%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW473+1 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.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 05:32:29 PM UTC 2026
% Result : Theorem 0.88s 1.73s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_494)
% Comments :
%------------------------------------------------------------------------------
fof(fact_276_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/sandbox/benchmark/theBenchmark.p',fact_276_subset__insert) ).
fof(fact_277_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/sandbox/benchmark/theBenchmark.p',fact_277_subset__insert) ).
fof(fact_192_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/sandbox/benchmark/theBenchmark.p',fact_192_insert__compr) ).
fof(fact_259_Collect__def,axiom,
! [X13] : collect_nat(X13) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_Collect__def) ).
fof(fact_195_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/sandbox/benchmark/theBenchmark.p',fact_195_insert__compr) ).
fof(fact_256_Collect__def,axiom,
! [X13] : collect_fun_nat_bool(X13) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_Collect__def) ).
fof(fact_184_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/sandbox/benchmark/theBenchmark.p',fact_184_insertCI) ).
fof(fact_185_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/sandbox/benchmark/theBenchmark.p',fact_185_insertCI) ).
fof(fact_275_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/sandbox/benchmark/theBenchmark.p',fact_275_subset__insert) ).
fof(fact_217_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/sandbox/benchmark/theBenchmark.p',fact_217_insert__ident) ).
fof(fact_218_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/sandbox/benchmark/theBenchmark.p',fact_218_insert__ident) ).
fof(fact_183_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/sandbox/benchmark/theBenchmark.p',fact_183_insertCI) ).
fof(fact_100_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/sandbox/benchmark/theBenchmark.p',fact_100_card__insert__if) ).
fof(fact_99_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/sandbox/benchmark/theBenchmark.p',fact_99_card__insert__if) ).
fof(fact_103_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/sandbox/benchmark/theBenchmark.p',fact_103_card__insert__if) ).
fof(fact_102_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/sandbox/benchmark/theBenchmark.p',fact_102_card__insert__if) ).
fof(fact_106_card__insert__disjoint,axiom,
! [X11,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X11),X5))
=> hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_card__insert__disjoint) ).
fof(fact_105_card__insert__disjoint,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X5))
=> ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X11),X5))
=> hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_card__insert__disjoint) ).
fof(fact_109_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/sandbox/benchmark/theBenchmark.p',fact_109_card__insert__disjoint) ).
fof(fact_108_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/sandbox/benchmark/theBenchmark.p',fact_108_card__insert__disjoint) ).
fof(fact_216_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/sandbox/benchmark/theBenchmark.p',fact_216_insert__ident) ).
fof(fact_98_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/sandbox/benchmark/theBenchmark.p',fact_98_card__insert__if) ).
fof(fact_101_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/sandbox/benchmark/theBenchmark.p',fact_101_card__insert__if) ).
fof(fact_104_card__insert__disjoint,axiom,
! [X11,X5] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X5))
=> ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X11),X5))
=> hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X11,X5)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_card__insert__disjoint) ).
fof(fact_107_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/sandbox/benchmark/theBenchmark.p',fact_107_card__insert__disjoint) ).
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/sandbox/benchmark/theBenchmark.p',conj_6) ).
fof(fact_194_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/sandbox/benchmark/theBenchmark.p',fact_194_insert__compr) ).
fof(fact_175_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/sandbox/benchmark/theBenchmark.p',fact_175_pigeonhole__infinite) ).
fof(fact_208_insert__commute,axiom,
! [X11,X33,X5] : insert_pname(X11,insert_pname(X33,X5)) = insert_pname(X33,insert_pname(X11,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_insert__commute) ).
fof(fact_193_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/sandbox/benchmark/theBenchmark.p',fact_193_insert__compr) ).
fof(fact_209_insert__commute,axiom,
! [X11,X33,X5] : insert_a(X11,insert_a(X33,X5)) = insert_a(X33,insert_a(X11,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_insert__commute) ).
fof(fact_273_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/sandbox/benchmark/theBenchmark.p',fact_273_insert__subset) ).
fof(fact_274_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/sandbox/benchmark/theBenchmark.p',fact_274_insert__subset) ).
fof(fact_282_insert__mono,axiom,
! [X8,X34,X37] :
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X34),X37))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X8,X34)),insert_pname(X8,X37))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_insert__mono) ).
fof(fact_283_insert__mono,axiom,
! [X8,X34,X37] :
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X34),X37))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X8,X34)),insert_a(X8,X37))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_insert__mono) ).
fof(fact_205_insert__absorb2,axiom,
! [X11,X5] : insert_pname(X11,insert_pname(X11,X5)) = insert_pname(X11,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_insert__absorb2) ).
fof(fact_206_insert__absorb2,axiom,
! [X11,X5] : insert_a(X11,insert_a(X11,X5)) = insert_a(X11,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_insert__absorb2) ).
fof(fact_94_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/sandbox/benchmark/theBenchmark.p',fact_94_card__insert__le) ).
fof(fact_197_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/sandbox/benchmark/theBenchmark.p',fact_197_insert__compr) ).
fof(fact_93_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/sandbox/benchmark/theBenchmark.p',fact_93_card__insert__le) ).
fof(fact_196_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/sandbox/benchmark/theBenchmark.p',fact_196_insert__compr) ).
fof(fact_97_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/sandbox/benchmark/theBenchmark.p',fact_97_card__insert__le) ).
fof(fact_95_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/sandbox/benchmark/theBenchmark.p',fact_95_card__insert__le) ).
fof(fact_211_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/sandbox/benchmark/theBenchmark.p',fact_211_insert__iff) ).
fof(fact_187_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/sandbox/benchmark/theBenchmark.p',fact_187_insertE) ).
fof(fact_212_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/sandbox/benchmark/theBenchmark.p',fact_212_insert__iff) ).
fof(fact_188_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/sandbox/benchmark/theBenchmark.p',fact_188_insertE) ).
fof(fact_272_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/sandbox/benchmark/theBenchmark.p',fact_272_insert__subset) ).
fof(fact_281_insert__mono,axiom,
! [X8,X34,X37] :
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X34),X37))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X8,X34)),insert_nat(X8,X37))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_insert__mono) ).
fof(fact_214_insert__code,axiom,
! [X33,X5,X11] :
( ( is_pname(X33)
& is_pname(X11) )
=> ( hBOOL(hAPP_pname_bool(insert_pname(X33,X5),X11))
<=> ( X33 = X11
| hBOOL(hAPP_pname_bool(X5,X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_insert__code) ).
fof(fact_215_insert__code,axiom,
! [X33,X5,X11] :
( ( is_a(X33)
& is_a(X11) )
=> ( hBOOL(hAPP_a_bool(insert_a(X33,X5),X11))
<=> ( X33 = X11
| hBOOL(hAPP_a_bool(X5,X11)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_insert__code) ).
fof(fact_139_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/sandbox/benchmark/theBenchmark.p',fact_139_finite__insert) ).
fof(fact_140_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/sandbox/benchmark/theBenchmark.p',fact_140_finite__insert) ).
fof(fact_136_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/sandbox/benchmark/theBenchmark.p',fact_136_finite__insert) ).
fof(fact_137_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/sandbox/benchmark/theBenchmark.p',fact_137_finite__insert) ).
fof(fact_207_insert__commute,axiom,
! [X11,X33,X5] : insert_nat(X11,insert_nat(X33,X5)) = insert_nat(X33,insert_nat(X11,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_insert__commute) ).
fof(fact_92_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/sandbox/benchmark/theBenchmark.p',fact_92_card__insert__le) ).
fof(fact_96_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/sandbox/benchmark/theBenchmark.p',fact_96_card__insert__le) ).
fof(fact_279_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/sandbox/benchmark/theBenchmark.p',fact_279_subset__insertI2) ).
fof(fact_220_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/sandbox/benchmark/theBenchmark.p',fact_220_insertI2) ).
fof(fact_280_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/sandbox/benchmark/theBenchmark.p',fact_280_subset__insertI2) ).
fof(fact_221_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/sandbox/benchmark/theBenchmark.p',fact_221_insertI2) ).
fof(fact_270_subset__insertI,axiom,
! [X10,X8] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),insert_pname(X8,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_subset__insertI) ).
fof(fact_190_insertI1,axiom,
! [X8,X10] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X8),insert_pname(X8,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_insertI1) ).
fof(fact_271_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/sandbox/benchmark/theBenchmark.p',fact_271_subset__insertI) ).
fof(fact_191_insertI1,axiom,
! [X8,X10] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X8),insert_a(X8,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_insertI1) ).
fof(fact_52_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/sandbox/benchmark/theBenchmark.p',fact_52_finite_OinsertI) ).
fof(fact_51_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/sandbox/benchmark/theBenchmark.p',fact_51_finite_OinsertI) ).
fof(fact_47_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/sandbox/benchmark/theBenchmark.p',fact_47_finite_OinsertI) ).
fof(fact_45_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/sandbox/benchmark/theBenchmark.p',fact_45_finite_OinsertI) ).
fof(fact_284_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/sandbox/benchmark/theBenchmark.p',fact_284_image__insert) ).
fof(fact_210_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/sandbox/benchmark/theBenchmark.p',fact_210_insert__iff) ).
fof(fact_186_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/sandbox/benchmark/theBenchmark.p',fact_186_insertE) ).
fof(fact_213_insert__code,axiom,
! [X33,X5,X11] :
( hBOOL(hAPP_nat_bool(insert_nat(X33,X5),X11))
<=> ( X33 = X11
| hBOOL(hAPP_nat_bool(X5,X11)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_insert__code) ).
fof(fact_138_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/sandbox/benchmark/theBenchmark.p',fact_138_finite__insert) ).
fof(fact_135_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/sandbox/benchmark/theBenchmark.p',fact_135_finite__insert) ).
fof(fact_204_insert__absorb2,axiom,
! [X11,X5] : insert_nat(X11,insert_nat(X11,X5)) = insert_nat(X11,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_insert__absorb2) ).
fof(fact_219_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/sandbox/benchmark/theBenchmark.p',fact_219_insertI2) ).
fof(fact_278_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/sandbox/benchmark/theBenchmark.p',fact_278_subset__insertI2) ).
fof(fact_202_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/sandbox/benchmark/theBenchmark.p',fact_202_insert__Collect) ).
fof(fact_203_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/sandbox/benchmark/theBenchmark.p',fact_203_insert__Collect) ).
fof(fact_199_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/sandbox/benchmark/theBenchmark.p',fact_199_insert__Collect) ).
fof(fact_200_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/sandbox/benchmark/theBenchmark.p',fact_200_insert__Collect) ).
fof(fact_285_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/sandbox/benchmark/theBenchmark.p',fact_285_insert__image) ).
fof(fact_288_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/sandbox/benchmark/theBenchmark.p',fact_288_imageE) ).
fof(fact_189_insertI1,axiom,
! [X8,X10] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),insert_nat(X8,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_insertI1) ).
fof(fact_269_subset__insertI,axiom,
! [X10,X8] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),insert_nat(X8,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_subset__insertI) ).
fof(fact_53_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/sandbox/benchmark/theBenchmark.p',fact_53_finite_OinsertI) ).
fof(fact_46_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/sandbox/benchmark/theBenchmark.p',fact_46_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000t__a) ).
fof(fact_223_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/sandbox/benchmark/theBenchmark.p',fact_223_insert__absorb) ).
fof(fact_224_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/sandbox/benchmark/theBenchmark.p',fact_224_insert__absorb) ).
fof(fact_158_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/sandbox/benchmark/theBenchmark.p',fact_158_not__less__eq__eq) ).
fof(fact_198_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/sandbox/benchmark/theBenchmark.p',fact_198_insert__Collect) ).
fof(fact_201_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/sandbox/benchmark/theBenchmark.p',fact_201_insert__Collect) ).
fof(fact_130_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/sandbox/benchmark/theBenchmark.p',fact_130_finite__Collect__disjI) ).
fof(fact_133_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/sandbox/benchmark/theBenchmark.p',fact_133_finite__Collect__disjI) ).
fof(fact_154_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/sandbox/benchmark/theBenchmark.p',fact_154_le__SucE) ).
fof(fact_159_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/sandbox/benchmark/theBenchmark.p',fact_159_Suc__n__not__le__n) ).
fof(fact_222_insert__absorb,axiom,
! [X8,X5] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X8),X5))
=> insert_nat(X8,X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_insert__absorb) ).
fof(fact_110_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/sandbox/benchmark/theBenchmark.p',fact_110_finite__Collect__conjI) ).
fof(fact_115_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/sandbox/benchmark/theBenchmark.p',fact_115_finite__Collect__conjI) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
fof(fact_1_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/sandbox/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
fof(help_fimplies_3_1_U,axiom,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X44),X45))
| ~ hBOOL(X44)
| hBOOL(X45) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
fof(help_fdisj_3_1_U,axiom,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X44),X45))
| hBOOL(X44)
| hBOOL(X45) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
fof(help_fconj_2_1_U,axiom,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X44),X45))
| hBOOL(X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
fof(help_fconj_3_1_U,axiom,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X44),X45))
| hBOOL(X45) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
fof(fact_117_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/sandbox/benchmark/theBenchmark.p',fact_117_finite__Collect__le__nat) ).
fof(help_fconj_1_1_U,axiom,
! [X45,X44] :
( ~ hBOOL(X44)
| ~ hBOOL(X45)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X44),X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
fof(help_fimplies_2_1_U,axiom,
! [X44,X45] :
( ~ hBOOL(X45)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X44),X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
fof(help_fdisj_1_1_U,axiom,
! [X45,X44] :
( ~ hBOOL(X44)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X44),X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
fof(help_fdisj_2_1_U,axiom,
! [X44,X45] :
( ~ hBOOL(X45)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X44),X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
fof(fact_249_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/sandbox/benchmark/theBenchmark.p',fact_249_equalityE) ).
fof(fact_250_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/sandbox/benchmark/theBenchmark.p',fact_250_equalityE) ).
fof(fact_251_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/sandbox/benchmark/theBenchmark.p',fact_251_equalityE) ).
fof(fact_118_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/sandbox/benchmark/theBenchmark.p',fact_118_card__Collect__le__nat) ).
fof(help_fNot_1_1_U,axiom,
! [X44] :
( ~ hBOOL(hAPP_bool_bool(fNot,X44))
| ~ hBOOL(X44) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
fof(fact_171_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/sandbox/benchmark/theBenchmark.p',fact_171_lift__Suc__mono__le) ).
fof(fact_172_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/sandbox/benchmark/theBenchmark.p',fact_172_lift__Suc__mono__le) ).
fof(fact_174_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/sandbox/benchmark/theBenchmark.p',fact_174_lift__Suc__mono__le) ).
fof(fact_173_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/sandbox/benchmark/theBenchmark.p',fact_173_lift__Suc__mono__le) ).
fof(fact_294_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/sandbox/benchmark/theBenchmark.p',fact_294_image__subsetI) ).
fof(fact_162_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/sandbox/benchmark/theBenchmark.p',fact_162_le__diff__iff) ).
fof(fact_170_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/sandbox/benchmark/theBenchmark.p',fact_170_finite__subset__image) ).
fof(fact_286_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)))
<=> ? [X38] :
( is_fun_pname_bool(X38)
& hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X38),X5))
& X10 = image_pname_a(X9,X38) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_subset__image__iff) ).
