(X2,X3) ) ).
cnf(i_0_3624,axiom,
( X1 != X2
| hAPP_f654413245e_bool(X3,X1) = hAPP_f654413245e_bool(X3,X2) ) ).
cnf(i_0_3625,axiom,
( X1 != X2
| hAPP_p1499970991t_bool(X1,X3) = hAPP_p1499970991t_bool(X2,X3) ) ).
cnf(i_0_3626,axiom,
( X1 != X2
| hAPP_p1499970991t_bool(X3,X1) = hAPP_p1499970991t_bool(X3,X2) ) ).
cnf(i_0_3627,axiom,
( X1 != X2
| image_2129980159t_bool(X1,X3) = image_2129980159t_bool(X2,X3) ) ).
cnf(i_0_3628,axiom,
( X1 != X2
| image_2129980159t_bool(X3,X1) = image_2129980159t_bool(X3,X2) ) ).
cnf(i_0_3629,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_3630,axiom,
( X1 != X2
| ~ is_pname(X1)
| is_pname(X2) ) ).
cnf(i_0_3631,axiom,
( X1 != X2
| ~ is_a(X1)
| is_a(X2) ) ).
cnf(i_0_3632,axiom,
( X1 != X2
| ~ is_fun_pname_bool(X1)
| is_fun_pname_bool(X2) ) ).
cnf(i_0_3633,axiom,
( X1 != X2
| ~ is_fun_a_bool(X1)
| is_fun_a_bool(X2) ) ).
cnf(i_0_3634,axiom,
( X1 != X2
| ~ is_fun949378684l_bool(X1)
| is_fun949378684l_bool(X2) ) ).
cnf(i_0_3635,axiom,
( X1 != X2
| ~ is_fun1661590463l_bool(X1)
| is_fun1661590463l_bool(X2) ) ).
cnf(i_0_3636,axiom,
( X1 != X2
| ~ is_bool(X1)
| is_bool(X2) ) ).
cnf(i_0_3450_001,axiom,
X1 = X1 ).
cnf(i_0_3451_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_3452_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_3453_004,axiom,
( X1 != X2
| hAPP_fun_a_bool_bool(X1,X3) = hAPP_fun_a_bool_bool(X2,X3) ) ).
cnf(i_0_3454_005,axiom,
( X1 != X2
| hAPP_fun_a_bool_bool(X3,X1) = hAPP_fun_a_bool_bool(X3,X2) ) ).
cnf(i_0_3455_006,axiom,
( X1 != X2
| image_47868345e_bool(X1,X3) = image_47868345e_bool(X2,X3) ) ).
cnf(i_0_3456_007,axiom,
( X1 != X2
| image_47868345e_bool(X3,X1) = image_47868345e_bool(X3,X2) ) ).
cnf(i_0_3457_008,axiom,
( X1 != X2
| hAPP_f1794073134e_bool(X1,X3) = hAPP_f1794073134e_bool(X2,X3) ) ).
cnf(i_0_3458_009,axiom,
( X1 != X2
| hAPP_f1794073134e_bool(X3,X1) = hAPP_f1794073134e_bool(X3,X2) ) ).
cnf(i_0_3459_010,axiom,
( X1 != X2
| hAPP_p1534023578a_bool(X1,X3) = hAPP_p1534023578a_bool(X2,X3) ) ).
cnf(i_0_3460_011,axiom,
( X1 != X2
| hAPP_p1534023578a_bool(X3,X1) = hAPP_p1534023578a_bool(X3,X2) ) ).
cnf(i_0_3461_012,axiom,
( X1 != X2
| image_112932426a_bool(X1,X3) = image_112932426a_bool(X2,X3) ) ).
cnf(i_0_3462_013,axiom,
( X1 != X2
| image_112932426a_bool(X3,X1) = image_112932426a_bool(X3,X2) ) ).
cnf(i_0_3463_014,axiom,
( X1 != X2
| hAPP_n1025906991e_bool(X1,X3) = hAPP_n1025906991e_bool(X2,X3) ) ).
cnf(i_0_3464_015,axiom,
( X1 != X2
| hAPP_n1025906991e_bool(X3,X1) = hAPP_n1025906991e_bool(X3,X2) ) ).
cnf(i_0_3465_016,axiom,
( X1 != X2
| hAPP_pname_nat(X1,X3) = hAPP_pname_nat(X2,X3) ) ).
cnf(i_0_3466_017,axiom,
( X1 != X2
| hAPP_pname_nat(X3,X1) = hAPP_pname_nat(X3,X2) ) ).
cnf(i_0_3467_018,axiom,
( X1 != X2
| image_pname_nat(X1,X3) = image_pname_nat(X2,X3) ) ).
cnf(i_0_3468_019,axiom,
( X1 != X2
| image_pname_nat(X3,X1) = image_pname_nat(X3,X2) ) ).
cnf(i_0_3469_020,axiom,
( X1 != X2
| image_pname_pname(X1,X3) = image_pname_pname(X2,X3) ) ).
cnf(i_0_3470_021,axiom,
( X1 != X2
| image_pname_pname(X3,X1) = image_pname_pname(X3,X2) ) ).
cnf(i_0_3471_022,axiom,
( X1 != X2
| hAPP_a93125764e_bool(X1,X3) = hAPP_a93125764e_bool(X2,X3) ) ).
cnf(i_0_3472_023,axiom,
( X1 != X2
| hAPP_a93125764e_bool(X3,X1) = hAPP_a93125764e_bool(X3,X2) ) ).
cnf(i_0_3473_024,axiom,
( X1 != X2
| hAPP_a_fun_nat_bool(X1,X3) = hAPP_a_fun_nat_bool(X2,X3) ) ).
cnf(i_0_3474_025,axiom,
( X1 != X2
| hAPP_a_fun_nat_bool(X3,X1) = hAPP_a_fun_nat_bool(X3,X2) ) ).
cnf(i_0_3475_026,axiom,
( X1 != X2
| image_a_fun_nat_bool(X1,X3) = image_a_fun_nat_bool(X2,X3) ) ).
cnf(i_0_3476_027,axiom,
( X1 != X2
| image_a_fun_nat_bool(X3,X1) = image_a_fun_nat_bool(X3,X2) ) ).
cnf(i_0_3477_028,axiom,
( X1 != X2
| image_819518260e_bool(X1,X3) = image_819518260e_bool(X2,X3) ) ).
cnf(i_0_3478_029,axiom,
( X1 != X2
| image_819518260e_bool(X3,X1) = image_819518260e_bool(X3,X2) ) ).
cnf(i_0_3479_030,axiom,
( X1 != X2
| image_a_fun_a_bool(X1,X3) = image_a_fun_a_bool(X2,X3) ) ).
cnf(i_0_3480_031,axiom,
( X1 != X2
| image_a_fun_a_bool(X3,X1) = image_a_fun_a_bool(X3,X2) ) ).
cnf(i_0_3481_032,axiom,
( X1 != X2
| hAPP_nat_fun_a_bool(X1,X3) = hAPP_nat_fun_a_bool(X2,X3) ) ).
cnf(i_0_3482_033,axiom,
( X1 != X2
| hAPP_nat_fun_a_bool(X3,X1) = hAPP_nat_fun_a_bool(X3,X2) ) ).
cnf(i_0_3483_034,axiom,
( X1 != X2
| hAPP_f1935102916l_bool(X1,X3) = hAPP_f1935102916l_bool(X2,X3) ) ).
cnf(i_0_3484_035,axiom,
( X1 != X2
| hAPP_f1935102916l_bool(X3,X1) = hAPP_f1935102916l_bool(X3,X2) ) ).
cnf(i_0_3485_036,axiom,
( X1 != X2
| hAPP_a_nat(X1,X3) = hAPP_a_nat(X2,X3) ) ).
cnf(i_0_3486_037,axiom,
( X1 != X2
| hAPP_a_nat(X3,X1) = hAPP_a_nat(X3,X2) ) ).
cnf(i_0_3487_038,axiom,
( X1 != X2
| image_a_nat(X1,X3) = image_a_nat(X2,X3) ) ).
cnf(i_0_3488_039,axiom,
( X1 != X2
| image_a_nat(X3,X1) = image_a_nat(X3,X2) ) ).
cnf(i_0_3489_040,axiom,
( X1 != X2
| image_a_pname(X1,X3) = image_a_pname(X2,X3) ) ).
cnf(i_0_3490_041,axiom,
( X1 != X2
| image_a_pname(X3,X1) = image_a_pname(X3,X2) ) ).
cnf(i_0_3491_042,axiom,
( X1 != X2
| image_a_a(X1,X3) = image_a_a(X2,X3) ) ).
cnf(i_0_3492_043,axiom,
( X1 != X2
| image_a_a(X3,X1) = image_a_a(X3,X2) ) ).
cnf(i_0_3493_044,axiom,
( X1 != X2
| hAPP_a85458249l_bool(X1,X3) = hAPP_a85458249l_bool(X2,X3) ) ).
cnf(i_0_3494_045,axiom,
( X1 != X2
| hAPP_a85458249l_bool(X3,X1) = hAPP_a85458249l_bool(X3,X2) ) ).
cnf(i_0_3495_046,axiom,
( X1 != X2
| hAPP_nat_nat(X1,X3) = hAPP_nat_nat(X2,X3) ) ).
cnf(i_0_3496_047,axiom,
( X1 != X2
| hAPP_nat_nat(X3,X1) = hAPP_nat_nat(X3,X2) ) ).
cnf(i_0_3497_048,axiom,
( X1 != X2
| hAPP_nat_bool(X1,X3) = hAPP_nat_bool(X2,X3) ) ).
cnf(i_0_3498_049,axiom,
( X1 != X2
| hAPP_nat_bool(X3,X1) = hAPP_nat_bool(X3,X2) ) ).
cnf(i_0_3499_050,axiom,
( X1 != X2
| collec1974731493e_bool(X1) = collec1974731493e_bool(X2) ) ).