fof(fact_260_image__iff,axiom,
! [X35,X9,X5] :
( is_a(X35)
=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X35),image_pname_a(X9,X5)))
<=> ? [X30] :
( is_pname(X30)
& hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X30),X5))
& X35 = hAPP_pname_a(X9,X30) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_image__iff) ).
fof(fact_292_zero__induct__lemma,axiom,
! [X39,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),X39))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_zero__induct__lemma) ).
fof(fact_131_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/sandbox/benchmark/theBenchmark.p',fact_131_finite__Collect__disjI) ).
fof(fact_132_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/sandbox/benchmark/theBenchmark.p',fact_132_finite__Collect__disjI) ).
fof(fact_129_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/sandbox/benchmark/theBenchmark.p',fact_129_finite__Collect__disjI) ).
fof(fact_134_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/sandbox/benchmark/theBenchmark.p',fact_134_finite__Collect__disjI) ).
fof(fact_87_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/sandbox/benchmark/theBenchmark.p',fact_87_card__seteq) ).
fof(fact_88_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/sandbox/benchmark/theBenchmark.p',fact_88_card__seteq) ).
fof(fact_89_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/sandbox/benchmark/theBenchmark.p',fact_89_card__seteq) ).
fof(fact_90_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/sandbox/benchmark/theBenchmark.p',fact_90_card__seteq) ).
fof(fact_86_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/sandbox/benchmark/theBenchmark.p',fact_86_card__seteq) ).
fof(fact_91_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/sandbox/benchmark/theBenchmark.p',fact_91_card__seteq) ).
fof(fact_76_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_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_card__image__le) ).
fof(fact_72_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_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_card__image__le) ).
fof(fact_75_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_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_card__image__le) ).
fof(fact_71_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_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_card__image__le) ).
fof(fact_70_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_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_card__image__le) ).
fof(fact_74_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_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_card__image__le) ).
fof(fact_62_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X9,X5))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_card__image__le) ).
fof(fact_63_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X9,X5))),hAPP_f98387925ol_nat(finite269641166l_bool,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_card__image__le) ).
fof(fact_64_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X9,X5))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_card__image__le) ).
fof(fact_67_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/sandbox/benchmark/theBenchmark.p',fact_67_card__image__le) ).
fof(fact_66_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/sandbox/benchmark/theBenchmark.p',fact_66_card__image__le) ).
fof(fact_65_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X9,X5))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_card__image__le) ).
fof(fact_73_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_fun_a_bool_nat(finite_card_a,image_nat_a(X9,X5))),hAPP_f22106695ol_nat(finite_card_nat,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_card__image__le) ).
fof(fact_61_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/sandbox/benchmark/theBenchmark.p',fact_61_card__image__le) ).
fof(fact_68_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/sandbox/benchmark/theBenchmark.p',fact_68_card__image__le) ).
fof(fact_77_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_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X9,X5))),hAPP_f696928925ol_nat(finite346522414t_bool,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_card__image__le) ).
fof(fact_78_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_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X9,X5))),hAPP_f55526627ol_nat(finite1340463720e_bool,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_card__image__le) ).
fof(fact_79_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_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X9,X5))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_card__image__le) ).
fof(fact_60_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/sandbox/benchmark/theBenchmark.p',fact_60_card__image__le) ).
fof(fact_69_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_card__image__le) ).
fof(fact_59_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/sandbox/benchmark/theBenchmark.p',fact_59_card__image__le) ).
fof(fact_54_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X9,X5))),hAPP_f921600141ol_nat(finite_card_pname,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_card__image__le) ).
fof(fact_55_card__image__le,axiom,
! [X9,X5] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X9,X5))),hAPP_fun_a_bool_nat(finite_card_a,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_card__image__le) ).
fof(fact_56_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/sandbox/benchmark/theBenchmark.p',fact_56_card__image__le) ).
fof(fact_57_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/sandbox/benchmark/theBenchmark.p',fact_57_card__image__le) ).
fof(fact_58_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/sandbox/benchmark/theBenchmark.p',fact_58_card__image__le) ).
fof(fact_166_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/sandbox/benchmark/theBenchmark.p',fact_166_diff__le__mono) ).
fof(fact_167_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/sandbox/benchmark/theBenchmark.p',fact_167_diff__le__mono2) ).
fof(fact_156_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/sandbox/benchmark/theBenchmark.p',fact_156_Suc__le__mono) ).
fof(fact_160_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/sandbox/benchmark/theBenchmark.p',fact_160_Suc__diff__diff) ).
fof(fact_163_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/sandbox/benchmark/theBenchmark.p',fact_163_Nat_Odiff__diff__eq) ).
fof(fact_111_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/sandbox/benchmark/theBenchmark.p',fact_111_finite__Collect__conjI) ).
fof(fact_112_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/sandbox/benchmark/theBenchmark.p',fact_112_finite__Collect__conjI) ).
fof(fact_114_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/sandbox/benchmark/theBenchmark.p',fact_114_finite__Collect__conjI) ).
fof(fact_113_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/sandbox/benchmark/theBenchmark.p',fact_113_finite__Collect__conjI) ).
fof(fact_82_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/sandbox/benchmark/theBenchmark.p',fact_82_card__mono) ).
fof(fact_81_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/sandbox/benchmark/theBenchmark.p',fact_81_card__mono) ).
fof(fact_80_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/sandbox/benchmark/theBenchmark.p',fact_80_card__mono) ).
fof(fact_84_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/sandbox/benchmark/theBenchmark.p',fact_84_card__mono) ).
fof(fact_83_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/sandbox/benchmark/theBenchmark.p',fact_83_card__mono) ).
fof(fact_85_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/sandbox/benchmark/theBenchmark.p',fact_85_card__mono) ).
fof(fact_289_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/sandbox/benchmark/theBenchmark.p',fact_289_subsetI) ).
fof(fact_291_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/sandbox/benchmark/theBenchmark.p',fact_291_subsetI) ).
fof(fact_290_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/sandbox/benchmark/theBenchmark.p',fact_290_subsetI) ).
fof(fact_287_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/sandbox/benchmark/theBenchmark.p',fact_287_image__mono) ).
fof(fact_261_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/sandbox/benchmark/theBenchmark.p',fact_261_imageI) ).
fof(fact_153_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/sandbox/benchmark/theBenchmark.p',fact_153_Suc__leD) ).
fof(fact_240_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/sandbox/benchmark/theBenchmark.p',fact_240_set__rev__mp) ).
fof(fact_243_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/sandbox/benchmark/theBenchmark.p',fact_243_set__mp) ).
fof(fact_237_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/sandbox/benchmark/theBenchmark.p',fact_237_in__mono) ).
fof(fact_180_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/sandbox/benchmark/theBenchmark.p',fact_180_subsetD) ).
fof(fact_246_subset__trans,axiom,
! [X34,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),X34))
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X34)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_subset__trans) ).
fof(fact_247_subset__trans,axiom,
! [X34,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),X34))
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X34)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_subset__trans) ).
fof(fact_242_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/sandbox/benchmark/theBenchmark.p',fact_242_set__rev__mp) ).
fof(fact_245_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/sandbox/benchmark/theBenchmark.p',fact_245_set__mp) ).
fof(fact_239_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/sandbox/benchmark/theBenchmark.p',fact_239_in__mono) ).
fof(fact_182_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/sandbox/benchmark/theBenchmark.p',fact_182_subsetD) ).
fof(fact_248_subset__trans,axiom,
! [X34,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),X34))
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X34)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_subset__trans) ).
fof(fact_241_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/sandbox/benchmark/theBenchmark.p',fact_241_set__rev__mp) ).
fof(fact_244_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/sandbox/benchmark/theBenchmark.p',fact_244_set__mp) ).
fof(fact_238_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/sandbox/benchmark/theBenchmark.p',fact_238_in__mono) ).
fof(fact_181_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/sandbox/benchmark/theBenchmark.p',fact_181_subsetD) ).
fof(fact_124_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/sandbox/benchmark/theBenchmark.p',fact_124_le__trans) ).
fof(fact_299_finite__nat__set__iff__bounded__le,axiom,
! [X43] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X43))
<=> ? [X41] :
! [X30] :
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X30),X43))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X30),X41)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_finite__nat__set__iff__bounded__le) ).
fof(fact_164_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/sandbox/benchmark/theBenchmark.p',fact_164_eq__diff__iff) ).
fof(fact_293_Suc__le__D,axiom,
! [X14,X40] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X14)),X40))
=> ? [X41] : X40 = hAPP_nat_nat(suc,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_Suc__le__D) ).
fof(fact_157_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/sandbox/benchmark/theBenchmark.p',fact_157_le__Suc__eq) ).
fof(fact_169_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/sandbox/benchmark/theBenchmark.p',fact_169_finite__surj) ).
fof(fact_176_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/sandbox/benchmark/theBenchmark.p',fact_176_image__eqI) ).
fof(fact_262_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/sandbox/benchmark/theBenchmark.p',fact_262_rev__image__eqI) ).
fof(fact_229_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/sandbox/benchmark/theBenchmark.p',fact_229_set__eq__subset) ).
fof(fact_178_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/sandbox/benchmark/theBenchmark.p',fact_178_equalityI) ).
fof(fact_230_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/sandbox/benchmark/theBenchmark.p',fact_230_set__eq__subset) ).
fof(fact_179_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/sandbox/benchmark/theBenchmark.p',fact_179_equalityI) ).
fof(fact_228_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/sandbox/benchmark/theBenchmark.p',fact_228_set__eq__subset) ).
fof(fact_177_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/sandbox/benchmark/theBenchmark.p',fact_177_equalityI) ).
fof(fact_123_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/sandbox/benchmark/theBenchmark.p',fact_123_le__antisym) ).
fof(fact_155_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/sandbox/benchmark/theBenchmark.p',fact_155_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/sandbox/benchmark/theBenchmark.p',conj_5) ).
fof(fact_116_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/sandbox/benchmark/theBenchmark.p',fact_116_Suc__diff__le) ).
fof(fact_168_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/sandbox/benchmark/theBenchmark.p',fact_168_diff__le__self) ).
fof(fact_4_finite__Collect__subsets,axiom,
! [X5] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X5))
=> hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X5)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_finite__Collect__subsets) ).
fof(fact_5_finite__Collect__subsets,axiom,
! [X5] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X5))
=> hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X5)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_finite__Collect__subsets) ).
fof(fact_6_finite__Collect__subsets,axiom,
! [X5] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X5))
=> hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X5)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_finite__Collect__subsets) ).
fof(fact_9_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/sandbox/benchmark/theBenchmark.p',fact_9_finite__Collect__subsets) ).
fof(fact_8_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/sandbox/benchmark/theBenchmark.p',fact_8_finite__Collect__subsets) ).
fof(fact_7_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/sandbox/benchmark/theBenchmark.p',fact_7_finite__Collect__subsets) ).
fof(fact_2_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/sandbox/benchmark/theBenchmark.p',fact_2_finite__Collect__subsets) ).
fof(fact_3_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/sandbox/benchmark/theBenchmark.p',fact_3_finite__Collect__subsets) ).
fof(fact_128_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/sandbox/benchmark/theBenchmark.p',fact_128_diff__commute) ).
fof(fact_141_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/sandbox/benchmark/theBenchmark.p',fact_141_finite__subset) ).
fof(fact_147_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/sandbox/benchmark/theBenchmark.p',fact_147_rev__finite__subset) ).
fof(fact_142_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/sandbox/benchmark/theBenchmark.p',fact_142_finite__subset) ).
fof(fact_148_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/sandbox/benchmark/theBenchmark.p',fact_148_rev__finite__subset) ).
fof(fact_144_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/sandbox/benchmark/theBenchmark.p',fact_144_finite__subset) ).
fof(fact_150_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/sandbox/benchmark/theBenchmark.p',fact_150_rev__finite__subset) ).
fof(fact_145_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/sandbox/benchmark/theBenchmark.p',fact_145_finite__subset) ).
fof(fact_151_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/sandbox/benchmark/theBenchmark.p',fact_151_rev__finite__subset) ).
fof(fact_146_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/sandbox/benchmark/theBenchmark.p',fact_146_finite__subset) ).
fof(fact_152_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/sandbox/benchmark/theBenchmark.p',fact_152_rev__finite__subset) ).
fof(fact_143_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/sandbox/benchmark/theBenchmark.p',fact_143_finite__subset) ).
fof(fact_149_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/sandbox/benchmark/theBenchmark.p',fact_149_rev__finite__subset) ).
fof(fact_165_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/sandbox/benchmark/theBenchmark.p',fact_165_diff__diff__cancel) ).
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/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
fof(fact_126_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/sandbox/benchmark/theBenchmark.p',fact_126_nat__le__linear) ).
fof(fact_252_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/sandbox/benchmark/theBenchmark.p',fact_252_mem__def) ).
fof(fact_254_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/sandbox/benchmark/theBenchmark.p',fact_254_mem__def) ).
fof(fact_253_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/sandbox/benchmark/theBenchmark.p',fact_253_mem__def) ).
fof(fact_48_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X5))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X8,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_finite_OinsertI) ).
fof(fact_32_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_finite__imageI) ).
fof(fact_25_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_finite__imageI) ).
fof(fact_49_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X5))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X8,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_finite_OinsertI) ).
fof(fact_33_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_finite__imageI) ).
fof(fact_26_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_finite__imageI) ).
fof(fact_50_finite_OinsertI,axiom,
! [X8,X5] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X5))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X8,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_finite_OinsertI) ).
fof(fact_34_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_finite__imageI) ).
fof(fact_27_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_finite__imageI) ).
fof(fact_37_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/sandbox/benchmark/theBenchmark.p',fact_37_finite__imageI) ).
fof(fact_30_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/sandbox/benchmark/theBenchmark.p',fact_30_finite__imageI) ).
fof(fact_29_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/sandbox/benchmark/theBenchmark.p',fact_29_finite__imageI) ).
fof(fact_36_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/sandbox/benchmark/theBenchmark.p',fact_36_finite__imageI) ).
fof(fact_28_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/sandbox/benchmark/theBenchmark.p',fact_28_finite__imageI) ).
fof(fact_35_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/sandbox/benchmark/theBenchmark.p',fact_35_finite__imageI) ).
fof(fact_43_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_finite__imageI) ).
fof(fact_17_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/sandbox/benchmark/theBenchmark.p',fact_17_finite__imageI) ).
fof(fact_16_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/sandbox/benchmark/theBenchmark.p',fact_16_finite__imageI) ).
fof(fact_15_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/sandbox/benchmark/theBenchmark.p',fact_15_finite__imageI) ).
fof(fact_14_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/sandbox/benchmark/theBenchmark.p',fact_14_finite__imageI) ).
fof(fact_13_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__imageI) ).
fof(fact_12_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_finite__imageI) ).
fof(fact_11_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X7))
=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_finite__imageI) ).
fof(fact_18_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_finite__imageI) ).
fof(fact_19_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_finite__imageI) ).
fof(fact_20_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
fof(fact_23_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/sandbox/benchmark/theBenchmark.p',fact_23_finite__imageI) ).
fof(fact_22_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/sandbox/benchmark/theBenchmark.p',fact_22_finite__imageI) ).
fof(fact_21_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/sandbox/benchmark/theBenchmark.p',fact_21_finite__imageI) ).
fof(fact_44_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_finite__imageI) ).
fof(fact_38_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X7))
=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_finite__imageI) ).
fof(fact_24_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/sandbox/benchmark/theBenchmark.p',fact_24_finite__imageI) ).
fof(fact_40_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_finite__imageI) ).
fof(fact_41_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_finite__imageI) ).
fof(fact_42_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_finite__imageI) ).
fof(fact_31_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/sandbox/benchmark/theBenchmark.p',fact_31_finite__imageI) ).
fof(fact_10_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/sandbox/benchmark/theBenchmark.p',fact_10_finite__imageI) ).
fof(fact_39_finite__imageI,axiom,
! [X6,X7] :
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X7))
=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X6,X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_finite__imageI) ).
fof(fact_161_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/sandbox/benchmark/theBenchmark.p',fact_161_diff__Suc__Suc) ).
fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
! [X44,X45,X46] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_f1748468828l_bool(X44,X46),hAPP_f54304608l_bool(X45,X46)),
file('/export/starexec/sandbox/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,
! [X44,X45,X46] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_f1476298914l_bool(X44,X46),hAPP_f1664156314l_bool(X45,X46)),
file('/export/starexec/sandbox/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,
! [X44,X45,X46] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_f198738859l_bool(X44,X46),hAPP_fun_a_bool_bool(X45,X46)),
file('/export/starexec/sandbox/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,
! [X44,X45,X46] : hAPP_nat_bool(cOMBS_nat_bool_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_n1006566506l_bool(X44,X46),hAPP_nat_bool(X45,X46)),
file('/export/starexec/sandbox/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,
! [X44,X45,X46] : hAPP_pname_bool(cOMBS_568398431l_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_p393069232l_bool(X44,X46),hAPP_pname_bool(X45,X46)),
file('/export/starexec/sandbox/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,
! [X44,X45,X46] : hAPP_a_bool(cOMBS_a_bool_bool(X44,X45),X46) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X44,X46),hAPP_a_bool(X45,X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool,axiom,
! [X44,X45,X46] : hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X44),X45),X46) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X44,X46),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,axiom,
! [X44,X45,X46] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X44),X45),X46) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X44,X46),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H,axiom,
! [X44,X45,X46] : hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X44),X45),X46) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X44,X46),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H,axiom,
! [X44,X45,X46] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X44),X45),X46) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X44,X46),X45),
file('/export/starexec/sandbox/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,
! [X44,X45,X46] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X44),X45),X46) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X44,X46),X45),
file('/export/starexec/sandbox/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,
! [X44,X45,X46] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X44),X45),X46) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X44,X46),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__011,axiom,
! [X44,X45,X46] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X44),X45),X46) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X44,X46),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__011) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
! [X44,X45,X46] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X44),X45),X46) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X44,X46),X45),
file('/export/starexec/sandbox/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_012,axiom,
! [X44,X45,X46] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X44),X45),X46) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X44,X46),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_012) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
! [X44,X45,X46] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X44),X45),X46) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X44,X46),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__,axiom,
! [X44,X45,X46] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X44),X45),X46) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X44,X46),X45),
file('/export/starexec/sandbox/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,
! [X44,X45,X46] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X44),X45),X46) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X44,X46),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [X44,X45,X46] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X44),X45),X46) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X44,X46),X45),
file('/export/starexec/sandbox/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,
! [X44,X45,X46] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X44),X45),X46) = hAPP_nat_bool(hAPP_n1699378549t_bool(X44,X46),X45),
file('/export/starexec/sandbox/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__Com__Opname_Mtc__HOL__Ob,axiom,
! [X44,X45,X46] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X44),X45),X46) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X44,X46),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U,axiom,
! [X44,X45,X46] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X44),X45),X46) = hAPP_pname_bool(hAPP_p61793385e_bool(X44,X46),X45),
file('/export/starexec/sandbox/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,
! [X44,X45,X46] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X44),X45),X46) = hAPP_a_bool(hAPP_p1534023578a_bool(X44,X46),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) ).
fof(help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo,axiom,
! [X44,X45,X46] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X44),X45),X46) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X44,X46),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).
fof(help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U,axiom,
! [X44,X45,X46] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X44),X45),X46) = hAPP_a_bool(hAPP_a_fun_a_bool(X44,X46),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).
fof(help_fimplies_1_1_U,axiom,
! [X45,X44] :
( hBOOL(X44)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X44),X45)) ),
file('/export/starexec/sandbox/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_010,axiom,
! [X44,X45,X46] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_f1664156314l_bool(X45,X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009,axiom,
! [X44,X45,X46] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_f54304608l_bool(X45,X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008,axiom,
! [X44,X45,X46] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_fun_a_bool_bool(X45,X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007,axiom,
! [X44,X45,X46] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_pname_bool(X45,X46)),
file('/export/starexec/sandbox/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_006,axiom,
! [X44,X45,X46] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_nat_bool(X45,X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
! [X44,X45,X46] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X44,X45),X46) = hAPP_b589554111l_bool(X44,hAPP_a_bool(X45,X46)),
file('/export/starexec/sandbox/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__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On,axiom,
! [X44,X45,X46] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_f54304608l_bool(X45,X46)),
file('/export/starexec/sandbox/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__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op,axiom,
! [X44,X45,X46] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_f1664156314l_bool(X45,X46)),
file('/export/starexec/sandbox/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__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H,axiom,
! [X44,X45,X46] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_fun_a_bool_bool(X45,X46)),
file('/export/starexec/sandbox/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__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
! [X44,X45,X46] : hAPP_nat_bool(cOMBB_bool_bool_nat(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_nat_bool(X45,X46)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
fof(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna,axiom,
! [X44,X45,X46] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X44,X45),X46) = hAPP_a_fun_a_bool(X44,hAPP_pname_a(X45,X46)),
file('/export/starexec/sandbox/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,
! [X44,X45,X46] : hAPP_pname_bool(cOMBB_647938656_pname(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_pname_bool(X45,X46)),
file('/export/starexec/sandbox/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__HOL__Obool_000tc__HOL__Obool_000t__a_U,axiom,
! [X44,X45,X46] : hAPP_a_bool(cOMBB_bool_bool_a(X44,X45),X46) = hAPP_bool_bool(X44,hAPP_a_bool(X45,X46)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
fof(fact_231_equalityD1,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_equalityD1) ).
fof(fact_234_equalityD2,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X10),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
fof(fact_232_equalityD1,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_equalityD1) ).
fof(fact_235_equalityD2,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X10),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
fof(fact_233_equalityD1,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_equalityD1) ).
fof(fact_236_equalityD2,axiom,
! [X5,X10] :
( X5 = X10
=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X10),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
fof(fact_125_eq__imp__le,axiom,
! [X15,X14] :
( X15 = X14
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X15),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_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/sandbox/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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).
fof(fact_295_order__refl,axiom,
! [X11] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X11),X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_order__refl) ).
fof(fact_225_subset__refl,axiom,
! [X5] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X5),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_subset__refl) ).
fof(fact_296_order__refl,axiom,
! [X11] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X11),X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_order__refl) ).
fof(fact_226_subset__refl,axiom,
! [X5] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X5),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_subset__refl) ).
fof(fact_298_order__refl,axiom,
! [X11] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X11),X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_order__refl) ).
fof(fact_227_subset__refl,axiom,
! [X5] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X5),X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_subset__refl) ).
fof(fact_297_order__refl,axiom,
! [X42] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X42),X42)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_order__refl) ).
fof(fact_127_le__refl,axiom,
! [X14] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X14),X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_le__refl) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000t__a_000tc__HOL__Obool) ).
fof(fact_120_nat_Oinject,axiom,
! [X20,X21] :
( hAPP_nat_nat(suc,X20) = hAPP_nat_nat(suc,X21)
<=> X20 = X21 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_nat_Oinject) ).
fof(fact_119_Suc__inject,axiom,
! [X18,X19] :
( hAPP_nat_nat(suc,X18) = hAPP_nat_nat(suc,X19)
=> X18 = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Suc__inject) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).
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/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000t__a) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005,axiom,
! [X1,X2] :
( is_fun1661590463l_bool(X2)
=> is_fun1661590463l_bool(hAPP_f559147733l_bool(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
fof(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_,axiom,
! [X1,X2] :
( is_fun_pname_bool(X2)
=> is_fun1661590463l_bool(image_47868345e_bool(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_) ).
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/sandbox/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/sandbox/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___004,axiom,
! [X1,X2] :
( is_fun949378684l_bool(X2)
=> is_fun949378684l_bool(hAPP_f2117159681l_bool(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___004) ).
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/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL) ).
fof(gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J,hypothesis,
! [X1,X2] :
( is_a(X2)
=> is_fun949378684l_bool(hAPP_a85458249l_bool(X1,X2)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op) ).
fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [X1,X2] :
( is_pname(X2)
=> is_fun_pname_bool(hAPP_p61793385e_bool(X1,X2)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname) ).
fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1,X2] :
( is_fun_a_bool(X2)
=> is_fun_a_bool(hAPP_f2050579477a_bool(X1,X2)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a) ).
fof(help_fNot_2_1_U,axiom,
! [X44] :
( hBOOL(X44)
| hBOOL(hAPP_bool_bool(fNot,X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [X1,X2] : is_bool(hAPP_f1295398978l_bool(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,axiom,
! [X1,X2] : is_bool(hAPP_f595608956l_bool(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HO,axiom,
! [X1,X2] : is_bool(hAPP_f1363661463l_bool(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HO) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__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/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(gsy_c_Set_Oimage_000tc__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/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
! [X1,X2] : is_fun_pname_bool(hAPP_n1025906991e_bool(X1,X2)),
file('/export/starexec/sandbox/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__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL___003,axiom,
! [X1,X2] : is_fun_pname_bool(image_1604018183_pname(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL___003) ).
fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL_002,axiom,
! [X1,X2] : is_fun_pname_bool(image_1705983821_pname(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL_002) ).
fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0_001,axiom,
! [X1,X2] : is_fun_pname_bool(image_990671762_pname(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0_001) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
! [X1,X2] : is_fun_a_bool(hAPP_nat_fun_a_bool(X1,X2)),
file('/export/starexec/sandbox/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__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__,axiom,
! [X1,X2] : is_fun_a_bool(image_526090948bool_a(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__) ).
fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL,axiom,
! [X1,X2] : is_fun_a_bool(image_349102846bool_a(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL) ).
fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0,axiom,
! [X1,X2] : is_fun_a_bool(image_573985017bool_a(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a) ).
fof(fact_121_Suc__n__not__n,axiom,
! [X14] : hAPP_nat_nat(suc,X14) != X14,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Suc__n__not__n) ).
fof(fact_122_n__not__Suc__n,axiom,
! [X14] : X14 != hAPP_nat_nat(suc,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_n__not__Suc__n) ).
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/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).
fof(gsy_v_P,axiom,
! [X1] :
( is_fun_a_bool(X1)
=> is_fun949378684l_bool(p(X1)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(gsy_c_Set_OCollect_000tc__Com__Opname,axiom,
! [X1] :
( is_fun_pname_bool(X1)
=> is_fun_pname_bool(collect_pname(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__Com__Opname) ).
fof(gsy_c_Set_OCollect_000t__a,axiom,
! [X1] :
( is_fun_a_bool(X1)
=> is_fun_a_bool(collect_a(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000t__a) ).
fof(fact_257_Collect__def,axiom,
! [X13] :
( is_fun1661590463l_bool(X13)
=> collec1974731493e_bool(X13) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_Collect__def) ).
fof(fact_258_Collect__def,axiom,
! [X13] :
( is_fun949378684l_bool(X13)
=> collect_fun_a_bool(X13) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_Collect__def) ).
fof(fact_255_Collect__def,axiom,
! [X13] :
( is_fun_pname_bool(X13)
=> collect_pname(X13) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Collect__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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(conj_4,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
fof(conj_0,hypothesis,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(gsy_c_HOL_Oundefined_000tc__Com__Opname,axiom,
is_pname(undefined_pname(pname)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000t__a) ).
fof(gsy_v_pn,hypothesis,
is_pname(pn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_pn) ).
fof(gsy_c_Finite__Set_Ofinite_000tc__Com__Opname,hypothesis,
is_fun1661590463l_bool(finite_finite_pname),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofinite_000tc__Com__Opname) ).
fof(gsy_c_Finite__Set_Ofinite_000t__a,axiom,
is_fun949378684l_bool(finite_finite_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofinite_000t__a) ).
fof(gsy_v_U,hypothesis,
is_fun_pname_bool(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_U) ).
fof(gsy_v_G,hypothesis,
is_fun_a_bool(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_G) ).
fof(i_0_443,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_276_subset__insert]) ).
fof(i_0_444,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_277_subset__insert]) ).
fof(i_0_445,plain,
! [X1539,X1540] : insert_nat(X1539,X1540) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1539)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),X1540))),
inference(variable_rename,[status(thm)],[fact_192_insert__compr]) ).
fof(i_0_446,plain,
! [X1693] : collect_nat(X1693) = X1693,
inference(variable_rename,[status(thm)],[fact_259_Collect__def]) ).
fof(i_0_447,plain,
! [X1545,X1546] : insert_fun_nat_bool(X1545,X1546) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X1545)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),X1546))),
inference(variable_rename,[status(thm)],[fact_195_insert__compr]) ).
fof(i_0_448,plain,
! [X1690] : collect_fun_nat_bool(X1690) = X1690,
inference(variable_rename,[status(thm)],[fact_256_Collect__def]) ).
fof(i_0_449,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_184_insertCI]) ).
fof(i_0_450,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_185_insertCI]) ).
fof(i_0_451,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_275_subset__insert]) ).
fof(i_0_452,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_217_insert__ident]) ).
fof(i_0_453,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_218_insert__ident]) ).
fof(i_0_454,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_183_insertCI]) ).
fof(i_0_455,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_100_card__insert__if]) ).
fof(i_0_456,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_99_card__insert__if]) ).
fof(i_0_457,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_103_card__insert__if]) ).
fof(i_0_458,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_102_card__insert__if]) ).
fof(i_0_459,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_106_card__insert__disjoint]) ).
fof(i_0_460,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_105_card__insert__disjoint]) ).
fof(i_0_461,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_109_card__insert__disjoint]) ).
fof(i_0_462,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_108_card__insert__disjoint]) ).
fof(i_0_463,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_216_insert__ident]) ).
fof(i_0_464,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_98_card__insert__if]) ).
fof(i_0_465,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_101_card__insert__if]) ).
fof(i_0_466,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_104_card__insert__disjoint]) ).
fof(i_0_467,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_107_card__insert__disjoint]) ).
fof(i_0_468,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_469,plain,
! [X1543,X1544] : insert_a(X1543,X1544) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X1543)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),X1544))),
inference(variable_rename,[status(thm)],[fact_194_insert__compr]) ).
fof(i_0_470,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_175_pigeonhole__infinite]) ).
fof(i_0_471,plain,
! [X1572,X1573,X1574] : insert_pname(X1572,insert_pname(X1573,X1574)) = insert_pname(X1573,insert_pname(X1572,X1574)),
inference(variable_rename,[status(thm)],[fact_208_insert__commute]) ).