cnf(i_0_3500_051,axiom,
( X1 != X2
| hAPP_bool_bool(X1,X3) = hAPP_bool_bool(X2,X3) ) ).
cnf(i_0_3501_052,axiom,
( X1 != X2
| hAPP_bool_bool(X3,X1) = hAPP_bool_bool(X3,X2) ) ).
cnf(i_0_3502_053,axiom,
( X1 != X2
| hAPP_b589554111l_bool(X1,X3) = hAPP_b589554111l_bool(X2,X3) ) ).
cnf(i_0_3503_054,axiom,
( X1 != X2
| hAPP_b589554111l_bool(X3,X1) = hAPP_b589554111l_bool(X3,X2) ) ).
cnf(i_0_3504_055,axiom,
( X1 != X2
| image_496248727ol_nat(X1,X3) = image_496248727ol_nat(X2,X3) ) ).
cnf(i_0_3505_056,axiom,
( X1 != X2
| image_496248727ol_nat(X3,X1) = image_496248727ol_nat(X3,X2) ) ).
cnf(i_0_3506_057,axiom,
( X1 != X2
| hAPP_n215258509l_bool(X1,X3) = hAPP_n215258509l_bool(X2,X3) ) ).
cnf(i_0_3507_058,axiom,
( X1 != X2
| hAPP_n215258509l_bool(X3,X1) = hAPP_n215258509l_bool(X3,X2) ) ).
cnf(i_0_3508_059,axiom,
( X1 != X2
| hAPP_f22106695ol_nat(X1,X3) = hAPP_f22106695ol_nat(X2,X3) ) ).
cnf(i_0_3509_060,axiom,
( X1 != X2
| hAPP_f22106695ol_nat(X3,X1) = hAPP_f22106695ol_nat(X3,X2) ) ).
cnf(i_0_3510_061,axiom,
( X1 != X2
| image_1921560913_pname(X1,X3) = image_1921560913_pname(X2,X3) ) ).
cnf(i_0_3511_062,axiom,
( X1 != X2
| image_1921560913_pname(X3,X1) = image_1921560913_pname(X3,X2) ) ).
cnf(i_0_3512_063,axiom,
( X1 != X2
| hAPP_p130839763l_bool(X1,X3) = hAPP_p130839763l_bool(X2,X3) ) ).
cnf(i_0_3513_064,axiom,
( X1 != X2
| hAPP_p130839763l_bool(X3,X1) = hAPP_p130839763l_bool(X3,X2) ) ).
cnf(i_0_3514_065,axiom,
( X1 != X2
| image_26036933t_bool(X1,X3) = image_26036933t_bool(X2,X3) ) ).
cnf(i_0_3515_066,axiom,
( X1 != X2
| image_26036933t_bool(X3,X1) = image_26036933t_bool(X3,X2) ) ).
cnf(i_0_3516_067,axiom,
( X1 != X2
| image_1655916159e_bool(X1,X3) = image_1655916159e_bool(X2,X3) ) ).
cnf(i_0_3517_068,axiom,
( X1 != X2
| image_1655916159e_bool(X3,X1) = image_1655916159e_bool(X3,X2) ) ).
cnf(i_0_3518_069,axiom,
( X1 != X2
| hAPP_f1066163005t_bool(X1,X3) = hAPP_f1066163005t_bool(X2,X3) ) ).
cnf(i_0_3519_070,axiom,
( X1 != X2
| hAPP_f1066163005t_bool(X3,X1) = hAPP_f1066163005t_bool(X3,X2) ) ).
cnf(i_0_3520_071,axiom,
( X1 != X2
| hAPP_f434788991l_bool(X1,X3) = hAPP_f434788991l_bool(X2,X3) ) ).
cnf(i_0_3521_072,axiom,
( X1 != X2
| hAPP_f434788991l_bool(X3,X1) = hAPP_f434788991l_bool(X3,X2) ) ).
cnf(i_0_3522_073,axiom,
( X1 != X2
| image_nat_fun_a_bool(X1,X3) = image_nat_fun_a_bool(X2,X3) ) ).
cnf(i_0_3523_074,axiom,
( X1 != X2
| image_nat_fun_a_bool(X3,X1) = image_nat_fun_a_bool(X3,X2) ) ).
cnf(i_0_3524_075,axiom,
( X1 != X2
| hAPP_f282463732t_bool(X1,X3) = hAPP_f282463732t_bool(X2,X3) ) ).
cnf(i_0_3525_076,axiom,
( X1 != X2
| hAPP_f282463732t_bool(X3,X1) = hAPP_f282463732t_bool(X3,X2) ) ).
cnf(i_0_3526_077,axiom,
( X1 != X2
| image_nat_nat(X1,X3) = image_nat_nat(X2,X3) ) ).
cnf(i_0_3527_078,axiom,
( X1 != X2
| image_nat_nat(X3,X1) = image_nat_nat(X3,X2) ) ).
cnf(i_0_3528_079,axiom,
( X1 != X2
| image_nat_pname(X1,X3) = image_nat_pname(X2,X3) ) ).
cnf(i_0_3529_080,axiom,
( X1 != X2
| image_nat_pname(X3,X1) = image_nat_pname(X3,X2) ) ).
cnf(i_0_3530_081,axiom,
( X1 != X2
| hAPP_nat_pname(X1,X3) = hAPP_nat_pname(X2,X3) ) ).
cnf(i_0_3531_082,axiom,
( X1 != X2
| hAPP_nat_pname(X3,X1) = hAPP_nat_pname(X3,X2) ) ).
cnf(i_0_3532_083,axiom,
( X1 != X2
| image_nat_a(X1,X3) = image_nat_a(X2,X3) ) ).
cnf(i_0_3533_084,axiom,
( X1 != X2
| image_nat_a(X3,X1) = image_nat_a(X3,X2) ) ).
cnf(i_0_3534_085,axiom,
( X1 != X2
| hAPP_nat_a(X1,X3) = hAPP_nat_a(X2,X3) ) ).
cnf(i_0_3535_086,axiom,
( X1 != X2
| hAPP_nat_a(X3,X1) = hAPP_nat_a(X3,X2) ) ).
cnf(i_0_3536_087,axiom,
( X1 != X2
| hAPP_f2009550088ol_nat(X1,X3) = hAPP_f2009550088ol_nat(X2,X3) ) ).
cnf(i_0_3537_088,axiom,
( X1 != X2
| hAPP_f2009550088ol_nat(X3,X1) = hAPP_f2009550088ol_nat(X3,X2) ) ).
cnf(i_0_3538_089,axiom,
( X1 != X2
| hAPP_f55526627ol_nat(X1,X3) = hAPP_f55526627ol_nat(X2,X3) ) ).
cnf(i_0_3539_090,axiom,
( X1 != X2
| hAPP_f55526627ol_nat(X3,X1) = hAPP_f55526627ol_nat(X3,X2) ) ).
cnf(i_0_3540_091,axiom,
( X1 != X2
| hAPP_pname_bool(X1,X3) = hAPP_pname_bool(X2,X3) ) ).
cnf(i_0_3541_092,axiom,
( X1 != X2
| hAPP_pname_bool(X3,X1) = hAPP_pname_bool(X3,X2) ) ).
cnf(i_0_3542_093,axiom,
( X1 != X2
| hAPP_a_bool(X1,X3) = hAPP_a_bool(X2,X3) ) ).
cnf(i_0_3543_094,axiom,
( X1 != X2
| hAPP_a_bool(X3,X1) = hAPP_a_bool(X3,X2) ) ).
cnf(i_0_3544_095,axiom,
( X1 != X2
| hAPP_f696928925ol_nat(X1,X3) = hAPP_f696928925ol_nat(X2,X3) ) ).
cnf(i_0_3545_096,axiom,
( X1 != X2
| hAPP_f696928925ol_nat(X3,X1) = hAPP_f696928925ol_nat(X3,X2) ) ).
cnf(i_0_3546_097,axiom,
( X1 != X2
| image_fun_nat_bool_a(X1,X3) = image_fun_nat_bool_a(X2,X3) ) ).
cnf(i_0_3547_098,axiom,
( X1 != X2
| image_fun_nat_bool_a(X3,X1) = image_fun_nat_bool_a(X3,X2) ) ).
cnf(i_0_3548_099,axiom,
( X1 != X2
| image_876012084bool_a(X1,X3) = image_876012084bool_a(X2,X3) ) ).
cnf(i_0_3549_100,axiom,
( X1 != X2
| image_876012084bool_a(X3,X1) = image_876012084bool_a(X3,X2) ) ).
cnf(i_0_3550_101,axiom,
( X1 != X2
| image_fun_a_bool_a(X1,X3) = image_fun_a_bool_a(X2,X3) ) ).
cnf(i_0_3551_102,axiom,
( X1 != X2
| image_fun_a_bool_a(X3,X1) = image_fun_a_bool_a(X3,X2) ) ).
cnf(i_0_3552_103,axiom,
( X1 != X2
| hAPP_f621171935l_bool(X1,X3) = hAPP_f621171935l_bool(X2,X3) ) ).
cnf(i_0_3553_104,axiom,
( X1 != X2
| hAPP_f621171935l_bool(X3,X1) = hAPP_f621171935l_bool(X3,X2) ) ).
cnf(i_0_3554_105,axiom,
( X1 != X2
| collect_fun_a_bool(X1) = collect_fun_a_bool(X2) ) ).
cnf(i_0_3555_106,axiom,
( X1 != X2
| collect_a(X1) = collect_a(X2) ) ).
cnf(i_0_3556_107,axiom,
( X1 != X2
| hAPP_f1631501043l_bool(X1,X3) = hAPP_f1631501043l_bool(X2,X3) ) ).
cnf(i_0_3557_108,axiom,
( X1 != X2
| hAPP_f1631501043l_bool(X3,X1) = hAPP_f1631501043l_bool(X3,X2) ) ).
cnf(i_0_3558_109,axiom,
( X1 != X2
| hAPP_f1748468828l_bool(X1,X3) = hAPP_f1748468828l_bool(X2,X3) ) ).
cnf(i_0_3559_110,axiom,
( X1 != X2
| hAPP_f1748468828l_bool(X3,X1) = hAPP_f1748468828l_bool(X3,X2) ) ).
cnf(i_0_3560_111,axiom,
( X1 != X2
| hAPP_f1476298914l_bool(X1,X3) = hAPP_f1476298914l_bool(X2,X3) ) ).
cnf(i_0_3561_112,axiom,
( X1 != X2
| hAPP_f1476298914l_bool(X3,X1) = hAPP_f1476298914l_bool(X3,X2) ) ).
cnf(i_0_3562_113,axiom,
( X1 != X2
| hAPP_f198738859l_bool(X1,X3) = hAPP_f198738859l_bool(X2,X3) ) ).
cnf(i_0_3563_114,axiom,
( X1 != X2
| hAPP_f198738859l_bool(X3,X1) = hAPP_f198738859l_bool(X3,X2) ) ).
cnf(i_0_3564_115,axiom,
( X1 != X2
| hAPP_n1006566506l_bool(X1,X3) = hAPP_n1006566506l_bool(X2,X3) ) ).
cnf(i_0_3565_116,axiom,
( X1 != X2
| hAPP_n1006566506l_bool(X3,X1) = hAPP_n1006566506l_bool(X3,X2) ) ).
cnf(i_0_3566_117,axiom,
( X1 != X2
| hAPP_p393069232l_bool(X1,X3) = hAPP_p393069232l_bool(X2,X3) ) ).
cnf(i_0_3567_118,axiom,
( X1 != X2
| hAPP_p393069232l_bool(X3,X1) = hAPP_p393069232l_bool(X3,X2) ) ).
cnf(i_0_3568_119,axiom,
( X1 != X2
| hAPP_a_fun_bool_bool(X1,X3) = hAPP_a_fun_bool_bool(X2,X3) ) ).
cnf(i_0_3569_120,axiom,
( X1 != X2
| hAPP_a_fun_bool_bool(X3,X1) = hAPP_a_fun_bool_bool(X3,X2) ) ).
cnf(i_0_3570_121,axiom,
( X1 != X2
| hAPP_a1392362872l_bool(X1,X3) = hAPP_a1392362872l_bool(X2,X3) ) ).
cnf(i_0_3571_122,axiom,
( X1 != X2
| hAPP_a1392362872l_bool(X3,X1) = hAPP_a1392362872l_bool(X3,X2) ) ).
cnf(i_0_3572_123,axiom,
( X1 != X2
| hAPP_a217006258l_bool(X1,X3) = hAPP_a217006258l_bool(X2,X3) ) ).
cnf(i_0_3573_124,axiom,
( X1 != X2
| hAPP_a217006258l_bool(X3,X1) = hAPP_a217006258l_bool(X3,X2) ) ).
cnf(i_0_3574_125,axiom,
( X1 != X2
| cOMBK_1994329625t_bool(X1) = cOMBK_1994329625t_bool(X2) ) ).
cnf(i_0_3575_126,axiom,
( X1 != X2
| cOMBK_bool_nat(X1) = cOMBK_bool_nat(X2) ) ).
cnf(i_0_3576_127,axiom,
( X1 != X2
| hAPP_f1664156314l_bool(X1,X3) = hAPP_f1664156314l_bool(X2,X3) ) ).
cnf(i_0_3577_128,axiom,
( X1 != X2
| hAPP_f1664156314l_bool(X3,X1) = hAPP_f1664156314l_bool(X3,X2) ) ).
cnf(i_0_3578_129,axiom,
( X1 != X2
| collect_pname(X1) = collect_pname(X2) ) ).
cnf(i_0_3579_130,axiom,
( X1 != X2
| hAPP_p61793385e_bool(X1,X3) = hAPP_p61793385e_bool(X2,X3) ) ).
cnf(i_0_3580_131,axiom,
( X1 != X2
| hAPP_p61793385e_bool(X3,X1) = hAPP_p61793385e_bool(X3,X2) ) ).
cnf(i_0_3581_132,axiom,
( X1 != X2
| hAPP_f759274231e_bool(X1,X3) = hAPP_f759274231e_bool(X2,X3) ) ).
cnf(i_0_3582_133,axiom,
( X1 != X2
| hAPP_f759274231e_bool(X3,X1) = hAPP_f759274231e_bool(X3,X2) ) ).
cnf(i_0_3583_134,axiom,
( X1 != X2
| image_pname_a(X1,X3) = image_pname_a(X2,X3) ) ).
cnf(i_0_3584_135,axiom,
( X1 != X2
| image_pname_a(X3,X1) = image_pname_a(X3,X2) ) ).
cnf(i_0_3585_136,axiom,
( X1 != X2
| hAPP_f1637334154l_bool(X1,X3) = hAPP_f1637334154l_bool(X2,X3) ) ).
cnf(i_0_3586_137,axiom,
( X1 != X2
| hAPP_f1637334154l_bool(X3,X1) = hAPP_f1637334154l_bool(X3,X2) ) ).
cnf(i_0_3587_138,axiom,
( X1 != X2
| cOMBS_1187019125l_bool(X1,X3) = cOMBS_1187019125l_bool(X2,X3) ) ).
cnf(i_0_3588_139,axiom,
( X1 != X2
| cOMBS_1187019125l_bool(X3,X1) = cOMBS_1187019125l_bool(X3,X2) ) ).
cnf(i_0_3589_140,axiom,
( X1 != X2
| hAPP_f103356543l_bool(X1,X3) = hAPP_f103356543l_bool(X2,X3) ) ).
cnf(i_0_3590_141,axiom,
( X1 != X2
| hAPP_f103356543l_bool(X3,X1) = hAPP_f103356543l_bool(X3,X2) ) ).
cnf(i_0_3591_142,axiom,
( X1 != X2
| hAPP_a_fun_a_bool(X1,X3) = hAPP_a_fun_a_bool(X2,X3) ) ).
cnf(i_0_3592_143,axiom,
( X1 != X2
| hAPP_a_fun_a_bool(X3,X1) = hAPP_a_fun_a_bool(X3,X2) ) ).
cnf(i_0_3593_144,axiom,
( X1 != X2
| hAPP_f54304608l_bool(X1,X3) = hAPP_f54304608l_bool(X2,X3) ) ).
cnf(i_0_3594_145,axiom,
( X1 != X2
| hAPP_f54304608l_bool(X3,X1) = hAPP_f54304608l_bool(X3,X2) ) ).
cnf(i_0_3595_146,axiom,
( X1 != X2
| cOMBS_nat_bool_bool(X1,X3) = cOMBS_nat_bool_bool(X2,X3) ) ).
cnf(i_0_3596_147,axiom,
( X1 != X2
| cOMBS_nat_bool_bool(X3,X1) = cOMBS_nat_bool_bool(X3,X2) ) ).
cnf(i_0_3597_148,axiom,
( X1 != X2
| hAPP_n1699378549t_bool(X1,X3) = hAPP_n1699378549t_bool(X2,X3) ) ).
cnf(i_0_3598_149,axiom,
( X1 != X2
| hAPP_n1699378549t_bool(X3,X1) = hAPP_n1699378549t_bool(X3,X2) ) ).
cnf(i_0_3599_150,axiom,
( X1 != X2
| hAPP_f800510211t_bool(X1,X3) = hAPP_f800510211t_bool(X2,X3) ) ).
cnf(i_0_3600_151,axiom,
( X1 != X2
| hAPP_f800510211t_bool(X3,X1) = hAPP_f800510211t_bool(X3,X2) ) ).
cnf(i_0_3601_152,axiom,
( X1 != X2
| hAPP_n850744903l_bool(X1,X3) = hAPP_n850744903l_bool(X2,X3) ) ).
cnf(i_0_3602_153,axiom,
( X1 != X2
| hAPP_n850744903l_bool(X3,X1) = hAPP_n850744903l_bool(X3,X2) ) ).
cnf(i_0_3603_154,axiom,
( X1 != X2
| hAPP_f921600141ol_nat(X1,X3) = hAPP_f921600141ol_nat(X2,X3) ) ).
cnf(i_0_3604_155,axiom,
( X1 != X2
| hAPP_f921600141ol_nat(X3,X1) = hAPP_f921600141ol_nat(X3,X2) ) ).
cnf(i_0_3605_156,axiom,
( X1 != X2
| image_1551609309ol_nat(X1,X3) = image_1551609309ol_nat(X2,X3) ) ).
cnf(i_0_3606_157,axiom,
( X1 != X2
| image_1551609309ol_nat(X3,X1) = image_1551609309ol_nat(X3,X2) ) ).
cnf(i_0_3607_158,axiom,
( X1 != X2
| hAPP_p338031245l_bool(X1,X3) = hAPP_p338031245l_bool(X2,X3) ) ).
cnf(i_0_3608_159,axiom,
( X1 != X2
| hAPP_p338031245l_bool(X3,X1) = hAPP_p338031245l_bool(X3,X2) ) ).
cnf(i_0_3609_160,axiom,
( X1 != X2
| hAPP_pname_a(X1,X3) = hAPP_pname_a(X2,X3) ) ).
cnf(i_0_3610_161,axiom,
( X1 != X2
| hAPP_pname_a(X3,X1) = hAPP_pname_a(X3,X2) ) ).
cnf(i_0_3611_162,axiom,
( X1 != X2
| image_1283814551_pname(X1,X3) = image_1283814551_pname(X2,X3) ) ).
cnf(i_0_3612_163,axiom,
( X1 != X2
| image_1283814551_pname(X3,X1) = image_1283814551_pname(X3,X2) ) ).
cnf(i_0_3613_164,axiom,
( X1 != X2
| hAPP_n1414589940l_bool(X1,X3) = hAPP_n1414589940l_bool(X2,X3) ) ).