fof(i_0_472,plain,
! [X1541,X1542] : insert_pname(X1541,X1542) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1541)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1542))),
inference(variable_rename,[status(thm)],[fact_193_insert__compr]) ).
fof(i_0_473,plain,
! [X1575,X1576,X1577] : insert_a(X1575,insert_a(X1576,X1577)) = insert_a(X1576,insert_a(X1575,X1577)),
inference(variable_rename,[status(thm)],[fact_209_insert__commute]) ).
fof(i_0_474,plain,
! [X1729,X1730,X1731] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1729),X1731))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1729,X1730)),X1731)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1730),X1731))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1729,X1730)),X1731)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1729),X1731))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1730),X1731))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1729,X1730)),X1731)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_273_insert__subset])])]) ).
fof(i_0_475,plain,
! [X1732,X1733,X1734] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1732),X1734))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1732,X1733)),X1734)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1733),X1734))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1732,X1733)),X1734)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1732),X1734))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1733),X1734))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1732,X1733)),X1734)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_274_insert__subset])])]) ).
fof(i_0_476,plain,
! [X1756,X1757,X1758] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1757),X1758))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X1756,X1757)),insert_pname(X1756,X1758))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_282_insert__mono])]) ).
fof(i_0_477,plain,
! [X1759,X1760,X1761] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1760),X1761))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X1759,X1760)),insert_a(X1759,X1761))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_283_insert__mono])]) ).
fof(i_0_478,plain,
! [X1565,X1566] : insert_pname(X1565,insert_pname(X1565,X1566)) = insert_pname(X1565,X1566),
inference(variable_rename,[status(thm)],[fact_205_insert__absorb2]) ).
fof(i_0_479,plain,
! [X1567,X1568] : insert_a(X1567,insert_a(X1567,X1568)) = insert_a(X1567,X1568),
inference(variable_rename,[status(thm)],[fact_206_insert__absorb2]) ).
fof(i_0_480,plain,
! [X1318,X1319] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1319))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1319)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X1318,X1319)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_94_card__insert__le])]) ).
fof(i_0_481,plain,
! [X1549,X1550] : insert_fun_a_bool(X1549,X1550) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X1549)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),X1550))),
inference(variable_rename,[status(thm)],[fact_197_insert__compr]) ).
fof(i_0_482,plain,
! [X1316,X1317] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1317))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1317)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X1316,X1317)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_93_card__insert__le])]) ).
fof(i_0_483,plain,
! [X1547,X1548] : insert1325755072e_bool(X1547,X1548) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1547)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),X1548))),
inference(variable_rename,[status(thm)],[fact_196_insert__compr]) ).
fof(i_0_484,plain,
! [X1324,X1325] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1325))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1325)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X1324,X1325)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_97_card__insert__le])]) ).
fof(i_0_485,plain,
! [X1320,X1321] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1321))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1321)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X1320,X1321)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_95_card__insert__le])]) ).
fof(i_0_486,plain,
! [X1738,X1739,X1740] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1740),insert_pname(X1739,X1738)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1740),X1738))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1739),X1740)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1740),X1738))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1740),insert_pname(X1739,X1738)))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1739),X1740)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_443])])]) ).
fof(i_0_487,plain,
! [X1741,X1742,X1743] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1743),insert_a(X1742,X1741)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1743),X1741))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1742),X1743)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1743),X1741))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1743),insert_a(X1742,X1741)))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1742),X1743)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_444])])]) ).
fof(i_0_488,plain,
! [X1581,X1582,X1583] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1581),insert_pname(X1582,X1583)))
| X1581 = X1582
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1581),X1583))
| ~ is_pname(X1581)
| ~ is_pname(X1582) )
& ( X1581 != X1582
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1581),insert_pname(X1582,X1583)))
| ~ is_pname(X1581)
| ~ is_pname(X1582) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1581),X1583))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1581),insert_pname(X1582,X1583)))
| ~ is_pname(X1581)
| ~ is_pname(X1582) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_211_insert__iff])])]) ).
fof(i_0_489,plain,
! [X1527,X1528,X1529] :
( ~ is_pname(X1527)
| ~ is_pname(X1528)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1527),insert_pname(X1528,X1529)))
| X1527 = X1528
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1527),X1529)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_187_insertE])]) ).
fof(i_0_490,plain,
! [X1584,X1585,X1586] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1584),insert_a(X1585,X1586)))
| X1584 = X1585
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1584),X1586))
| ~ is_a(X1584)
| ~ is_a(X1585) )
& ( X1584 != X1585
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1584),insert_a(X1585,X1586)))
| ~ is_a(X1584)
| ~ is_a(X1585) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1584),X1586))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1584),insert_a(X1585,X1586)))
| ~ is_a(X1584)
| ~ is_a(X1585) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_212_insert__iff])])]) ).
fof(i_0_491,plain,
! [X1530,X1531,X1532] :
( ~ is_a(X1530)
| ~ is_a(X1531)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1530),insert_a(X1531,X1532)))
| X1530 = X1531
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1530),X1532)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_188_insertE])]) ).
fof(i_0_492,plain,
! [X1726,X1727,X1728] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1726),X1728))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1726,X1727)),X1728)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1727),X1728))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1726,X1727)),X1728)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1726),X1728))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1727),X1728))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1726,X1727)),X1728)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_272_insert__subset])])]) ).
cnf(i_0_493,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_445]) ).
cnf(i_0_494,plain,
collect_nat(X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_446]) ).
fof(i_0_495,plain,
! [X1753,X1754,X1755] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1754),X1755))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X1753,X1754)),insert_nat(X1753,X1755))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_281_insert__mono])]) ).
fof(i_0_496,plain,
! [X1590,X1591,X1592] :
( ( ~ hBOOL(hAPP_pname_bool(insert_pname(X1590,X1591),X1592))
| X1590 = X1592
| hBOOL(hAPP_pname_bool(X1591,X1592))
| ~ is_pname(X1590)
| ~ is_pname(X1592) )
& ( X1590 != X1592
| hBOOL(hAPP_pname_bool(insert_pname(X1590,X1591),X1592))
| ~ is_pname(X1590)
| ~ is_pname(X1592) )
& ( ~ hBOOL(hAPP_pname_bool(X1591,X1592))
| hBOOL(hAPP_pname_bool(insert_pname(X1590,X1591),X1592))
| ~ is_pname(X1590)
| ~ is_pname(X1592) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_214_insert__code])])]) ).
fof(i_0_497,plain,
! [X1593,X1594,X1595] :
( ( ~ hBOOL(hAPP_a_bool(insert_a(X1593,X1594),X1595))
| X1593 = X1595
| hBOOL(hAPP_a_bool(X1594,X1595))
| ~ is_a(X1593)
| ~ is_a(X1595) )
& ( X1593 != X1595
| hBOOL(hAPP_a_bool(insert_a(X1593,X1594),X1595))
| ~ is_a(X1593)
| ~ is_a(X1595) )
& ( ~ hBOOL(hAPP_a_bool(X1594,X1595))
| hBOOL(hAPP_a_bool(insert_a(X1593,X1594),X1595))
| ~ is_a(X1593)
| ~ is_a(X1595) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_215_insert__code])])]) ).
fof(i_0_498,plain,
! [X1405,X1406] :
( ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X1405,X1406)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1406)) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1406))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X1405,X1406))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_139_finite__insert])]) ).
fof(i_0_499,plain,
! [X1407,X1408] :
( ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X1407,X1408)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1408)) )
& ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1408))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X1407,X1408))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_140_finite__insert])]) ).
fof(i_0_500,plain,
! [X1399,X1400] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X1399,X1400)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1400)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1400))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X1399,X1400))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_136_finite__insert])]) ).
fof(i_0_501,plain,
! [X1401,X1402] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X1401,X1402)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1402)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1402))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X1401,X1402))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_137_finite__insert])]) ).
fof(i_0_502,plain,
! [X1569,X1570,X1571] : insert_nat(X1569,insert_nat(X1570,X1571)) = insert_nat(X1570,insert_nat(X1569,X1571)),
inference(variable_rename,[status(thm)],[fact_207_insert__commute]) ).
fof(i_0_503,plain,
! [X1314,X1315] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1315))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1315)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X1314,X1315)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_92_card__insert__le])]) ).
cnf(i_0_504,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_447]) ).
cnf(i_0_505,plain,
collect_fun_nat_bool(X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_448]) ).
fof(i_0_506,plain,
! [X1322,X1323] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1323))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1323)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X1322,X1323)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_96_card__insert__le])]) ).
fof(i_0_507,plain,
! [X1747,X1748,X1749] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1748),X1749))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1748),insert_pname(X1747,X1749))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_279_subset__insertI2])]) ).
fof(i_0_508,plain,
! [X1608,X1609,X1610] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1609),X1610))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1609),insert_pname(X1608,X1610))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_220_insertI2])]) ).
fof(i_0_509,plain,
! [X1518,X1519,X1520] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1519),X1520))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1519),insert_pname(X1518,X1520))) )
& ( X1519 != X1518
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1519),insert_pname(X1518,X1520))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_449])])]) ).
fof(i_0_510,plain,
! [X1750,X1751,X1752] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1751),X1752))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1751),insert_a(X1750,X1752))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_280_subset__insertI2])]) ).
fof(i_0_511,plain,
! [X1611,X1612,X1613] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1612),X1613))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1612),insert_a(X1611,X1613))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_221_insertI2])]) ).
fof(i_0_512,plain,
! [X1521,X1522,X1523] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1522),X1523))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1522),insert_a(X1521,X1523))) )
& ( X1522 != X1521
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1522),insert_a(X1521,X1523))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_450])])]) ).
fof(i_0_513,plain,
! [X1722,X1723] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1722),insert_pname(X1723,X1722))),
inference(variable_rename,[status(thm)],[fact_270_subset__insertI]) ).
fof(i_0_514,plain,
! [X1535,X1536] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1535),insert_pname(X1535,X1536))),
inference(variable_rename,[status(thm)],[fact_190_insertI1]) ).
fof(i_0_515,plain,
! [X1724,X1725] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1724),insert_a(X1725,X1724))),
inference(variable_rename,[status(thm)],[fact_271_subset__insertI]) ).
fof(i_0_516,plain,
! [X1537,X1538] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1537),insert_a(X1537,X1538))),
inference(variable_rename,[status(thm)],[fact_191_insertI1]) ).
fof(i_0_517,plain,
! [X1234,X1235] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1235))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(X1234,X1235))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_52_finite_OinsertI])]) ).
fof(i_0_518,plain,
! [X1232,X1233] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1233))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(X1232,X1233))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_51_finite_OinsertI])]) ).
fof(i_0_519,plain,
! [X1224,X1225] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1225))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(X1224,X1225))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_47_finite_OinsertI])]) ).
fof(i_0_520,plain,
! [X1220,X1221] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1221))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(X1220,X1221))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_45_finite_OinsertI])]) ).
fof(i_0_521,plain,
! [X1762,X1763,X1764] : image_pname_a(X1762,insert_pname(X1763,X1764)) = insert_a(hAPP_pname_a(X1762,X1763),image_pname_a(X1762,X1764)),
inference(variable_rename,[status(thm)],[fact_284_image__insert]) ).
fof(i_0_522,plain,
! [X1735,X1736,X1737] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1737),insert_nat(X1736,X1735)))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1737),X1735))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1736),X1737)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1737),X1735))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1737),insert_nat(X1736,X1735)))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1736),X1737)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_451])])]) ).
fof(i_0_523,plain,
! [X1578,X1579,X1580] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1578),insert_nat(X1579,X1580)))
| X1578 = X1579
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1578),X1580)) )
& ( X1578 != X1579
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1578),insert_nat(X1579,X1580))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1578),X1580))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1578),insert_nat(X1579,X1580))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_210_insert__iff])])]) ).
fof(i_0_524,plain,
! [X1524,X1525,X1526] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1524),insert_nat(X1525,X1526)))
| X1524 = X1525
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1524),X1526)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_186_insertE])]) ).
fof(i_0_525,plain,
! [X1599,X1600,X1601] :
( ( insert_pname(X1600,X1601) != insert_pname(X1600,X1599)
| X1601 = X1599
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1600),X1599))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1600),X1601))
| ~ is_fun_pname_bool(X1599)
| ~ is_fun_pname_bool(X1601) )
& ( X1601 != X1599
| insert_pname(X1600,X1601) = insert_pname(X1600,X1599)
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1600),X1599))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1600),X1601))
| ~ is_fun_pname_bool(X1599)
| ~ is_fun_pname_bool(X1601) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_452])])]) ).
fof(i_0_526,plain,
! [X1602,X1603,X1604] :
( ( insert_a(X1603,X1604) != insert_a(X1603,X1602)
| X1604 = X1602
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1603),X1602))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1603),X1604))
| ~ is_fun_a_bool(X1602)
| ~ is_fun_a_bool(X1604) )
& ( X1604 != X1602
| insert_a(X1603,X1604) = insert_a(X1603,X1602)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1603),X1602))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1603),X1604))
| ~ is_fun_a_bool(X1602)
| ~ is_fun_a_bool(X1604) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_453])])]) ).
fof(i_0_527,plain,
! [X1587,X1588,X1589] :
( ( ~ hBOOL(hAPP_nat_bool(insert_nat(X1587,X1588),X1589))
| X1587 = X1589
| hBOOL(hAPP_nat_bool(X1588,X1589)) )
& ( X1587 != X1589
| hBOOL(hAPP_nat_bool(insert_nat(X1587,X1588),X1589)) )
& ( ~ hBOOL(hAPP_nat_bool(X1588,X1589))
| hBOOL(hAPP_nat_bool(insert_nat(X1587,X1588),X1589)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_213_insert__code])])]) ).
fof(i_0_528,plain,
! [X1403,X1404] :
( ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X1403,X1404)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1404)) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1404))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X1403,X1404))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_138_finite__insert])]) ).
fof(i_0_529,plain,
! [X1397,X1398] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X1397,X1398)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1398)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1398))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X1397,X1398))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_135_finite__insert])]) ).
fof(i_0_530,plain,
! [X1563,X1564] : insert_nat(X1563,insert_nat(X1563,X1564)) = insert_nat(X1563,X1564),
inference(variable_rename,[status(thm)],[fact_204_insert__absorb2]) ).
fof(i_0_531,plain,
! [X1605,X1606,X1607] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1606),X1607))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1606),insert_nat(X1605,X1607))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_219_insertI2])]) ).
fof(i_0_532,plain,
! [X1515,X1516,X1517] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1516),X1517))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1516),insert_nat(X1515,X1517))) )
& ( X1516 != X1515
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1516),insert_nat(X1515,X1517))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_454])])]) ).
fof(i_0_533,plain,
! [X1744,X1745,X1746] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1745),X1746))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1745),insert_nat(X1744,X1746))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_278_subset__insertI2])]) ).
fof(i_0_534,plain,
! [X1330,X1331] :
( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X1330),X1331))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X1330,X1331)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,X1331)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1331)) )
& ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X1330),X1331))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X1330,X1331)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1331))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1331)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_455])])]) ).