cnf(i_0_3614_165,axiom,
( X1 != X2
| hAPP_n1414589940l_bool(X3,X1) = hAPP_n1414589940l_bool(X3,X2) ) ).
cnf(i_0_3615_166,axiom,
( X1 != X2
| hAPP_fun_a_bool_nat(X1,X3) = hAPP_fun_a_bool_nat(X2,X3) ) ).
cnf(i_0_3616_167,axiom,
( X1 != X2
| hAPP_fun_a_bool_nat(X3,X1) = hAPP_fun_a_bool_nat(X3,X2) ) ).
cnf(i_0_3617_168,axiom,
( X1 != X2
| image_fun_a_bool_nat(X1,X3) = image_fun_a_bool_nat(X2,X3) ) ).
cnf(i_0_3618_169,axiom,
( X1 != X2
| image_fun_a_bool_nat(X3,X1) = image_fun_a_bool_nat(X3,X2) ) ).
cnf(i_0_3619_170,axiom,
( X1 != X2
| hAPP_p1824510254l_bool(X1,X3) = hAPP_p1824510254l_bool(X2,X3) ) ).
cnf(i_0_3620_171,axiom,
( X1 != X2
| hAPP_p1824510254l_bool(X3,X1) = hAPP_p1824510254l_bool(X3,X2) ) ).
cnf(i_0_3621_172,axiom,
( X1 != X2
| image_1854862208_pname(X1,X3) = image_1854862208_pname(X2,X3) ) ).
cnf(i_0_3622_173,axiom,
( X1 != X2
| image_1854862208_pname(X3,X1) = image_1854862208_pname(X3,X2) ) ).
cnf(i_0_3623_174,axiom,
( X1 != X2
| hAPP_f654413245e_bool(X1,X3) = hAPP_f654413245e_bool(X2,X3) ) ).
cnf(i_0_3624_175,axiom,
( X1 != X2
| hAPP_f654413245e_bool(X3,X1) = hAPP_f654413245e_bool(X3,X2) ) ).
cnf(i_0_3625_176,axiom,
( X1 != X2
| hAPP_p1499970991t_bool(X1,X3) = hAPP_p1499970991t_bool(X2,X3) ) ).
cnf(i_0_3626_177,axiom,
( X1 != X2
| hAPP_p1499970991t_bool(X3,X1) = hAPP_p1499970991t_bool(X3,X2) ) ).
cnf(i_0_3627_178,axiom,
( X1 != X2
| image_2129980159t_bool(X1,X3) = image_2129980159t_bool(X2,X3) ) ).
cnf(i_0_3628_179,axiom,
( X1 != X2
| image_2129980159t_bool(X3,X1) = image_2129980159t_bool(X3,X2) ) ).
cnf(i_0_3629_180,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_3630_181,axiom,
( X1 != X2
| ~ is_pname(X1)
| is_pname(X2) ) ).
cnf(i_0_3631_182,axiom,
( X1 != X2
| ~ is_a(X1)
| is_a(X2) ) ).
cnf(i_0_3632_183,axiom,
( X1 != X2
| ~ is_fun_pname_bool(X1)
| is_fun_pname_bool(X2) ) ).
cnf(i_0_3633_184,axiom,
( X1 != X2
| ~ is_fun_a_bool(X1)
| is_fun_a_bool(X2) ) ).
cnf(i_0_3634_185,axiom,
( X1 != X2
| ~ is_fun949378684l_bool(X1)
| is_fun949378684l_bool(X2) ) ).
cnf(i_0_3635_186,axiom,
( X1 != X2
| ~ is_fun1661590463l_bool(X1)
| is_fun1661590463l_bool(X2) ) ).
cnf(i_0_3636_187,axiom,
( X1 != X2
| ~ is_bool(X1)
| is_bool(X2) ) ).
cnf(i_0_3637,plain,
( ~ is_pname(X1)
| ~ is_pname(X2)
| ~ is_pname(X1)
| ~ is_pname(X2)
| X2 = X2
| X2 = X1 ),
inference(equality_inference,[],[2143]) ).
cnf(i_0_3638,plain,
( ~ is_pname(X1)
| ~ is_pname(X2)
| ~ is_pname(X1)
| ~ is_pname(X2)
| X2 = X2
| X2 = X1 ),
inference(equality_inference,[],[2144]) ).
cnf(i_0_3639,plain,
( ~ is_a(X1)
| ~ is_a(X2)
| ~ is_a(X1)
| ~ is_a(X2)
| X2 = X2
| X2 = X1 ),
inference(equality_inference,[],[2145]) ).
cnf(i_0_3640,plain,
( ~ is_a(X1)
| ~ is_a(X2)
| ~ is_a(X1)
| ~ is_a(X2)
| X2 = X2
| X2 = X1 ),
inference(equality_inference,[],[2146]) ).
cnf(i_0_3641,plain,
( ~ is_pname(X1)
| ~ is_pname(X2)
| ~ is_pname(X2)
| ~ is_pname(X1)
| X2 = X2
| X1 = X2 ),
inference(equality_inference,[],[2147]) ).
cnf(i_0_3642,plain,
( ~ is_pname(X1)
| ~ is_pname(X2)
| ~ is_pname(X2)
| ~ is_pname(X1)
| X2 = X2
| X1 = X2 ),
inference(equality_inference,[],[2148]) ).
cnf(i_0_3643,plain,
( ~ is_a(X1)
| ~ is_a(X2)
| ~ is_a(X2)
| ~ is_a(X1)
| X2 = X2
| X1 = X2 ),
inference(equality_inference,[],[2149]) ).
cnf(i_0_3644,plain,
( ~ is_a(X1)
| ~ is_a(X2)
| ~ is_a(X2)
| ~ is_a(X1)
| X2 = X2
| X1 = X2 ),
inference(equality_inference,[],[2150]) ).
cnf(i_0_3645,plain,
( X1 = X1
| X1 = X2 ),
inference(equality_inference,[],[2206]) ).
cnf(i_0_3646,plain,
( X1 = X1
| X1 = X2 ),
inference(equality_inference,[],[2207]) ).
cnf(i_0_3647,plain,
( X1 = X1
| X2 = X1 ),
inference(equality_inference,[],[2208]) ).
cnf(i_0_3648,plain,
( X1 = X1
| X2 = X1 ),
inference(equality_inference,[],[2209]) ).
cnf(i_0_3649,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),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(equality_inference,[],[2267]) ).
cnf(i_0_3650,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),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(equality_inference,[],[2268]) ).
cnf(i_0_3651,plain,
( ~ is_pname(X1)
| ~ is_pname(X1)
| hBOOL(hAPP_pname_bool(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))),X1)) ),
inference(equality_inference,[],[2285]) ).
cnf(i_0_3652,plain,
( ~ is_a(X1)
| ~ is_a(X1)
| hBOOL(hAPP_a_bool(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))),X1)) ),
inference(equality_inference,[],[2286]) ).
cnf(i_0_3653,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,[],[2292]) ).
cnf(i_0_3654,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,[],[2293]) ).
cnf(i_0_3655,plain,
( ~ is_pname(X1)
| ~ is_pname(X1)
| X1 = X1 ),
inference(equality_inference,[],[2303]) ).
cnf(i_0_3656,plain,
( ~ is_a(X1)
| ~ is_a(X1)
| X1 = X1 ),
inference(equality_inference,[],[2304]) ).
cnf(i_0_3657,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),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(equality_inference,[],[2392]) ).
cnf(i_0_3658,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,[],[2404]) ).
cnf(i_0_3659,plain,
hBOOL(hAPP_nat_bool(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)),X1)),
inference(equality_inference,[],[2405]) ).
cnf(i_0_3660,plain,
X1 = X1,
inference(equality_inference,[],[2531]) ).
cnf(i_0_3661,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,[],[2716]) ).
cnf(i_0_3662,plain,
( ~ is_fun_pname_bool(image_a_pname(X1,X2))
| ~ is_fun_a_bool(X2)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X3))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(X1,X2)),image_a_pname(X1,X3))) ),
inference(equality_inference,[],[2742]) ).
cnf(i_0_3663,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,[],[2743]) ).
cnf(i_0_3664,plain,
( ~ is_fun_a_bool(X1)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(X3,X1)),image_a_nat(X3,X2))) ),
inference(equality_inference,[],[2748]) ).
cnf(i_0_3665,plain,
( ~ is_fun_a_bool(image_nat_a(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(X1,X2)),image_nat_a(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X3)) ),
inference(equality_inference,[],[2749]) ).
cnf(i_0_3666,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(X1,X2)),image_pname_nat(X1,X3)))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X2),X3)) ),
inference(equality_inference,[],[2792]) ).
cnf(i_0_3667,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(X1,X2)),image_a_nat(X1,X3)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X2),X3)) ),
inference(equality_inference,[],[2793]) ).
cnf(i_0_3668,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(X1,X2)),image_nat_pname(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3)) ),
inference(equality_inference,[],[2795]) ).
cnf(i_0_3669,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(X1,X2)),image_nat_a(X1,X3)))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X2),X3)) ),
inference(equality_inference,[],[2798]) ).
cnf(i_0_3670,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,[],[2799]) ).
cnf(i_0_3671,plain,
( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X2) = X1
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),hAPP_nat_nat(plus_plus_nat(X1),X2))) ),
inference(equality_inference,[],[2944]) ).
cnf(i_0_3672,plain,
( X1 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X2)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X1)) ),
inference(equality_inference,[],[2945]) ).
cnf(i_0_3673,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),X2)))),
inference(equality_inference,[],[2950]) ).
cnf(i_0_3674,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X1))),
inference(equality_inference,[],[2993]) ).
cnf(i_0_3675,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(equality_inference,[],[3012]) ).
cnf(i_0_3676,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(equality_inference,[],[3013]) ).
cnf(i_0_3677,plain,
~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),bot_bo844097828e_bool)),
inference(equality_inference,[],[3032]) ).
cnf(i_0_3678,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),bot_bot_fun_a_bool)),
inference(equality_inference,[],[3033]) ).
cnf(i_0_3679,plain,
~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),bot_bot_fun_nat_bool)),
inference(equality_inference,[],[3034]) ).
cnf(i_0_3680,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X1),X2))),
inference(equality_inference,[],[3058]) ).
cnf(i_0_3681,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X1)),
inference(equality_inference,[],[3178]) ).
cnf(i_0_3682,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(equality_inference,[],[3185]) ).
cnf(i_0_3683,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(equality_inference,[],[3187]) ).
cnf(i_0_3684,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X1)),
inference(equality_inference,[],[3188]) ).
cnf(i_0_3685,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X1)),
inference(equality_inference,[],[3192]) ).
cnf(i_0_3686,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X1)),
inference(equality_inference,[],[3193]) ).
cnf(i_0_3687,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X1)),
inference(equality_inference,[],[3194]) ).
cnf(i_0_3688,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(equality_inference,[],[3198]) ).
cnf(i_0_3689,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(equality_inference,[],[3199]) ).
cnf(i_0_3690,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X1)),
inference(equality_inference,[],[3200]) ).
cnf(i_0_3691,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(equality_inference,[],[3204]) ).
cnf(i_0_3692,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(equality_inference,[],[3206]) ).
cnf(i_0_3693,plain,
hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X1)),
inference(equality_inference,[],[3207]) ).
cnf(i_0_3694,plain,
hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X1)),
inference(equality_inference,[],[3208]) ).
cnf(i_0_3695,plain,
X1 = X1,
inference(equality_inference,[],[3236]) ).
cnf(i_0_3696,plain,
X1 = X1,
inference(equality_inference,[],[3237]) ).
cnf(i_0_3697,plain,
~ hBOOL(hAPP_f54304608l_bool(bot_bo1701429464l_bool,X1)),
inference(equality_inference,[],[3260]) ).
cnf(i_0_3698,plain,
~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1)),
inference(equality_inference,[],[3261]) ).
cnf(i_0_3699,plain,
~ hBOOL(hAPP_f54304608l_bool(bot_bo1701429464l_bool,X1)),
inference(equality_inference,[],[3262]) ).
cnf(i_0_3700,plain,
~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X1)),
inference(equality_inference,[],[3263]) ).
cnf(i_0_3701,plain,
X1 = X1,
inference(equality_inference,[],[3291]) ).
cnf(i_0_3702,plain,
( ~ is_fun_pname_bool(bot_bo844097828e_bool)
| image_pname_a(X1,bot_bo844097828e_bool) = bot_bot_fun_a_bool ),
inference(equality_inference,[],[3385]) ).
cnf(i_0_3703,plain,
( ~ is_fun_pname_bool(bot_bo844097828e_bool)
| bot_bot_fun_a_bool = image_pname_a(X1,bot_bo844097828e_bool) ),
inference(equality_inference,[],[3386]) ).
cnf(i_0_3704,plain,
~ hBOOL(bot_bot_bool),
inference(scs_inference,[],[i_0_3698,i_0_3339]) ).
cnf(i_0_3705,plain,
bot_bot_fun_a_bool = image_pname_a(X1,bot_bo844097828e_bool),
inference(scs_inference,[],[i_0_3444,i_0_3703]) ).
cnf(i_0_3706,plain,
is_a(esk84_2(collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))),image_pname_a(mgt_call,u))),
inference(scs_inference,[],[i_0_2152,i_0_3069]) ).
cnf(i_0_3707,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| is_a(esk84_2(X1,X2)) ),
inference(rename_variables,[],[i_0_3069]) ).
cnf(i_0_3708,plain,
is_a(esk71_2(image_pname_a(mgt_call,u),collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))))),
inference(scs_inference,[],[i_0_2152,i_0_3069,i_0_3070]) ).
cnf(i_0_3709,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| is_a(esk71_2(X2,X1)) ),
inference(rename_variables,[],[i_0_3070]) ).
cnf(i_0_3710,plain,
collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))) != image_pname_a(mgt_call,u),
inference(scs_inference,[],[i_0_2152,i_0_3069,i_0_3070,i_0_3198]) ).
cnf(i_0_3711,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_3198]) ).
cnf(i_0_3712,plain,
image_pname_a(mgt_call,u) != collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(mgt_call,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),g))),
inference(scs_inference,[],[i_0_2152,i_0_3069,i_0_3070,i_0_3198,i_0_3199]) ).
cnf(i_0_3713,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X2 != X1 ),
inference(rename_variables,[],[i_0_3199]) ).
cnf(i_0_3714,plain,
collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),hAPP_pname_pname(X1,pn))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),image_pname_pname(X1,u)))) = image_pname_pname(X1,u),
inference(scs_inference,[],[i_0_2152,i_0_3234,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356]) ).
cnf(i_0_3715,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),hAPP_pname_pname(X3,X1))),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),image_pname_pname(X3,X2)))) = image_pname_pname(X3,X2) ),
inference(rename_variables,[],[i_0_2356]) ).
cnf(i_0_3716,plain,
collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(X1,pn))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X1,u)))) = image_pname_a(X1,u),
inference(scs_inference,[],[i_0_2152,i_0_3234,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359]) ).
cnf(i_0_3717,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),hAPP_pname_a(X3,X1))),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),image_pname_a(X3,X2)))) = image_pname_a(X3,X2) ),
inference(rename_variables,[],[i_0_2359]) ).
cnf(i_0_3718,plain,
~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),image_a_nat(X2,bot_bot_fun_a_bool))),
inference(scs_inference,[],[i_0_2152,i_0_3054,i_0_3234,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369]) ).
cnf(i_0_3719,plain,
~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),bot_bot_fun_a_bool)),
inference(rename_variables,[],[i_0_3054]) ).
cnf(i_0_3720,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk67_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),image_a_nat(X2,X3))) ),
inference(rename_variables,[],[i_0_2369]) ).
cnf(i_0_3721,plain,
cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),hAPP_pname_nat(X1,pn))),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),image_pname_nat(X1,u))) = image_pname_nat(X1,u),
inference(scs_inference,[],[i_0_2152,i_0_3054,i_0_3234,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522]) ).
cnf(i_0_3722,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),hAPP_pname_nat(X3,X1))),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),image_pname_nat(X3,X2))) = image_pname_nat(X3,X2) ),
inference(rename_variables,[],[i_0_2522]) ).
cnf(i_0_3723,plain,
image_pname_a(cOMBK_a_pname(X1),u) = 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),bot_bot_fun_a_bool))),
inference(scs_inference,[],[i_0_2152,i_0_3054,i_0_3234,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533]) ).
cnf(i_0_3724,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| image_pname_a(cOMBK_a_pname(X3),X2) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X3)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),bot_bot_fun_a_bool))) ),
inference(rename_variables,[],[i_0_2533]) ).
cnf(i_0_3725,plain,
hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X2),X2))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),hAPP_nat_nat(suc,X2)),
inference(scs_inference,[],[i_0_2152,i_0_3054,i_0_3216,i_0_3234,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600]) ).
cnf(i_0_3726,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(minus_minus_nat(X3),hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X2),X1))) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3),X1)),hAPP_nat_nat(suc,X2)) ),
inference(rename_variables,[],[i_0_2600]) ).
cnf(i_0_3727,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(X1,X2)),image_a_nat(X1,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))))),
inference(scs_inference,[],[i_0_2152,i_0_3054,i_0_2272,i_0_3216,i_0_3234,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608]) ).
cnf(i_0_3728,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_a_nat(X3,X1)),image_a_nat(X3,X2))) ),
inference(rename_variables,[],[i_0_2608]) ).
cnf(i_0_3729,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(X1,bot_bot_fun_a_bool)),image_a_nat(X1,X2))),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3216,i_0_3234,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609]) ).
cnf(i_0_3730,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_a_nat(X3,X1)),image_a_nat(X3,X2))) ),
inference(rename_variables,[],[i_0_2609]) ).
cnf(i_0_3731,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(X1,bot_bot_fun_a_bool)),image_a_pname(X1,X2))),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3216,i_0_3234,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610]) ).
cnf(i_0_3732,plain,
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,image_a_pname(X3,X1)),image_a_pname(X3,X2))) ),
inference(rename_variables,[],[i_0_2610]) ).
cnf(i_0_3733,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(X1,bot_bot_fun_nat_bool)),image_nat_a(X1,X2))),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3216,i_0_3225,i_0_3234,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612]) ).
cnf(i_0_3734,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_nat_a(X3,X1)),image_nat_a(X3,X2))) ),
inference(rename_variables,[],[i_0_2612]) ).
cnf(i_0_3735,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,bot_bo844097828e_bool)),image_pname_a(X1,X2))),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3216,i_0_3225,i_0_3227,i_0_3234,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613]) ).
cnf(i_0_3736,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X3,X1)),image_pname_a(X3,X2))) ),
inference(rename_variables,[],[i_0_2613]) ).
cnf(i_0_3737,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(X1,X2)),image_nat_a(X1,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X3))))),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3216,i_0_3225,i_0_3227,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614]) ).
cnf(i_0_3738,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_nat_a(X3,X1)),image_nat_a(X3,X2))) ),
inference(rename_variables,[],[i_0_2614]) ).
cnf(i_0_3739,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_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3216,i_0_3225,i_0_3227,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615]) ).
cnf(i_0_3740,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_2615]) ).
cnf(i_0_3741,plain,
hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(bot_bot_fun_a_bool,X1)),hAPP_a_bool(X2,X1))),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3216,i_0_3225,i_0_3227,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622]) ).
cnf(i_0_3742,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_2622]) ).
cnf(i_0_3743,plain,
image_a_nat(X1,X2) = image_a_nat(X1,esk62_3(image_a_nat(X1,X2),X1,X2)),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3225,i_0_3227,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675]) ).