fof(i_0_535,plain,
! [X1328,X1329] :
( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X1328),X1329))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X1328,X1329)) = hAPP_f55526627ol_nat(finite1340463720e_bool,X1329)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1329)) )
& ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X1328),X1329))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X1328,X1329)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1329))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1329)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_456])])]) ).
fof(i_0_536,plain,
! [X1336,X1337] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1336),X1337))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X1336,X1337)) = hAPP_fun_a_bool_nat(finite_card_a,X1337)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1337)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1336),X1337))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X1336,X1337)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1337))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1337)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_457])])]) ).
fof(i_0_537,plain,
! [X1334,X1335] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1334),X1335))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X1334,X1335)) = hAPP_f921600141ol_nat(finite_card_pname,X1335)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1335)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1334),X1335))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X1334,X1335)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1335))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1335)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_458])])]) ).
fof(i_0_538,plain,
! [X1559,X1560] : insert1325755072e_bool(X1559,collec1974731493e_bool(X1560)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X1559))),X1560)),
inference(variable_rename,[status(thm)],[fact_202_insert__Collect]) ).
fof(i_0_539,plain,
! [X1561,X1562] : insert_fun_a_bool(X1561,collect_fun_a_bool(X1562)) = 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),X1561))),X1562)),
inference(variable_rename,[status(thm)],[fact_203_insert__Collect]) ).
fof(i_0_540,plain,
! [X1553,X1554] : insert_pname(X1553,collect_pname(X1554)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X1553))),X1554)),
inference(variable_rename,[status(thm)],[fact_199_insert__Collect]) ).
fof(i_0_541,plain,
! [X1555,X1556] : insert_a(X1555,collect_a(X1556)) = 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),X1555))),X1556)),
inference(variable_rename,[status(thm)],[fact_200_insert__Collect]) ).
fof(i_0_542,plain,
! [X1765,X1766,X1767] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1766),X1767))
| insert_a(hAPP_pname_a(X1765,X1766),image_pname_a(X1765,X1767)) = image_pname_a(X1765,X1767) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_285_insert__image])]) ).
fof(i_0_543,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_288_imageE]) ).
fof(i_0_544,plain,
! [X1342,X1343] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1343))
| hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X1342),X1343))
| hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X1342,X1343)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1343)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_459])]) ).
fof(i_0_545,plain,
! [X1340,X1341] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1341))
| hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X1340),X1341))
| hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X1340,X1341)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,X1341)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_460])]) ).
fof(i_0_546,plain,
! [X1348,X1349] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1349))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1348),X1349))
| hAPP_fun_a_bool_nat(finite_card_a,insert_a(X1348,X1349)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,X1349)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_461])]) ).
fof(i_0_547,plain,
! [X1346,X1347] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1347))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1346),X1347))
| hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X1346,X1347)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,X1347)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_462])]) ).
fof(i_0_548,plain,
! [X1533,X1534] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1533),insert_nat(X1533,X1534))),
inference(variable_rename,[status(thm)],[fact_189_insertI1]) ).
fof(i_0_549,plain,
! [X1720,X1721] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1720),insert_nat(X1721,X1720))),
inference(variable_rename,[status(thm)],[fact_269_subset__insertI]) ).
fof(i_0_550,plain,
! [X1236,X1237] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1237))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(X1236,X1237))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_53_finite_OinsertI])]) ).
fof(i_0_551,plain,
! [X1222,X1223] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1223))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(X1222,X1223))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_46_finite_OinsertI])]) ).
fof(i_0_552,plain,
! [X1596,X1597,X1598] :
( ( insert_nat(X1597,X1598) != insert_nat(X1597,X1596)
| X1598 = X1596
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1597),X1596))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1597),X1598)) )
& ( X1598 != X1596
| insert_nat(X1597,X1598) = insert_nat(X1597,X1596)
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1597),X1596))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1597),X1598)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_463])])]) ).
fof(i_0_553,plain,
! [X1074,X1075] :
( ~ is_fun_pname_bool(X1074)
| ~ is_fun1661590463l_bool(X1075)
| is_fun1661590463l_bool(insert1325755072e_bool(X1074,X1075)) ),
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_554,plain,
! [X1072,X1073] :
( ~ is_fun_a_bool(X1072)
| ~ is_fun949378684l_bool(X1073)
| is_fun949378684l_bool(insert_fun_a_bool(X1072,X1073)) ),
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_555,plain,
! [X1070,X1071] :
( ~ is_pname(X1070)
| ~ is_fun_pname_bool(X1071)
| is_fun_pname_bool(insert_pname(X1070,X1071)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oinsert_000tc__Com__Opname])]) ).
fof(i_0_556,hypothesis,
! [X1068,X1069] :
( ~ is_a(X1068)
| ~ is_fun_a_bool(X1069)
| is_fun_a_bool(insert_a(X1068,X1069)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oinsert_000t__a])]) ).
fof(i_0_557,plain,
! [X1326,X1327] :
( ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1326),X1327))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X1326,X1327)) = hAPP_f696928925ol_nat(finite346522414t_bool,X1327)
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1327)) )
& ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1326),X1327))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X1326,X1327)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1327))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1327)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_464])])]) ).
fof(i_0_558,plain,
! [X1332,X1333] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1332),X1333))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X1332,X1333)) = hAPP_f22106695ol_nat(finite_card_nat,X1333)
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1333)) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1332),X1333))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X1332,X1333)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1333))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1333)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_465])])]) ).
fof(i_0_559,plain,
! [X1338,X1339] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1339))
| hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X1338),X1339))
| hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X1338,X1339)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,X1339)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_466])]) ).
fof(i_0_560,plain,
! [X1344,X1345] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1345))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1344),X1345))
| hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X1344,X1345)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,X1345)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_467])]) ).
fof(i_0_561,plain,
! [X1616,X1617] :
( ~ is_fun_pname_bool(X1617)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1616),X1617))
| insert_pname(X1616,X1617) = X1617 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_223_insert__absorb])]) ).
fof(i_0_562,plain,
! [X1618,X1619] :
( ~ is_fun_a_bool(X1619)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1618),X1619))
| insert_a(X1618,X1619) = X1619 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_224_insert__absorb])]) ).
fof(i_0_563,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_158_not__less__eq__eq]) ).
fof(i_0_564,plain,
! [X1551,X1552] : insert_nat(X1551,collect_nat(X1552)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X1551))),X1552)),
inference(variable_rename,[status(thm)],[fact_198_insert__Collect]) ).
fof(i_0_565,plain,
! [X1557,X1558] : insert_fun_nat_bool(X1557,collect_fun_nat_bool(X1558)) = 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),X1557))),X1558)),
inference(variable_rename,[status(thm)],[fact_201_insert__Collect]) ).
fof(i_0_566,plain,
! [X1387,X1388] :
( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1387)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1387),X1388)))) )
& ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1388)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1387),X1388)))) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1387)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1388)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,X1387),X1388)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_130_finite__Collect__disjI])])]) ).
fof(i_0_567,plain,
! [X1393,X1394] :
( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1393)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1393),X1394)))) )
& ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1394)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1393),X1394)))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1393)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1394)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,X1393),X1394)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_133_finite__Collect__disjI])])]) ).
fof(i_0_568,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_154_le__SucE]) ).
fof(i_0_569,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_159_Suc__n__not__le__n]) ).
fof(i_0_570,plain,
! [X1614,X1615] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1614),X1615))
| insert_nat(X1614,X1615) = X1615 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_222_insert__absorb])]) ).
fof(i_0_571,plain,
! [X1350,X1351] :
( ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1351)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1351),X1350)))) )
& ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(X1350)))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,X1351),X1350)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_110_finite__Collect__conjI])])]) ).
fof(i_0_572,plain,
! [X1360,X1361] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1361)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1361),X1360)))) )
& ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(X1360)))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,X1361),X1360)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_115_finite__Collect__conjI])])]) ).
fof(i_0_573,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_574,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_575,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_576,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_577,plain,
! [X1141] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1141))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),X1141)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1_finite__Collect__subsets])]) ).
fof(i_0_578,plain,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X44),X45))
| ~ hBOOL(X44)
| hBOOL(X45) ),
inference(fof_simplification,[status(thm)],[help_fimplies_3_1_U]) ).
fof(i_0_579,plain,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X44),X45))
| hBOOL(X44)
| hBOOL(X45) ),
inference(fof_simplification,[status(thm)],[help_fdisj_3_1_U]) ).
fof(i_0_580,plain,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X44),X45))
| hBOOL(X44) ),
inference(fof_simplification,[status(thm)],[help_fconj_2_1_U]) ).
fof(i_0_581,plain,
! [X44,X45] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X44),X45))
| hBOOL(X45) ),
inference(fof_simplification,[status(thm)],[help_fconj_3_1_U]) ).
fof(i_0_582,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_583,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_584,plain,
! [X1364] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X1364)))),
inference(variable_rename,[status(thm)],[fact_117_finite__Collect__le__nat]) ).
fof(i_0_585,plain,
! [X45,X44] :
( ~ hBOOL(X44)
| ~ hBOOL(X45)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X44),X45)) ),
inference(fof_simplification,[status(thm)],[help_fconj_1_1_U]) ).
fof(i_0_586,plain,
! [X44,X45] :
( ~ hBOOL(X45)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X44),X45)) ),
inference(fof_simplification,[status(thm)],[help_fimplies_2_1_U]) ).
fof(i_0_587,plain,
! [X45,X44] :
( ~ hBOOL(X44)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X44),X45)) ),
inference(fof_simplification,[status(thm)],[help_fdisj_1_1_U]) ).
fof(i_0_588,plain,
! [X44,X45] :
( ~ hBOOL(X45)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X44),X45)) ),
inference(fof_simplification,[status(thm)],[help_fdisj_2_1_U]) ).
fof(i_0_589,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_249_equalityE]) ).
fof(i_0_590,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_250_equalityE]) ).
fof(i_0_591,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_251_equalityE]) ).
fof(i_0_592,plain,
! [X1365] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),X1365))) = hAPP_nat_nat(suc,X1365),
inference(variable_rename,[status(thm)],[fact_118_card__Collect__le__nat]) ).
fof(i_0_593,plain,
! [X44] :
( ~ hBOOL(hAPP_bool_bool(fNot,X44))
| ~ hBOOL(X44) ),
inference(fof_simplification,[status(thm)],[help_fNot_1_1_U]) ).
cnf(i_0_594,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_468]) ).
cnf(i_0_595,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_469]) ).
fof(i_0_596,plain,
! [X1493,X1494] :
( ( is_pname(esk6_2(X1493,X1494))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X1493,X1494)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1494)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk6_2(X1493,X1494)),X1494))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X1493,X1494)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1494)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),X1494)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,X1493)),hAPP_pname_a(X1493,esk6_2(X1493,X1494)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X1493,X1494)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1494)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_470])])])]) ).
cnf(i_0_597,plain,
insert_pname(X1,insert_pname(X2,X3)) = insert_pname(X2,insert_pname(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_471]) ).
cnf(i_0_598,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_472]) ).
cnf(i_0_599,plain,
insert_a(X1,insert_a(X2,X3)) = insert_a(X2,insert_a(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_473]) ).
cnf(i_0_600,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_474]) ).
cnf(i_0_601,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_474]) ).
cnf(i_0_602,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_475]) ).
cnf(i_0_603,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_475]) ).
fof(i_0_604,plain,
! [X1477,X1478,X1479] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1479,esk2_3(X1477,X1478,X1479))),hAPP_n1699378549t_bool(X1479,hAPP_nat_nat(suc,esk2_3(X1477,X1478,X1479)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1477),X1478))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(X1479,X1477)),hAPP_n1699378549t_bool(X1479,X1478))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_171_lift__Suc__mono__le])])]) ).
fof(i_0_605,plain,
! [X1481,X1482,X1483] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X1483,esk3_3(X1481,X1482,X1483))),hAPP_n1025906991e_bool(X1483,hAPP_nat_nat(suc,esk3_3(X1481,X1482,X1483)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1481),X1482))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(X1483,X1481)),hAPP_n1025906991e_bool(X1483,X1482))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_172_lift__Suc__mono__le])])]) ).
fof(i_0_606,plain,
! [X1489,X1490,X1491] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X1491,esk5_3(X1489,X1490,X1491))),hAPP_nat_fun_a_bool(X1491,hAPP_nat_nat(suc,esk5_3(X1489,X1490,X1491)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1489),X1490))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(X1491,X1489)),hAPP_nat_fun_a_bool(X1491,X1490))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_174_lift__Suc__mono__le])])]) ).
fof(i_0_607,plain,
! [X1485,X1486,X1487] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1487,esk4_3(X1485,X1486,X1487))),hAPP_nat_nat(X1487,hAPP_nat_nat(suc,esk4_3(X1485,X1486,X1487)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1485),X1486))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(X1487,X1485)),hAPP_nat_nat(X1487,X1486))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_173_lift__Suc__mono__le])])]) ).
cnf(i_0_608,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_476]) ).
cnf(i_0_609,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_477]) ).
cnf(i_0_610,plain,
insert_pname(X1,insert_pname(X1,X2)) = insert_pname(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_478]) ).
cnf(i_0_611,plain,
insert_a(X1,insert_a(X1,X2)) = insert_a(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_479]) ).
cnf(i_0_612,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_474]) ).
cnf(i_0_613,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_475]) ).
cnf(i_0_614,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_480]) ).
cnf(i_0_615,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_481]) ).
cnf(i_0_616,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_482]) ).
cnf(i_0_617,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_483]) ).
cnf(i_0_618,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_484]) ).
cnf(i_0_619,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_485]) ).
cnf(i_0_620,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_486]) ).
cnf(i_0_621,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_487]) ).
cnf(i_0_622,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_488]) ).
cnf(i_0_623,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_489]) ).
cnf(i_0_624,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_490]) ).
cnf(i_0_625,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_491]) ).
cnf(i_0_626,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_492]) ).
cnf(i_0_627,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_493,c_0_494]) ).
cnf(i_0_628,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_492]) ).
fof(i_0_629,plain,
! [X1798,X1799,X1800] :
( ( is_pname(esk15_3(X1798,X1799,X1800))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1798,X1800)),X1799)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk15_3(X1798,X1799,X1800)),X1800))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1798,X1800)),X1799)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1798,esk15_3(X1798,X1799,X1800))),X1799))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1798,X1800)),X1799)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_294_image__subsetI])])])]) ).
cnf(i_0_630,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_495]) ).
cnf(i_0_631,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_496]) ).
cnf(i_0_632,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_497]) ).
cnf(i_0_633,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_498]) ).
cnf(i_0_634,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_499]) ).
cnf(i_0_635,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_500]) ).
cnf(i_0_636,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_501]) ).
cnf(i_0_637,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_492]) ).
cnf(i_0_638,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_486]) ).
cnf(i_0_639,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_487]) ).
cnf(i_0_640,plain,
insert_nat(X1,insert_nat(X2,X3)) = insert_nat(X2,insert_nat(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_502]) ).
cnf(i_0_641,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_503]) ).
cnf(i_0_642,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_504,c_0_505]) ).
cnf(i_0_643,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_506]) ).
cnf(i_0_644,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_488]) ).
cnf(i_0_645,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_490]) ).
cnf(i_0_646,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_507]) ).
cnf(i_0_647,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_508]) ).