cnf(i_0_3744,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(rename_variables,[],[i_0_3210]) ).
cnf(i_0_3745,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),image_a_nat(X2,X3)))
| X1 = image_a_nat(X2,esk62_3(X1,X2,X3)) ),
inference(rename_variables,[],[i_0_2675]) ).
cnf(i_0_3746,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X1),X1)),X2) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X1),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3225,i_0_3227,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707]) ).
cnf(i_0_3747,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),X3) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X2),X3)),X1) ),
inference(rename_variables,[],[i_0_2707]) ).
cnf(i_0_3748,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X1),X1)),X2),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3225,i_0_3227,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708]) ).
cnf(i_0_3749,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X2),X3)),X1) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),X3) ),
inference(rename_variables,[],[i_0_2708]) ).
cnf(i_0_3750,plain,
hAPP_nat_nat(suc,hAPP_nat_nat(suc,X1)) = hAPP_nat_nat(suc,esk133_2(X1,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X1)))),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3225,i_0_3227,i_0_3037,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717]) ).
cnf(i_0_3751,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X1))),
inference(rename_variables,[],[i_0_3037]) ).
cnf(i_0_3752,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X2))
| X2 = hAPP_nat_nat(suc,esk133_2(X1,X2)) ),
inference(rename_variables,[],[i_0_2717]) ).
cnf(i_0_3753,plain,
hAPP_nat_nat(suc,X1) = hAPP_nat_nat(suc,esk58_2(X1,hAPP_nat_nat(suc,X1))),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3225,i_0_3227,i_0_3037,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718]) ).
cnf(i_0_3754,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(rename_variables,[],[i_0_3216]) ).
cnf(i_0_3755,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| X2 = hAPP_nat_nat(suc,esk58_2(X1,X2)) ),
inference(rename_variables,[],[i_0_2718]) ).
cnf(i_0_3756,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X2) = hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(minus_minus_nat(X2),X2)),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752]) ).
cnf(i_0_3757,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3),X2)),X1) = hAPP_nat_nat(plus_plus_nat(X3),hAPP_nat_nat(minus_minus_nat(X2),X1)) ),
inference(rename_variables,[],[i_0_2752]) ).
cnf(i_0_3758,plain,
hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(minus_minus_nat(X2),X2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X2),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753]) ).
cnf(i_0_3759,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(plus_plus_nat(X3),hAPP_nat_nat(minus_minus_nat(X2),X1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3),X2)),X1) ),
inference(rename_variables,[],[i_0_2753]) ).
cnf(i_0_3760,plain,
hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X2),X2)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X2),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754]) ).
cnf(i_0_3761,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(minus_minus_nat(X3),hAPP_nat_nat(minus_minus_nat(X2),X1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X3),X1)),X2) ),
inference(rename_variables,[],[i_0_2754]) ).
cnf(i_0_3762,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X1) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1),X1)),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859]) ).
cnf(i_0_3763,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X2)),X1) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X2),X1)) ),
inference(rename_variables,[],[i_0_2859]) ).
cnf(i_0_3764,plain,
hAPP_nat_nat(suc,X1) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),esk129_2(X1,hAPP_nat_nat(suc,X1)))),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3751,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865]) ).
cnf(i_0_3765,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),esk129_2(X1,X2))) ),
inference(rename_variables,[],[i_0_2865]) ).
cnf(i_0_3766,plain,
hAPP_nat_nat(suc,X1) = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),esk125_2(X1,hAPP_nat_nat(suc,X1)))),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3751,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866]) ).
cnf(i_0_3767,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 = hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),esk125_2(X1,X2))) ),
inference(rename_variables,[],[i_0_2866]) ).
cnf(i_0_3768,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X1),X1)),X1) = X1,
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3751,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867]) ).
cnf(i_0_3769,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),X1) = X2 ),
inference(rename_variables,[],[i_0_2867]) ).
cnf(i_0_3770,plain,
hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X1)) = X1,
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3751,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941]) ).
cnf(i_0_3771,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(minus_minus_nat(X2),X1)) = X2 ),
inference(rename_variables,[],[i_0_2941]) ).
cnf(i_0_3772,plain,
hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X1)) = X1,
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3751,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942]) ).
cnf(i_0_3773,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(minus_minus_nat(X2),hAPP_nat_nat(minus_minus_nat(X2),X1)) = X1 ),
inference(rename_variables,[],[i_0_2942]) ).
cnf(i_0_3774,plain,
X1 = hAPP_nat_nat(plus_plus_nat(X1),esk122_2(X1,X1)),
inference(scs_inference,[],[i_0_2152,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3751,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947]) ).
cnf(i_0_3775,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 = hAPP_nat_nat(plus_plus_nat(X1),esk122_2(X1,X2)) ),
inference(rename_variables,[],[i_0_2947]) ).
cnf(i_0_3776,plain,
hBOOL(hAPP_fun_a_bool_bool(p(X1),X1)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3751,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948]) ).
cnf(i_0_3777,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_2948]) ).
cnf(i_0_3778,plain,
hBOOL(hAPP_a_bool(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))),X1)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3751,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964]) ).
cnf(i_0_3779,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_2964]) ).
cnf(i_0_3780,plain,
hAPP_nat_nat(minus_minus_nat(bot_bot_nat),X1) = zero_zero_nat,
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3751,i_0_3232,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975]) ).
cnf(i_0_3781,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(minus_minus_nat(X1),X2) = zero_zero_nat ),
inference(rename_variables,[],[i_0_2975]) ).
cnf(i_0_3782,plain,
hAPP_nat_nat(plus_plus_nat(zero_zero_nat),hAPP_nat_nat(minus_minus_nat(X1),zero_zero_nat)) = X1,
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3751,i_0_3232,i_0_3055,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984]) ).
cnf(i_0_3783,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(minus_minus_nat(X1),X2)) = X1 ),
inference(rename_variables,[],[i_0_2984]) ).
cnf(i_0_3784,plain,
~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X1)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3751,i_0_3232,i_0_3055,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002]) ).
cnf(i_0_3785,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_3002]) ).
cnf(i_0_3786,plain,
image_nat_a(X1,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X3))) != bot_bot_fun_a_bool,
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3037,i_0_3751,i_0_3232,i_0_3055,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033]) ).
cnf(i_0_3787,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_3033]) ).
cnf(i_0_3788,plain,
zero_zero_nat = bot_bot_nat,
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3232,i_0_3055,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044]) ).
cnf(i_0_3789,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),X1)),
inference(rename_variables,[],[i_0_3231]) ).
cnf(i_0_3790,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_3044]) ).
cnf(i_0_3791,plain,
image_a_nat(X1,bot_bot_fun_a_bool) = bot_bot_fun_nat_bool,
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3232,i_0_3055,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077]) ).
cnf(i_0_3792,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk100_1(X1)),X1))
| X1 = bot_bot_fun_nat_bool ),
inference(rename_variables,[],[i_0_3077]) ).
cnf(i_0_3793,plain,
collect_a(bot_bot_fun_a_bool) = bot_bot_fun_a_bool,
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3232,i_0_3055,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270]) ).
cnf(i_0_3794,plain,
( hBOOL(hAPP_a_bool(X1,esk89_1(X1)))
| collect_a(X1) = bot_bot_fun_a_bool ),
inference(rename_variables,[],[i_0_3270]) ).
cnf(i_0_3795,plain,
hAPP_nat_nat(suc,X1) = esk133_2(X1,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X1))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3232,i_0_3055,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291]) ).
cnf(i_0_3796,plain,
( hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3291]) ).
cnf(i_0_3797,plain,
X1 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X1),X1)),X1),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3232,i_0_3055,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672]) ).
cnf(i_0_3798,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X2),X1)),X1) ),
inference(rename_variables,[],[i_0_3672]) ).
cnf(i_0_3799,plain,
~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),image_pname_nat(X2,bot_bo844097828e_bool))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367]) ).
cnf(i_0_3800,plain,
~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),bot_bo844097828e_bool)),
inference(rename_variables,[],[i_0_3052]) ).
cnf(i_0_3801,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk66_3(X1,X2,X3)),X3))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),image_pname_nat(X2,X3))) ),
inference(rename_variables,[],[i_0_2367]) ).
cnf(i_0_3802,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),X2))),X2))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433]) ).
cnf(i_0_3803,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X1))),
inference(rename_variables,[],[i_0_3037]) ).
cnf(i_0_3804,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(minus_minus_nat(X3),X2))) ),
inference(rename_variables,[],[i_0_2433]) ).
cnf(i_0_3805,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(minus_minus_nat(X1),X2)),X2))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434]) ).
cnf(i_0_3806,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(rename_variables,[],[i_0_3216]) ).
cnf(i_0_3807,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),X3))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X3),X2))) ),
inference(rename_variables,[],[i_0_2434]) ).
cnf(i_0_3808,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X2))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2394,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483]) ).
cnf(i_0_3809,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(rename_variables,[],[i_0_3039]) ).
cnf(i_0_3810,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X3))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(minus_minus_nat(X3),X2))) ),
inference(rename_variables,[],[i_0_2483]) ).
cnf(i_0_3811,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3)))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2394,i_0_2756,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505]) ).
cnf(i_0_3812,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),X2)))),
inference(rename_variables,[],[i_0_2756]) ).
cnf(i_0_3813,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_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_2505]) ).
cnf(i_0_3814,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_2394,i_0_2756,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508]) ).
cnf(i_0_3815,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X1),X2))),
inference(rename_variables,[],[i_0_2960]) ).
cnf(i_0_3816,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_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_2508]) ).
cnf(i_0_3817,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X2),X1)),X3))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3210,i_0_3216,i_0_3754,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_2394,i_0_2756,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509]) ).
cnf(i_0_3818,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X1),X2))),
inference(rename_variables,[],[i_0_2960]) ).
cnf(i_0_3819,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_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_2509]) ).
cnf(i_0_3820,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_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3210,i_0_3216,i_0_3754,i_0_3806,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_2394,i_0_2756,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510]) ).
cnf(i_0_3821,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(rename_variables,[],[i_0_3216]) ).
cnf(i_0_3822,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_2510]) ).
cnf(i_0_3823,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,X1)),X2))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3210,i_0_3216,i_0_3754,i_0_3806,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529]) ).
cnf(i_0_3824,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),X2)))),
inference(rename_variables,[],[i_0_2756]) ).
cnf(i_0_3825,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_2529]) ).
cnf(i_0_3826,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),esk133_2(X1,hAPP_nat_nat(suc,hAPP_nat_nat(suc,X1))))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3210,i_0_3216,i_0_3754,i_0_3806,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538]) ).
cnf(i_0_3827,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X1))),
inference(rename_variables,[],[i_0_3037]) ).
cnf(i_0_3828,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),esk133_2(X1,X2))) ),
inference(rename_variables,[],[i_0_2538]) ).
cnf(i_0_3829,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,X1)),X2)),X1)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3210,i_0_3216,i_0_3754,i_0_3806,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547]) ).
cnf(i_0_3830,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X1),X2))),
inference(rename_variables,[],[i_0_2960]) ).
cnf(i_0_3831,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_2547]) ).
cnf(i_0_3832,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(X1,pn)),image_pname_nat(X1,u))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3210,i_0_3216,i_0_3754,i_0_3806,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607]) ).
cnf(i_0_3833,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_pname_nat(X3,X1)),image_pname_nat(X3,X2))) ),
inference(rename_variables,[],[i_0_2607]) ).
cnf(i_0_3834,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(X1,X2)),image_nat_pname(X1,cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X3))))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3210,i_0_3216,i_0_3754,i_0_3806,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611]) ).
cnf(i_0_3835,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_nat_pname(X3,X1)),image_nat_pname(X3,X2))) ),
inference(rename_variables,[],[i_0_2611]) ).
cnf(i_0_3836,plain,
hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(bot_bot_fun_nat_bool,X1)),hAPP_nat_bool(X2,X1))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3210,i_0_3216,i_0_3754,i_0_3806,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618]) ).
cnf(i_0_3837,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_2618]) ).
cnf(i_0_3838,plain,
hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(bot_bo844097828e_bool,X1)),hAPP_pname_bool(X2,X1))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3210,i_0_3216,i_0_3754,i_0_3806,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620]) ).
cnf(i_0_3839,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_pname_bool(X1,X3)),hAPP_pname_bool(X2,X3))) ),
inference(rename_variables,[],[i_0_2620]) ).
cnf(i_0_3840,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(minus_minus_nat(X1),X2))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3210,i_0_3216,i_0_3754,i_0_3806,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623]) ).
cnf(i_0_3841,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(rename_variables,[],[i_0_3039]) ).
cnf(i_0_3842,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_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_2623]) ).
cnf(i_0_3843,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_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3210,i_0_3216,i_0_3754,i_0_3806,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634]) ).
cnf(i_0_3844,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X1))),
inference(rename_variables,[],[i_0_3037]) ).
cnf(i_0_3845,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_2634]) ).
cnf(i_0_3846,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(suc,X1)))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3210,i_0_3216,i_0_3754,i_0_3806,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637]) ).
cnf(i_0_3847,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X1))),
inference(rename_variables,[],[i_0_2961]) ).
cnf(i_0_3848,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_2637]) ).
cnf(i_0_3849,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X1))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3210,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638]) ).
cnf(i_0_3850,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(rename_variables,[],[i_0_3216]) ).
cnf(i_0_3851,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_2638]) ).
cnf(i_0_3852,plain,
is_pname(esk66_3(hAPP_pname_nat(X1,pn),X1,u)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3210,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709]) ).
cnf(i_0_3853,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),image_pname_nat(X2,X3)))
| is_pname(esk66_3(X1,X2,X3)) ),
inference(rename_variables,[],[i_0_2709]) ).
cnf(i_0_3854,plain,
is_a(esk67_3(hAPP_a_nat(X1,X2),X1,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3))))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3210,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710]) ).
cnf(i_0_3855,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),image_a_nat(X2,X3)))
| is_a(esk67_3(X1,X2,X3)) ),
inference(rename_variables,[],[i_0_2710]) ).
cnf(i_0_3856,plain,
is_fun_a_bool(esk62_3(image_a_nat(X1,X2),X1,X2)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711]) ).
cnf(i_0_3857,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(rename_variables,[],[i_0_3210]) ).
cnf(i_0_3858,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),image_a_nat(X2,X3)))
| is_fun_a_bool(esk62_3(X1,X2,X3)) ),
inference(rename_variables,[],[i_0_2711]) ).
cnf(i_0_3859,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3)),X1)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712]) ).
cnf(i_0_3860,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_2712]) ).
cnf(i_0_3861,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(plus_plus_nat(X2),X3))),X2)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2594,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759]) ).
cnf(i_0_3862,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X2)),
inference(rename_variables,[],[i_0_2594]) ).
cnf(i_0_3863,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2)) ),
inference(rename_variables,[],[i_0_2759]) ).
cnf(i_0_3864,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(X1),X2)),X3)),X2)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2593,i_0_2594,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761]) ).
cnf(i_0_3865,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X1)),
inference(rename_variables,[],[i_0_2593]) ).
cnf(i_0_3866,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(X2),X3)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X3)) ),
inference(rename_variables,[],[i_0_2761]) ).
cnf(i_0_3867,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),X2))),X1)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_2593,i_0_2594,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763]) ).
cnf(i_0_3868,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X1)),
inference(rename_variables,[],[i_0_2805]) ).
cnf(i_0_3869,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_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_2763]) ).
cnf(i_0_3870,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),X2))),X2)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_2593,i_0_2594,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765]) ).
cnf(i_0_3871,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X1)),
inference(rename_variables,[],[i_0_2805]) ).
cnf(i_0_3872,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_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_2765]) ).
cnf(i_0_3873,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,image_pname_nat(X1,bot_bo844097828e_bool)),X2)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_2593,i_0_2594,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824]) ).
cnf(i_0_3874,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk69_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
inference(rename_variables,[],[i_0_2824]) ).
cnf(i_0_3875,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,X1)),X1)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_2593,i_0_2594,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852]) ).
cnf(i_0_3876,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X1)),
inference(rename_variables,[],[i_0_3039]) ).
cnf(i_0_3877,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_2852]) ).
cnf(i_0_3878,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(plus_plus_nat(X1),hAPP_nat_nat(suc,X2))),X2)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_2593,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854]) ).
cnf(i_0_3879,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X2)),
inference(rename_variables,[],[i_0_2594]) ).
cnf(i_0_3880,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_2854]) ).
cnf(i_0_3881,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_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_2593,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856]) ).
cnf(i_0_3882,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X1)),
inference(rename_variables,[],[i_0_2805]) ).
cnf(i_0_3883,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_2856]) ).
cnf(i_0_3884,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,X1)),X2)),X3))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_2593,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899]) ).
cnf(i_0_3885,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_2899]) ).
cnf(i_0_3886,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1),X2)),hAPP_nat_nat(suc,X1))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_2593,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911]) ).
cnf(i_0_3887,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_2911]) ).
cnf(i_0_3888,plain,
X1 != hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),X2)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_2593,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950]) ).
cnf(i_0_3889,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 != hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),X3)) ),
inference(rename_variables,[],[i_0_2950]) ).
cnf(i_0_3890,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,X1)),X2))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_2593,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959]) ).
cnf(i_0_3891,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_2959]) ).
cnf(i_0_3892,plain,
hBOOL(hAPP_nat_bool(image_a_nat(X1,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))),hAPP_a_nat(X1,X2))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_2593,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962]) ).
cnf(i_0_3893,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| hBOOL(hAPP_nat_bool(X2,X1)) ),
inference(rename_variables,[],[i_0_2962]) ).
cnf(i_0_3894,plain,
hBOOL(hAPP_pname_bool(u,pn)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_2593,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963]) ).
cnf(i_0_3895,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hBOOL(hAPP_pname_bool(X2,X1)) ),
inference(rename_variables,[],[i_0_2963]) ).
cnf(i_0_3896,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,X1)),X2) != X1,
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993]) ).
cnf(i_0_3897,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(plus_plus_nat(X1),X2)),X1)),
inference(rename_variables,[],[i_0_2593]) ).
cnf(i_0_3898,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),hAPP_nat_nat(suc,X2)))
| X1 != X2 ),
inference(rename_variables,[],[i_0_2993]) ).
cnf(i_0_3899,plain,
~ hBOOL(hAPP_nat_bool(image_a_nat(X1,bot_bot_fun_a_bool),esk100_1(image_a_nat(X1,bot_bot_fun_a_bool)))),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000]) ).
cnf(i_0_3900,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| ~ hBOOL(hAPP_nat_bool(X2,X1)) ),
inference(rename_variables,[],[i_0_3000]) ).
cnf(i_0_3901,plain,
~ hBOOL(hAPP_pname_bool(bot_bo844097828e_bool,X1)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001]) ).
cnf(i_0_3902,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| ~ hBOOL(hAPP_pname_bool(X2,X1)) ),
inference(rename_variables,[],[i_0_3001]) ).
cnf(i_0_3903,plain,
hAPP_nat_nat(suc,X1) != hAPP_nat_nat(minus_minus_nat(X1),X2),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012]) ).
cnf(i_0_3904,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X2 != X1 ),
inference(rename_variables,[],[i_0_3012]) ).
cnf(i_0_3905,plain,
hAPP_nat_nat(minus_minus_nat(X1),X2) != hAPP_nat_nat(suc,X1),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013]) ).
cnf(i_0_3906,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_3013]) ).
cnf(i_0_3907,plain,
u != bot_bo844097828e_bool,
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032]) ).
cnf(i_0_3908,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| X2 != bot_bo844097828e_bool ),
inference(rename_variables,[],[i_0_3032]) ).