cnf(i_0_648,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_509]) ).
cnf(i_0_649,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_510]) ).
cnf(i_0_650,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_511]) ).
cnf(i_0_651,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_512]) ).
cnf(i_0_652,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_488]) ).
cnf(i_0_653,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_490]) ).
cnf(i_0_654,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_496]) ).
cnf(i_0_655,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_497]) ).
cnf(i_0_656,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X2,X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_509]) ).
cnf(i_0_657,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_512]) ).
cnf(i_0_658,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),insert_pname(X2,X1))),
inference(split_conjunct,[status(thm)],[i_0_513]) ).
cnf(i_0_659,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),insert_pname(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_514]) ).
cnf(i_0_660,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_515]) ).
cnf(i_0_661,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1),insert_a(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_516]) ).
cnf(i_0_662,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_498]) ).
cnf(i_0_663,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_517]) ).
cnf(i_0_664,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_499]) ).
cnf(i_0_665,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_518]) ).
cnf(i_0_666,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_500]) ).
cnf(i_0_667,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_519]) ).
cnf(i_0_668,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_501]) ).
cnf(i_0_669,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_520]) ).
cnf(i_0_670,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_521]) ).
cnf(i_0_671,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_496]) ).
cnf(i_0_672,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_497]) ).
cnf(i_0_673,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_522]) ).
cnf(i_0_674,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_523]) ).
cnf(i_0_675,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_524]) ).
cnf(i_0_676,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_525]) ).
cnf(i_0_677,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_526]) ).
cnf(i_0_678,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_527]) ).
cnf(i_0_679,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_528]) ).
cnf(i_0_680,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_529]) ).
cnf(i_0_681,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_522]) ).
fof(i_0_682,plain,
! [X1451,X1452,X1453] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1453),X1452)),hAPP_nat_nat(minus_minus_nat(X1451),X1452)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1453),X1451))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1452),X1451))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1452),X1453)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1453),X1451))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1453),X1452)),hAPP_nat_nat(minus_minus_nat(X1451),X1452)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1452),X1451))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1452),X1453)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_162_le__diff__iff])])]) ).
cnf(i_0_683,plain,
insert_nat(X1,insert_nat(X1,X2)) = insert_nat(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_530]) ).
fof(i_0_684,plain,
! [X1473,X1474,X1475] :
( ( is_fun_pname_bool(esk1_3(X1473,X1474,X1475))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1475),image_pname_a(X1473,X1474)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1475))
| ~ is_fun_a_bool(X1475) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk1_3(X1473,X1474,X1475)),X1474))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1475),image_pname_a(X1473,X1474)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1475))
| ~ is_fun_a_bool(X1475) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk1_3(X1473,X1474,X1475)))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1475),image_pname_a(X1473,X1474)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1475))
| ~ is_fun_a_bool(X1475) )
& ( X1475 = image_pname_a(X1473,esk1_3(X1473,X1474,X1475))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1475),image_pname_a(X1473,X1474)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1475))
| ~ is_fun_a_bool(X1475) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_170_finite__subset__image])])])]) ).
cnf(i_0_685,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_531]) ).
cnf(i_0_686,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_523]) ).
cnf(i_0_687,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_532]) ).
cnf(i_0_688,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_533]) ).
cnf(i_0_689,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_534]) ).
cnf(i_0_690,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_535]) ).
cnf(i_0_691,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_536]) ).
cnf(i_0_692,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_537]) ).
cnf(i_0_693,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_538]) ).
cnf(i_0_694,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_539]) ).
cnf(i_0_695,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_540]) ).
cnf(i_0_696,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_541]) ).
cnf(i_0_697,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_542]) ).
fof(i_0_698,plain,
! [X1768,X1769,X1770,X1772,X1773,X1774] :
( ( is_fun_pname_bool(esk8_3(X1768,X1769,X1770))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1768),image_pname_a(X1769,X1770)))
| ~ is_fun_a_bool(X1768) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk8_3(X1768,X1769,X1770)),X1770))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1768),image_pname_a(X1769,X1770)))
| ~ is_fun_a_bool(X1768) )
& ( X1768 = image_pname_a(X1769,esk8_3(X1768,X1769,X1770))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1768),image_pname_a(X1769,X1770)))
| ~ is_fun_a_bool(X1768) )
& ( ~ is_fun_pname_bool(X1774)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1774),X1773))
| X1768 != image_pname_a(X1772,X1774)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1768),image_pname_a(X1772,X1773)))
| ~ is_fun_a_bool(X1768) ) ),
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_286_subset__image__iff])])])])])]) ).
fof(i_0_699,plain,
! [X1778,X1779,X1780] :
( ( is_pname(esk9_3(X1778,X1779,X1780))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1778),image_pname_a(X1779,X1780)))
| ~ is_a(X1778) )
& ( X1778 = hAPP_pname_a(X1779,esk9_3(X1778,X1779,X1780))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1778),image_pname_a(X1779,X1780)))
| ~ is_a(X1778) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk9_3(X1778,X1779,X1780)),X1780))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1778),image_pname_a(X1779,X1780)))
| ~ is_a(X1778) ) ),
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_543])])])])])]) ).
fof(i_0_700,plain,
! [X1694,X1695,X1696,X1698,X1699,X1700] :
( ( is_pname(esk7_3(X1694,X1695,X1696))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1694),image_pname_a(X1695,X1696)))
| ~ is_a(X1694) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk7_3(X1694,X1695,X1696)),X1696))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1694),image_pname_a(X1695,X1696)))
| ~ is_a(X1694) )
& ( X1694 = hAPP_pname_a(X1695,esk7_3(X1694,X1695,X1696))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1694),image_pname_a(X1695,X1696)))
| ~ is_a(X1694) )
& ( ~ is_pname(X1700)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1700),X1699))
| X1694 != hAPP_pname_a(X1698,X1700)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1694),image_pname_a(X1698,X1699)))
| ~ is_a(X1694) ) ),
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_260_image__iff])])])])])]) ).
cnf(i_0_701,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_534]) ).
cnf(i_0_702,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_544]) ).
cnf(i_0_703,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_535]) ).
cnf(i_0_704,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_545]) ).
cnf(i_0_705,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_536]) ).
cnf(i_0_706,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_546]) ).
cnf(i_0_707,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_537]) ).
cnf(i_0_708,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_547]) ).
fof(i_0_709,plain,
! [X1791,X1792,X1793] :
( ( hBOOL(hAPP_nat_bool(X1792,hAPP_nat_nat(suc,esk13_3(X1791,X1792,X1793))))
| hBOOL(hAPP_nat_bool(X1792,hAPP_nat_nat(minus_minus_nat(X1793),X1791)))
| ~ hBOOL(hAPP_nat_bool(X1792,X1793)) )
& ( ~ hBOOL(hAPP_nat_bool(X1792,esk13_3(X1791,X1792,X1793)))
| hBOOL(hAPP_nat_bool(X1792,hAPP_nat_nat(minus_minus_nat(X1793),X1791)))
| ~ hBOOL(hAPP_nat_bool(X1792,X1793)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_292_zero__induct__lemma])])])]) ).
cnf(i_0_710,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_523]) ).
cnf(i_0_711,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X2,X3)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_532]) ).
cnf(i_0_712,plain,
( hBOOL(hAPP_nat_bool(insert_nat(X3,X1),X2))
| ~ hBOOL(hAPP_nat_bool(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_527]) ).
cnf(i_0_713,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),insert_nat(X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_548]) ).
cnf(i_0_714,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),insert_nat(X2,X1))),
inference(split_conjunct,[status(thm)],[i_0_549]) ).
cnf(i_0_715,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_528]) ).
cnf(i_0_716,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_550]) ).
cnf(i_0_717,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_529]) ).
cnf(i_0_718,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_551]) ).
cnf(i_0_719,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_552]) ).
cnf(i_0_720,plain,
( hBOOL(hAPP_nat_bool(insert_nat(X1,X3),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_527]) ).
cnf(i_0_721,plain,
( is_fun1661590463l_bool(insert1325755072e_bool(X1,X2))
| ~ is_fun_pname_bool(X1)
| ~ is_fun1661590463l_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_553]) ).
cnf(i_0_722,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_554]) ).
cnf(i_0_723,plain,
( is_fun_pname_bool(insert_pname(X1,X2))
| ~ is_pname(X1)
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_555]) ).
cnf(i_0_724,hypothesis,
( is_fun_a_bool(insert_a(X1,X2))
| ~ is_a(X1)
| ~ is_fun_a_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_556]) ).
fof(i_0_725,plain,
! [X1389,X1390] :
( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1389)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1389),X1390)))) )
& ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1390)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1389),X1390)))) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1389)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1390)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,X1389),X1390)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_131_finite__Collect__disjI])])]) ).
fof(i_0_726,plain,
! [X1391,X1392] :
( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1391)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1391),X1392)))) )
& ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1392)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1391),X1392)))) )
& ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1391)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1392)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,X1391),X1392)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_132_finite__Collect__disjI])])]) ).
fof(i_0_727,plain,
! [X1385,X1386] :
( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1385)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1385),X1386)))) )
& ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1386)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1385),X1386)))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1385)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1386)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,X1385),X1386)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_129_finite__Collect__disjI])])]) ).
fof(i_0_728,plain,
! [X1395,X1396] :
( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1395)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1395),X1396)))) )
& ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1396)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1395),X1396)))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1395)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1396)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,X1395),X1396)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_134_finite__Collect__disjI])])]) ).
fof(i_0_729,plain,
! [X1304,X1305] :
( ~ is_fun1661590463l_bool(X1304)
| ~ is_fun1661590463l_bool(X1305)
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1305))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1304),X1305))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1305)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1304)))
| X1304 = X1305 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_87_card__seteq])]) ).
fof(i_0_730,plain,
! [X1306,X1307] :
( ~ is_fun949378684l_bool(X1306)
| ~ is_fun949378684l_bool(X1307)
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1307))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1306),X1307))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1307)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1306)))
| X1306 = X1307 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_88_card__seteq])]) ).
fof(i_0_731,plain,
! [X1308,X1309] :
( ~ is_fun_pname_bool(X1308)
| ~ is_fun_pname_bool(X1309)
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1309))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1308),X1309))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1309)),hAPP_f921600141ol_nat(finite_card_pname,X1308)))
| X1308 = X1309 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_89_card__seteq])]) ).
fof(i_0_732,plain,
! [X1310,X1311] :
( ~ is_fun_a_bool(X1310)
| ~ is_fun_a_bool(X1311)
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1311))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1310),X1311))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1311)),hAPP_fun_a_bool_nat(finite_card_a,X1310)))
| X1310 = X1311 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_90_card__seteq])]) ).
fof(i_0_733,plain,
! [X1302,X1303] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1303))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1302),X1303))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1303)),hAPP_f696928925ol_nat(finite346522414t_bool,X1302)))
| X1302 = X1303 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_86_card__seteq])]) ).
fof(i_0_734,plain,
! [X1312,X1313] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1313))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1312),X1313))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1313)),hAPP_f22106695ol_nat(finite_card_nat,X1312)))
| X1312 = X1313 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_91_card__seteq])]) ).
fof(i_0_735,plain,
! [X1282,X1283] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1283))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X1282,X1283))),hAPP_f22106695ol_nat(finite_card_nat,X1283))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_76_card__image__le])]) ).
fof(i_0_736,plain,
! [X1274,X1275] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1275))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X1274,X1275))),hAPP_f921600141ol_nat(finite_card_pname,X1275))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_72_card__image__le])]) ).
fof(i_0_737,plain,
! [X1280,X1281] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1281))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X1280,X1281))),hAPP_f22106695ol_nat(finite_card_nat,X1281))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_75_card__image__le])]) ).
fof(i_0_738,plain,
! [X1272,X1273] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1273))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X1272,X1273))),hAPP_f921600141ol_nat(finite_card_pname,X1273))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_71_card__image__le])]) ).
fof(i_0_739,plain,
! [X1270,X1271] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1271))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X1270,X1271))),hAPP_f921600141ol_nat(finite_card_pname,X1271))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_70_card__image__le])]) ).
fof(i_0_740,plain,
! [X1278,X1279] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1279))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X1278,X1279))),hAPP_f22106695ol_nat(finite_card_nat,X1279))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_74_card__image__le])]) ).
fof(i_0_741,plain,
! [X1254,X1255] :
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1255))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X1254,X1255))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X1255))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_62_card__image__le])]) ).
fof(i_0_742,plain,
! [X1256,X1257] :
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1257))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X1256,X1257))),hAPP_f98387925ol_nat(finite269641166l_bool,X1257))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_63_card__image__le])]) ).
fof(i_0_743,plain,
! [X1258,X1259] :
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1259))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X1258,X1259))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X1259))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_64_card__image__le])]) ).
fof(i_0_744,plain,
! [X1264,X1265] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1265))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(X1264,X1265))),hAPP_f696928925ol_nat(finite346522414t_bool,X1265))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_67_card__image__le])]) ).
fof(i_0_745,plain,
! [X1262,X1263] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1263))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(X1262,X1263))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1263))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_66_card__image__le])]) ).
fof(i_0_746,plain,
! [X1260,X1261] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1261))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(X1260,X1261))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1261))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_65_card__image__le])]) ).
fof(i_0_747,plain,
! [X1276,X1277] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1277))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X1276,X1277))),hAPP_f22106695ol_nat(finite_card_nat,X1277))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_73_card__image__le])]) ).
fof(i_0_748,plain,
! [X1252,X1253] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1253))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(X1252,X1253))),hAPP_f921600141ol_nat(finite_card_pname,X1253))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_61_card__image__le])]) ).
fof(i_0_749,plain,
! [X1266,X1267] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1267))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(X1266,X1267))),hAPP_fun_a_bool_nat(finite_card_a,X1267))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_68_card__image__le])]) ).
fof(i_0_750,plain,
! [X1284,X1285] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1285))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X1284,X1285))),hAPP_f696928925ol_nat(finite346522414t_bool,X1285))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_77_card__image__le])]) ).
fof(i_0_751,plain,
! [X1286,X1287] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1287))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X1286,X1287))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1287))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_78_card__image__le])]) ).
fof(i_0_752,plain,
! [X1288,X1289] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1289))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X1288,X1289))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1289))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_79_card__image__le])]) ).
fof(i_0_753,plain,
! [X1250,X1251] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1251))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(X1250,X1251))),hAPP_f22106695ol_nat(finite_card_nat,X1251))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_60_card__image__le])]) ).
fof(i_0_754,plain,
! [X1268,X1269] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1269))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(X1268,X1269))),hAPP_f921600141ol_nat(finite_card_pname,X1269))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_69_card__image__le])]) ).
fof(i_0_755,plain,
! [X1248,X1249] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1249))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(X1248,X1249))),hAPP_fun_a_bool_nat(finite_card_a,X1249))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_59_card__image__le])]) ).
fof(i_0_756,plain,
! [X1238,X1239] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1239))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(X1238,X1239))),hAPP_f921600141ol_nat(finite_card_pname,X1239))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_54_card__image__le])]) ).
fof(i_0_757,plain,
! [X1240,X1241] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1241))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(X1240,X1241))),hAPP_fun_a_bool_nat(finite_card_a,X1241))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_55_card__image__le])]) ).
fof(i_0_758,plain,
! [X1242,X1243] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1243))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(X1242,X1243))),hAPP_f696928925ol_nat(finite346522414t_bool,X1243))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_56_card__image__le])]) ).
fof(i_0_759,plain,
! [X1244,X1245] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1245))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(X1244,X1245))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1245))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_57_card__image__le])]) ).
fof(i_0_760,plain,
! [X1246,X1247] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1247))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(X1246,X1247))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1247))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_58_card__image__le])]) ).
cnf(i_0_761,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_557]) ).
cnf(i_0_762,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_558]) ).
cnf(i_0_763,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_557]) ).
cnf(i_0_764,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_559]) ).
cnf(i_0_765,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_558]) ).
cnf(i_0_766,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_560]) ).
fof(i_0_767,plain,
! [X1462,X1463,X1464] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1463),X1464))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1463),X1462)),hAPP_nat_nat(minus_minus_nat(X1464),X1462))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_166_diff__le__mono])]) ).
fof(i_0_768,plain,
! [X1465,X1466,X1467] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1466),X1467))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1465),X1467)),hAPP_nat_nat(minus_minus_nat(X1465),X1466))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_167_diff__le__mono2])]) ).
fof(i_0_769,plain,
! [X1439,X1440] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1439)),hAPP_nat_nat(suc,X1440)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1439),X1440)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1439),X1440))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1439)),hAPP_nat_nat(suc,X1440))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_156_Suc__le__mono])]) ).
fof(i_0_770,plain,
! [X1446,X1447,X1448] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1446)),X1447)),hAPP_nat_nat(suc,X1448)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1446),X1447)),X1448),
inference(variable_rename,[status(thm)],[fact_160_Suc__diff__diff]) ).
cnf(i_0_771,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_561]) ).
cnf(i_0_772,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_562]) ).
fof(i_0_773,plain,
! [X1454,X1455,X1456] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1455),X1456))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1455),X1454))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1456),X1455)),hAPP_nat_nat(minus_minus_nat(X1454),X1455)) = hAPP_nat_nat(minus_minus_nat(X1456),X1454) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_163_Nat_Odiff__diff__eq])]) ).
fof(i_0_774,plain,
! [X1352,X1353] :
( ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1353)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1353),X1352)))) )
& ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(X1352)))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,X1353),X1352)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_111_finite__Collect__conjI])])]) ).
fof(i_0_775,plain,
! [X1354,X1355] :
( ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1355)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1355),X1354)))) )
& ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(X1354)))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,X1355),X1354)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_112_finite__Collect__conjI])])]) ).
fof(i_0_776,plain,
! [X1358,X1359] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1359)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1359),X1358)))) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(X1358)))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,X1359),X1358)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_114_finite__Collect__conjI])])]) ).
fof(i_0_777,plain,
! [X1356,X1357] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1357)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1357),X1356)))) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(X1356)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,X1357),X1356)))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_113_finite__Collect__conjI])])]) ).
fof(i_0_778,plain,
! [X1443,X1444] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1443),X1444))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1444)),X1443)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1444)),X1443))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1443),X1444)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_563])]) ).
fof(i_0_779,plain,
! [X1294,X1295] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1295))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1294),X1295))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,X1294)),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1295))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_82_card__mono])]) ).
fof(i_0_780,plain,
! [X1292,X1293] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1293))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1292),X1293))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,X1292)),hAPP_f55526627ol_nat(finite1340463720e_bool,X1293))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_81_card__mono])]) ).
fof(i_0_781,plain,
! [X1290,X1291] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1291))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1290),X1291))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,X1290)),hAPP_f696928925ol_nat(finite346522414t_bool,X1291))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_80_card__mono])]) ).
fof(i_0_782,plain,
! [X1298,X1299] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1299))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1298),X1299))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,X1298)),hAPP_fun_a_bool_nat(finite_card_a,X1299))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_84_card__mono])]) ).
fof(i_0_783,plain,
! [X1296,X1297] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1297))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1296),X1297))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,X1296)),hAPP_f921600141ol_nat(finite_card_pname,X1297))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_83_card__mono])]) ).
fof(i_0_784,plain,
! [X1300,X1301] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1301))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1300),X1301))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,X1300)),hAPP_f22106695ol_nat(finite_card_nat,X1301))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_85_card__mono])]) ).
fof(i_0_785,plain,
! [X1782,X1783] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk10_2(X1782,X1783)),X1783))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1783),X1782)) )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk10_2(X1782,X1783)),X1782))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1783),X1782)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_289_subsetI])])])]) ).
fof(i_0_786,plain,
! [X1788,X1789] :
( ( is_pname(esk12_2(X1788,X1789))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1789),X1788)) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk12_2(X1788,X1789)),X1789))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1789),X1788)) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk12_2(X1788,X1789)),X1788))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1789),X1788)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_291_subsetI])])])]) ).
fof(i_0_787,plain,
! [X1785,X1786] :
( ( is_a(esk11_2(X1785,X1786))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1786),X1785)) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk11_2(X1785,X1786)),X1786))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1786),X1785)) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk11_2(X1785,X1786)),X1785))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1786),X1785)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_290_subsetI])])])]) ).
fof(i_0_788,plain,
! [X1775,X1776,X1777] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1776),X1777))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1775,X1776)),image_pname_a(X1775,X1777))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_287_image__mono])]) ).
fof(i_0_789,plain,
! [X1701,X1702,X1703] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1702),X1703))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(X1701,X1702)),image_pname_a(X1701,X1703))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_261_imageI])]) ).
cnf(i_0_790,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_564]) ).
cnf(i_0_791,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_565]) ).
fof(i_0_792,plain,
! [X1433,X1434] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1433)),X1434))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1433),X1434)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_153_Suc__leD])]) ).
fof(i_0_793,plain,
! [X1650,X1651,X1652] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1651),X1652))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1652),X1650))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1651),X1650)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_240_set__rev__mp])]) ).
fof(i_0_794,plain,
! [X1659,X1660,X1661] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1660),X1661))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1659),X1660))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1659),X1661)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_243_set__mp])]) ).
fof(i_0_795,plain,
! [X1641,X1642,X1643] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1642),X1643))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1641),X1642))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1641),X1643)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_237_in__mono])]) ).
fof(i_0_796,plain,
! [X1506,X1507,X1508] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1507),X1508))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1506),X1507))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1506),X1508)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_180_subsetD])]) ).
fof(i_0_797,plain,
! [X1668,X1669,X1670] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1669),X1670))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1670),X1668))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1669),X1668)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_246_subset__trans])]) ).
fof(i_0_798,plain,
! [X1671,X1672,X1673] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1672),X1673))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1673),X1671))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1672),X1671)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_247_subset__trans])]) ).
fof(i_0_799,plain,
! [X1656,X1657,X1658] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1657),X1658))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1658),X1656))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1657),X1656)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_242_set__rev__mp])]) ).
fof(i_0_800,plain,
! [X1665,X1666,X1667] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1666),X1667))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1665),X1666))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1665),X1667)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_245_set__mp])]) ).
fof(i_0_801,plain,
! [X1647,X1648,X1649] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1648),X1649))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1647),X1648))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1647),X1649)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_239_in__mono])]) ).
fof(i_0_802,plain,
! [X1512,X1513,X1514] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1513),X1514))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1512),X1513))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1512),X1514)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_182_subsetD])]) ).
fof(i_0_803,plain,
! [X1674,X1675,X1676] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1675),X1676))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1676),X1674))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1675),X1674)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_248_subset__trans])]) ).
fof(i_0_804,plain,
! [X1653,X1654,X1655] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1654),X1655))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1655),X1653))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1654),X1653)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_241_set__rev__mp])]) ).
fof(i_0_805,plain,
! [X1662,X1663,X1664] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1663),X1664))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1662),X1663))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1662),X1664)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_244_set__mp])]) ).
fof(i_0_806,plain,
! [X1644,X1645,X1646] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1645),X1646))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1644),X1645))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1644),X1646)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_238_in__mono])]) ).
fof(i_0_807,plain,
! [X1509,X1510,X1511] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1510),X1511))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1509),X1510))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1509),X1511)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_181_subsetD])]) ).
fof(i_0_808,plain,
! [X1374,X1375,X1376] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1375),X1376))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1376),X1374))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1375),X1374)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_124_le__trans])]) ).
fof(i_0_809,plain,
! [X1806,X1808,X1809,X1810] :
( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1806))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1808),X1806))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1808),esk16_1(X1806))) )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk17_2(X1809,X1810)),X1809))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1809)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk17_2(X1809,X1810)),X1810))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1809)) ) ),
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_299_finite__nat__set__iff__bounded__le])])])])])]) ).
fof(i_0_810,plain,
! [X1457,X1458,X1459] :
( ( hAPP_nat_nat(minus_minus_nat(X1459),X1458) != hAPP_nat_nat(minus_minus_nat(X1457),X1458)
| X1459 = X1457
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1458),X1457))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1458),X1459)) )
& ( X1459 != X1457
| hAPP_nat_nat(minus_minus_nat(X1459),X1458) = hAPP_nat_nat(minus_minus_nat(X1457),X1458)
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1458),X1457))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1458),X1459)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_164_eq__diff__iff])])]) ).
fof(i_0_811,plain,
! [X1795,X1796] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1795)),X1796))
| X1796 = hAPP_nat_nat(suc,esk14_2(X1795,X1796)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_293_Suc__le__D])])]) ).
cnf(i_0_812,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_566]) ).
cnf(i_0_813,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_566]) ).
cnf(i_0_814,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_567]) ).
cnf(i_0_815,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_567]) ).
fof(i_0_816,plain,
! [X1441,X1442] :
( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1441),hAPP_nat_nat(suc,X1442)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1441),X1442))
| X1441 = hAPP_nat_nat(suc,X1442) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1441),X1442))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1441),hAPP_nat_nat(suc,X1442))) )
& ( X1441 != hAPP_nat_nat(suc,X1442)
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1441),hAPP_nat_nat(suc,X1442))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_157_le__Suc__eq])])]) ).
fof(i_0_817,plain,
! [X1435,X1436] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1435),hAPP_nat_nat(suc,X1436)))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1435),X1436))
| X1435 = hAPP_nat_nat(suc,X1436) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_568])]) ).
fof(i_0_818,plain,
! [X1470,X1471,X1472] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1472))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1470),image_pname_a(X1471,X1472)))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1470)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_169_finite__surj])]) ).
fof(i_0_819,plain,
! [X1496,X1497,X1498,X1499] :
( X1497 != hAPP_pname_a(X1498,X1499)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1499),X1496))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1497),image_pname_a(X1498,X1496))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_176_image__eqI])]) ).
fof(i_0_820,plain,
! [X1704,X1705,X1706,X1707] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1706),X1707))
| X1704 != hAPP_pname_a(X1705,X1706)
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1704),image_pname_a(X1705,X1707))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_262_rev__image__eqI])]) ).
fof(i_0_821,plain,
! [X1445] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1445)),X1445)),
inference(variable_rename,[status(thm)],[i_0_569]) ).
cnf(i_0_822,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_566]) ).
cnf(i_0_823,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_567]) ).
fof(i_0_824,plain,
! [X1625,X1626] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1625),X1626))
| X1625 != X1626
| ~ is_fun_pname_bool(X1625)
| ~ is_fun_pname_bool(X1626) )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1626),X1625))
| X1625 != X1626
| ~ is_fun_pname_bool(X1625)
| ~ is_fun_pname_bool(X1626) )
& ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1625),X1626))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1626),X1625))
| X1625 = X1626
| ~ is_fun_pname_bool(X1625)
| ~ is_fun_pname_bool(X1626) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_229_set__eq__subset])])]) ).
fof(i_0_825,plain,
! [X1502,X1503] :
( ~ is_fun_pname_bool(X1502)
| ~ is_fun_pname_bool(X1503)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1502),X1503))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1503),X1502))
| X1502 = X1503 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_178_equalityI])]) ).
fof(i_0_826,plain,
! [X1627,X1628] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1627),X1628))
| X1627 != X1628
| ~ is_fun_a_bool(X1627)
| ~ is_fun_a_bool(X1628) )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1628),X1627))
| X1627 != X1628
| ~ is_fun_a_bool(X1627)
| ~ is_fun_a_bool(X1628) )
& ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1627),X1628))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1628),X1627))
| X1627 = X1628
| ~ is_fun_a_bool(X1627)
| ~ is_fun_a_bool(X1628) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_230_set__eq__subset])])]) ).
fof(i_0_827,plain,
! [X1504,X1505] :
( ~ is_fun_a_bool(X1504)
| ~ is_fun_a_bool(X1505)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1504),X1505))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1505),X1504))
| X1504 = X1505 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_179_equalityI])]) ).
cnf(i_0_828,plain,
( insert_nat(X1,X2) = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_570]) ).
fof(i_0_829,plain,
! [X1623,X1624] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1623),X1624))
| X1623 != X1624 )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1624),X1623))
| X1623 != X1624 )
& ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1623),X1624))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1624),X1623))
| X1623 = X1624 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_228_set__eq__subset])])]) ).
fof(i_0_830,plain,
! [X1500,X1501] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1500),X1501))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1501),X1500))
| X1500 = X1501 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_177_equalityI])]) ).
fof(i_0_831,plain,
! [X1372,X1373] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1372),X1373))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1373),X1372))
| X1372 = X1373 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_123_le__antisym])]) ).
fof(i_0_832,plain,
! [X1437,X1438] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1437),X1438))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1437),hAPP_nat_nat(suc,X1438))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_155_le__SucI])]) ).
fof(i_0_833,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_834,plain,
! [X1362,X1363] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1362),X1363))
| hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1363)),X1362) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(X1363),X1362)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_116_Suc__diff__le])]) ).
fof(i_0_835,plain,
! [X1468,X1469] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(X1468),X1469)),X1468)),
inference(variable_rename,[status(thm)],[fact_168_diff__le__self]) ).
cnf(i_0_836,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_571]) ).
cnf(i_0_837,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_571]) ).
cnf(i_0_838,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_572]) ).
cnf(i_0_839,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_572]) ).
fof(i_0_840,plain,
! [X1144] :
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1144))
| hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X1144)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_4_finite__Collect__subsets])]) ).
fof(i_0_841,plain,
! [X1145] :
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1145))
| hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X1145)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_finite__Collect__subsets])]) ).
fof(i_0_842,plain,
! [X1146] :
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1146))
| hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X1146)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_6_finite__Collect__subsets])]) ).
fof(i_0_843,plain,
! [X1149] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1149))
| hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),X1149)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_9_finite__Collect__subsets])]) ).
fof(i_0_844,plain,
! [X1148] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1148))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),X1148)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_8_finite__Collect__subsets])]) ).
fof(i_0_845,plain,
! [X1147] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1147))
| hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),X1147)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_7_finite__Collect__subsets])]) ).
fof(i_0_846,plain,
! [X1142] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1142))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),X1142)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2_finite__Collect__subsets])]) ).
fof(i_0_847,plain,
! [X1143] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1143))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),X1143)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_3_finite__Collect__subsets])]) ).
fof(i_0_848,plain,
! [X1382,X1383,X1384] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1382),X1383)),X1384) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(X1382),X1384)),X1383),
inference(variable_rename,[status(thm)],[fact_128_diff__commute]) ).