cnf(i_0_3909,plain,
image_a_nat(X1,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X3)))) != bot_bot_fun_nat_bool,
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034]) ).
cnf(i_0_3910,plain,
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2))
| X2 != bot_bot_fun_nat_bool ),
inference(rename_variables,[],[i_0_3034]) ).
cnf(i_0_3911,plain,
X1 != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(suc,X1)),X2),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058]) ).
cnf(i_0_3912,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 != hAPP_nat_nat(plus_plus_nat(X1),X3) ),
inference(rename_variables,[],[i_0_3058]) ).
cnf(i_0_3913,plain,
hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1)),X1) != zero_zero_nat,
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066]) ).
cnf(i_0_3914,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| hAPP_nat_nat(minus_minus_nat(X1),X2) != zero_zero_nat ),
inference(rename_variables,[],[i_0_3066]) ).
cnf(i_0_3915,plain,
X1 != hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X2),X1)),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066,i_0_3204]) ).
cnf(i_0_3916,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X2 != X1 ),
inference(rename_variables,[],[i_0_3204]) ).
cnf(i_0_3917,plain,
hAPP_nat_nat(suc,hAPP_nat_nat(plus_plus_nat(X1),X2)) != X1,
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066,i_0_3204,i_0_3206]) ).
cnf(i_0_3918,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_3206]) ).
cnf(i_0_3919,plain,
bot_bo1701429464l_bool != hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3681,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066,i_0_3204,i_0_3206,i_0_3260]) ).
cnf(i_0_3920,plain,
( ~ hBOOL(hAPP_f54304608l_bool(X1,X2))
| bot_bo1701429464l_bool != X1 ),
inference(rename_variables,[],[i_0_3260]) ).
cnf(i_0_3921,plain,
bot_bot_fun_nat_bool != hAPP_n1699378549t_bool(fequal_nat,X1),
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3681,i_0_3690,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066,i_0_3204,i_0_3206,i_0_3260,i_0_3261]) ).
cnf(i_0_3922,plain,
( ~ hBOOL(hAPP_nat_bool(X1,X2))
| bot_bot_fun_nat_bool != X1 ),
inference(rename_variables,[],[i_0_3261]) ).
cnf(i_0_3923,plain,
hAPP_f103356543l_bool(fequal_fun_nat_bool,X1) != bot_bo1701429464l_bool,
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3681,i_0_3690,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066,i_0_3204,i_0_3206,i_0_3260,i_0_3261,i_0_3262]) ).
cnf(i_0_3924,plain,
( ~ hBOOL(hAPP_f54304608l_bool(X1,X2))
| X1 != bot_bo1701429464l_bool ),
inference(rename_variables,[],[i_0_3262]) ).
cnf(i_0_3925,plain,
hAPP_n1699378549t_bool(fequal_nat,X1) != bot_bot_fun_nat_bool,
inference(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3681,i_0_3690,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066,i_0_3204,i_0_3206,i_0_3260,i_0_3261,i_0_3262,i_0_3263]) ).
cnf(i_0_3926,plain,
( ~ hBOOL(hAPP_nat_bool(X1,X2))
| X1 != bot_bot_fun_nat_bool ),
inference(rename_variables,[],[i_0_3263]) ).
cnf(i_0_3927,plain,
is_pname(esk85_1(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(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3681,i_0_3690,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2524,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066,i_0_3204,i_0_3206,i_0_3260,i_0_3261,i_0_3262,i_0_3263,i_0_3413]) ).
cnf(i_0_3928,plain,
( collect_pname(X1) = bot_bo844097828e_bool
| is_pname(esk85_1(X1)) ),
inference(rename_variables,[],[i_0_3413]) ).
cnf(i_0_3929,plain,
is_a(esk89_1(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(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3681,i_0_3690,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2524,i_0_2525,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066,i_0_3204,i_0_3206,i_0_3260,i_0_3261,i_0_3262,i_0_3263,i_0_3413,i_0_3414]) ).
cnf(i_0_3930,plain,
( collect_a(X1) = bot_bot_fun_a_bool
| is_a(esk89_1(X1)) ),
inference(rename_variables,[],[i_0_3414]) ).
cnf(i_0_3931,plain,
is_pname(esk91_1(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(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3681,i_0_3690,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2524,i_0_2525,i_0_2526,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066,i_0_3204,i_0_3206,i_0_3260,i_0_3261,i_0_3262,i_0_3263,i_0_3413,i_0_3414,i_0_3417]) ).
cnf(i_0_3932,plain,
( bot_bo844097828e_bool = collect_pname(X1)
| is_pname(esk91_1(X1)) ),
inference(rename_variables,[],[i_0_3417]) ).
cnf(i_0_3933,plain,
is_a(esk95_1(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(scs_inference,[],[i_0_2152,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3681,i_0_3690,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2524,i_0_2525,i_0_2526,i_0_2527,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066,i_0_3204,i_0_3206,i_0_3260,i_0_3261,i_0_3262,i_0_3263,i_0_3413,i_0_3414,i_0_3417,i_0_3418]) ).
cnf(i_0_3934,plain,
( bot_bot_fun_a_bool = collect_a(X1)
| is_a(esk95_1(X1)) ),
inference(rename_variables,[],[i_0_3418]) ).
cnf(i_0_3935,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_2152,i_0_3071,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3681,i_0_3690,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2524,i_0_2525,i_0_2526,i_0_2527,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066,i_0_3204,i_0_3206,i_0_3260,i_0_3261,i_0_3262,i_0_3263,i_0_3413,i_0_3414,i_0_3417,i_0_3418,i_0_3451]) ).
cnf(i_0_3936,plain,
plus_plus_nat(hAPP_nat_nat(suc,hAPP_nat_nat(X1,X2))) != X1,
inference(scs_inference,[],[i_0_2152,i_0_3071,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3681,i_0_3690,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2524,i_0_2525,i_0_2526,i_0_2527,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066,i_0_3204,i_0_3206,i_0_3260,i_0_3261,i_0_3262,i_0_3263,i_0_3413,i_0_3414,i_0_3417,i_0_3418,i_0_3451,i_0_3495]) ).
cnf(i_0_3937,plain,
X1 != hAPP_nat_nat(plus_plus_nat(X2),hAPP_nat_nat(suc,X1)),
inference(scs_inference,[],[i_0_2152,i_0_3071,i_0_3214,i_0_3229,i_0_3054,i_0_3719,i_0_2272,i_0_3681,i_0_3690,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2524,i_0_2525,i_0_2526,i_0_2527,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066,i_0_3204,i_0_3206,i_0_3260,i_0_3261,i_0_3262,i_0_3263,i_0_3413,i_0_3414,i_0_3417,i_0_3418,i_0_3451,i_0_3495,i_0_3496]) ).
cnf(i_0_3938,plain,
$false,
inference(scs_inference,[],[i_0_2152,i_0_3071,i_0_3214,i_0_3229,i_0_3059,i_0_3054,i_0_3719,i_0_2272,i_0_3681,i_0_3690,i_0_3039,i_0_3809,i_0_3841,i_0_3876,i_0_3210,i_0_3744,i_0_3216,i_0_3754,i_0_3806,i_0_3821,i_0_3225,i_0_3227,i_0_3231,i_0_3037,i_0_3751,i_0_3803,i_0_3827,i_0_2755,i_0_3232,i_0_3052,i_0_3800,i_0_3055,i_0_3234,i_0_2524,i_0_2525,i_0_2526,i_0_2527,i_0_2960,i_0_3815,i_0_3818,i_0_2961,i_0_2805,i_0_3868,i_0_3871,i_0_3882,i_0_2593,i_0_3865,i_0_2594,i_0_3862,i_0_2394,i_0_2756,i_0_3812,i_0_3069,i_0_3070,i_0_3198,i_0_3199,i_0_2356,i_0_2359,i_0_2369,i_0_2522,i_0_2533,i_0_2600,i_0_2608,i_0_2609,i_0_2610,i_0_2612,i_0_2613,i_0_2614,i_0_2615,i_0_2622,i_0_2675,i_0_2707,i_0_2708,i_0_2717,i_0_2718,i_0_2752,i_0_2753,i_0_2754,i_0_2859,i_0_2865,i_0_2866,i_0_2867,i_0_2941,i_0_2942,i_0_2947,i_0_2948,i_0_2964,i_0_2975,i_0_2984,i_0_3002,i_0_3033,i_0_3044,i_0_3077,i_0_3270,i_0_3291,i_0_3672,i_0_2367,i_0_2433,i_0_2434,i_0_2483,i_0_2505,i_0_2508,i_0_2509,i_0_2510,i_0_2529,i_0_2538,i_0_2547,i_0_2607,i_0_2611,i_0_2618,i_0_2620,i_0_2623,i_0_2634,i_0_2637,i_0_2638,i_0_2709,i_0_2710,i_0_2711,i_0_2712,i_0_2759,i_0_2761,i_0_2763,i_0_2765,i_0_2824,i_0_2852,i_0_2854,i_0_2856,i_0_2899,i_0_2911,i_0_2950,i_0_2959,i_0_2962,i_0_2963,i_0_2993,i_0_3000,i_0_3001,i_0_3012,i_0_3013,i_0_3032,i_0_3034,i_0_3058,i_0_3066,i_0_3204,i_0_3206,i_0_3260,i_0_3261,i_0_3262,i_0_3263,i_0_3413,i_0_3414,i_0_3417,i_0_3418,i_0_3451,i_0_3495,i_0_3496,i_0_2201]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW473+2 : 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
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 06:56:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.73/1.79 % Version : CSE_E---1.7
% 1.73/1.79 % Problem : theBenchmark.p
% 1.73/1.79 % SZS status Theorem for theBenchmark.p
% 1.73/1.79 % SZS output start CNFRefutation
% See solution above
% 3.48/3.58 % Total time : 1.437s
%------------------------------------------------------------------------------