fof(i_0_849,plain,
! [X1409,X1410] :
( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1409),X1410))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1410))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1409)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_141_finite__subset])]) ).
fof(i_0_850,plain,
! [X1421,X1422] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1422))
| ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,X1421),X1422))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1421)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_147_rev__finite__subset])]) ).
fof(i_0_851,plain,
! [X1411,X1412] :
( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1411),X1412))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1412))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1411)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_142_finite__subset])]) ).
fof(i_0_852,plain,
! [X1423,X1424] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1424))
| ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,X1423),X1424))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1423)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_148_rev__finite__subset])]) ).
fof(i_0_853,plain,
! [X1415,X1416] :
( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1415),X1416))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1416))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1415)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_144_finite__subset])]) ).
fof(i_0_854,plain,
! [X1427,X1428] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1428))
| ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,X1427),X1428))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1427)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_150_rev__finite__subset])]) ).
fof(i_0_855,plain,
! [X1417,X1418] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1417),X1418))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1418))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1417)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_145_finite__subset])]) ).
fof(i_0_856,plain,
! [X1429,X1430] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1430))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1429),X1430))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1429)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_151_rev__finite__subset])]) ).
fof(i_0_857,plain,
! [X1419,X1420] :
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1419),X1420))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1420))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1419)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_146_finite__subset])]) ).
fof(i_0_858,plain,
! [X1431,X1432] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1432))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1431),X1432))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1431)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_152_rev__finite__subset])]) ).
fof(i_0_859,plain,
! [X1413,X1414] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1413),X1414))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1414))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1413)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_143_finite__subset])]) ).
fof(i_0_860,plain,
! [X1425,X1426] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1426))
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1425),X1426))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1425)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_149_rev__finite__subset])]) ).
fof(i_0_861,plain,
! [X1460,X1461] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1460),X1461))
| hAPP_nat_nat(minus_minus_nat(X1461),hAPP_nat_nat(minus_minus_nat(X1461),X1460)) = X1460 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_165_diff__diff__cancel])]) ).
fof(i_0_862,plain,
! [X1139,X1140] :
( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1139),X1140))
| hBOOL(hAPP_fun_a_bool_bool(p(X1140),X1139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_assms_I1_J])]) ).
fof(i_0_863,plain,
! [X1379,X1380] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1379),X1380))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1380),X1379)) ),
inference(variable_rename,[status(thm)],[fact_126_nat__le__linear]) ).
fof(i_0_864,plain,
! [X1683,X1684] :
( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1683),X1684))
| hBOOL(hAPP_nat_bool(X1684,X1683)) )
& ( ~ hBOOL(hAPP_nat_bool(X1684,X1683))
| hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X1683),X1684)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_252_mem__def])]) ).
fof(i_0_865,plain,
! [X1687,X1688] :
( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1687),X1688))
| hBOOL(hAPP_pname_bool(X1688,X1687)) )
& ( ~ hBOOL(hAPP_pname_bool(X1688,X1687))
| hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1687),X1688)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_254_mem__def])]) ).
fof(i_0_866,plain,
! [X1685,X1686] :
( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1685),X1686))
| hBOOL(hAPP_a_bool(X1686,X1685)) )
& ( ~ hBOOL(hAPP_a_bool(X1686,X1685))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X1685),X1686)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_253_mem__def])]) ).
fof(i_0_867,plain,
! [X1840,X1841] :
( ~ is_pname(X1840)
| ~ is_pname(X1841)
| ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1840),X1841))
| X1840 = X1841 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_573])]) ).
fof(i_0_868,plain,
! [X1832,X1833] :
( ~ is_a(X1832)
| ~ is_a(X1833)
| ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1832),X1833))
| X1832 = X1833 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_574])]) ).
fof(i_0_869,plain,
! [X1864,X1865] :
( ~ is_fun_pname_bool(X1864)
| ~ is_fun_pname_bool(X1865)
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1864),X1865))
| X1864 = X1865 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_575])]) ).
fof(i_0_870,plain,
! [X1847,X1848] :
( ~ is_fun_a_bool(X1847)
| ~ is_fun_a_bool(X1848)
| ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1847),X1848))
| X1847 = X1848 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_576])]) ).
cnf(i_0_871,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_577]) ).
fof(i_0_872,plain,
! [X1830,X1831] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1830),X1831))
| ~ hBOOL(X1830)
| hBOOL(X1831) ),
inference(variable_rename,[status(thm)],[i_0_578]) ).
fof(i_0_873,plain,
! [X1824,X1825] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1824),X1825))
| hBOOL(X1824)
| hBOOL(X1825) ),
inference(variable_rename,[status(thm)],[i_0_579]) ).
fof(i_0_874,plain,
! [X1816,X1817] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1816),X1817))
| hBOOL(X1816) ),
inference(variable_rename,[status(thm)],[i_0_580]) ).
fof(i_0_875,plain,
! [X1818,X1819] :
( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1818),X1819))
| hBOOL(X1819) ),
inference(variable_rename,[status(thm)],[i_0_581]) ).
fof(i_0_876,plain,
! [X1226,X1227] :
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1227))
| hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X1226,X1227))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_48_finite_OinsertI])]) ).
fof(i_0_877,plain,
! [X1194,X1195] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1195))
| hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X1194,X1195))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_32_finite__imageI])]) ).
fof(i_0_878,plain,
! [X1180,X1181] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1181))
| hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X1180,X1181))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_25_finite__imageI])]) ).
fof(i_0_879,plain,
! [X1228,X1229] :
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1229))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X1228,X1229))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_49_finite_OinsertI])]) ).
fof(i_0_880,plain,
! [X1196,X1197] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1197))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X1196,X1197))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_33_finite__imageI])]) ).
fof(i_0_881,plain,
! [X1182,X1183] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1183))
| hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X1182,X1183))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_26_finite__imageI])]) ).
fof(i_0_882,plain,
! [X1230,X1231] :
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1231))
| hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X1230,X1231))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_50_finite_OinsertI])]) ).
fof(i_0_883,plain,
! [X1198,X1199] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1199))
| hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X1198,X1199))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_34_finite__imageI])]) ).
fof(i_0_884,plain,
! [X1184,X1185] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1185))
| hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X1184,X1185))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_27_finite__imageI])]) ).
fof(i_0_885,plain,
! [X1204,X1205] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1205))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(X1204,X1205))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_37_finite__imageI])]) ).
fof(i_0_886,plain,
! [X1190,X1191] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1191))
| hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(X1190,X1191))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_30_finite__imageI])]) ).
fof(i_0_887,plain,
! [X1188,X1189] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1189))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(X1188,X1189))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_29_finite__imageI])]) ).
fof(i_0_888,plain,
! [X1202,X1203] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1203))
| hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(X1202,X1203))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_36_finite__imageI])]) ).
fof(i_0_889,plain,
! [X1186,X1187] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1187))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(X1186,X1187))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_28_finite__imageI])]) ).
fof(i_0_890,plain,
! [X1200,X1201] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1201))
| hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(X1200,X1201))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_35_finite__imageI])]) ).
fof(i_0_891,plain,
! [X1216,X1217] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1217))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X1216,X1217))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_43_finite__imageI])]) ).
fof(i_0_892,plain,
! [X1164,X1165] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1165))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(X1164,X1165))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_17_finite__imageI])]) ).
fof(i_0_893,plain,
! [X1162,X1163] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1163))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(X1162,X1163))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_16_finite__imageI])]) ).
fof(i_0_894,plain,
! [X1160,X1161] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1161))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(X1160,X1161))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_15_finite__imageI])]) ).
fof(i_0_895,plain,
! [X1158,X1159] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1159))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(X1158,X1159))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_14_finite__imageI])]) ).
fof(i_0_896,plain,
! [X1156,X1157] :
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1157))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X1156,X1157))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_13_finite__imageI])]) ).
fof(i_0_897,plain,
! [X1154,X1155] :
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1155))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X1154,X1155))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_12_finite__imageI])]) ).
fof(i_0_898,plain,
! [X1152,X1153] :
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1153))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X1152,X1153))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_11_finite__imageI])]) ).
fof(i_0_899,plain,
! [X1166,X1167] :
( ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1167))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X1166,X1167))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_18_finite__imageI])]) ).
fof(i_0_900,plain,
! [X1168,X1169] :
( ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1169))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X1168,X1169))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_19_finite__imageI])]) ).
fof(i_0_901,plain,
! [X1170,X1171] :
( ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1171))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X1170,X1171))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_20_finite__imageI])]) ).
fof(i_0_902,plain,
! [X1176,X1177] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1177))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(X1176,X1177))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_23_finite__imageI])]) ).
fof(i_0_903,plain,
! [X1174,X1175] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1175))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(X1174,X1175))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_22_finite__imageI])]) ).
fof(i_0_904,plain,
! [X1172,X1173] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1173))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(X1172,X1173))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_21_finite__imageI])]) ).
fof(i_0_905,plain,
! [X1218,X1219] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1219))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X1218,X1219))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_44_finite__imageI])]) ).
fof(i_0_906,plain,
! [X1206,X1207] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1207))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X1206,X1207))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_38_finite__imageI])]) ).
fof(i_0_907,plain,
! [X1178,X1179] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1179))
| hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(X1178,X1179))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_24_finite__imageI])]) ).
fof(i_0_908,plain,
! [X1210,X1211] :
( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1211))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X1210,X1211))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_40_finite__imageI])]) ).
fof(i_0_909,plain,
! [X1212,X1213] :
( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1213))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X1212,X1213))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_41_finite__imageI])]) ).
fof(i_0_910,plain,
! [X1214,X1215] :
( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1215))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X1214,X1215))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_42_finite__imageI])]) ).
fof(i_0_911,plain,
! [X1192,X1193] :
( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1193))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(X1192,X1193))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_31_finite__imageI])]) ).
fof(i_0_912,plain,
! [X1150,X1151] :
( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1151))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X1150,X1151))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_10_finite__imageI])]) ).
fof(i_0_913,plain,
! [X1208,X1209] :
( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1209))
| hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X1208,X1209))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_39_finite__imageI])]) ).
fof(i_0_914,plain,
! [X1860,X1861] :
( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1860),X1861))
| X1860 = X1861 ),
inference(variable_rename,[status(thm)],[i_0_582]) ).
fof(i_0_915,plain,
! [X1836,X1837] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1836),X1837))
| X1836 = X1837 ),
inference(variable_rename,[status(thm)],[i_0_583]) ).
fof(i_0_916,plain,
! [X1449,X1450] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,X1449)),hAPP_nat_nat(suc,X1450)) = hAPP_nat_nat(minus_minus_nat(X1449),X1450),
inference(variable_rename,[status(thm)],[fact_161_diff__Suc__Suc]) ).
fof(i_0_917,plain,
! [X1910,X1911,X1912] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(X1910,X1911),X1912) = hAPP_bool_bool(hAPP_f1748468828l_bool(X1910,X1912),hAPP_f54304608l_bool(X1911,X1912)),
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_918,plain,
! [X1919,X1920,X1921] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(X1919,X1920),X1921) = hAPP_bool_bool(hAPP_f1476298914l_bool(X1919,X1921),hAPP_f1664156314l_bool(X1920,X1921)),
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_919,plain,
! [X1898,X1899,X1900] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(X1898,X1899),X1900) = hAPP_bool_bool(hAPP_f198738859l_bool(X1898,X1900),hAPP_fun_a_bool_bool(X1899,X1900)),
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_920,plain,
! [X1874,X1875,X1876] : hAPP_nat_bool(cOMBS_nat_bool_bool(X1874,X1875),X1876) = hAPP_bool_bool(hAPP_n1006566506l_bool(X1874,X1876),hAPP_nat_bool(X1875,X1876)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).
fof(i_0_921,plain,
! [X1880,X1881,X1882] : hAPP_pname_bool(cOMBS_568398431l_bool(X1880,X1881),X1882) = hAPP_bool_bool(hAPP_p393069232l_bool(X1880,X1882),hAPP_pname_bool(X1881,X1882)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).
fof(i_0_922,plain,
! [X1854,X1855,X1856] : hAPP_a_bool(cOMBS_a_bool_bool(X1854,X1855),X1856) = hAPP_bool_bool(hAPP_a_fun_bool_bool(X1854,X1856),hAPP_a_bool(X1855,X1856)),
inference(variable_rename,[status(thm)],[help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).
fof(i_0_923,plain,
! [X1964,X1965,X1966] : hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X1964),X1965),X1966) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X1964,X1966),X1965),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool]) ).
fof(i_0_924,plain,
! [X1967,X1968,X1969] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X1967),X1968),X1969) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X1967,X1969),X1968),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo]) ).
fof(i_0_925,plain,
! [X1961,X1962,X1963] : hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X1961),X1962),X1963) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X1961,X1963),X1962),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H]) ).
fof(i_0_926,plain,
! [X1955,X1956,X1957] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(X1955),X1956),X1957) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(X1955,X1957),X1956),
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_927,plain,
! [X1958,X1959,X1960] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(X1958),X1959),X1960) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(X1958,X1960),X1959),
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_928,plain,
! [X1952,X1953,X1954] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(X1952),X1953),X1954) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(X1952,X1954),X1953),
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_929,plain,
! [X1946,X1947,X1948] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(X1946),X1947),X1948) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(X1946,X1948),X1947),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__011]) ).
fof(i_0_930,plain,
! [X1931,X1932,X1933] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(X1931),X1932),X1933) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(X1931,X1933),X1932),
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_931,plain,
! [X1949,X1950,X1951] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(X1949),X1950),X1951) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(X1949,X1951),X1950),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_012]) ).
fof(i_0_932,plain,
! [X1940,X1941,X1942] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(X1940),X1941),X1942) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(X1940,X1942),X1941),
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_933,plain,
! [X1943,X1944,X1945] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(X1943),X1944),X1945) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(X1943,X1945),X1944),
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_934,plain,
! [X1925,X1926,X1927] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(X1925),X1926),X1927) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(X1925,X1927),X1926),
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_935,plain,
! [X1901,X1902,X1903] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(X1901),X1902),X1903) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(X1901,X1903),X1902),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).
fof(i_0_936,plain,
! [X1868,X1869,X1870] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(X1868),X1869),X1870) = hAPP_nat_bool(hAPP_n1699378549t_bool(X1868,X1870),X1869),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U]) ).
fof(i_0_937,plain,
! [X1922,X1923,X1924] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(X1922),X1923),X1924) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(X1922,X1924),X1923),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob]) ).
fof(i_0_938,plain,
! [X1883,X1884,X1885] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(X1883),X1884),X1885) = hAPP_pname_bool(hAPP_p61793385e_bool(X1883,X1885),X1884),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U]) ).
fof(i_0_939,plain,
! [X1857,X1858,X1859] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(X1857),X1858),X1859) = hAPP_a_bool(hAPP_p1534023578a_bool(X1857,X1859),X1858),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U]) ).
fof(i_0_940,plain,
! [X1886,X1887,X1888] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(X1886),X1887),X1888) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(X1886,X1888),X1887),
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_941,plain,
! [X1844,X1845,X1846] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(X1844),X1845),X1846) = hAPP_a_bool(hAPP_a_fun_a_bool(X1844,X1846),X1845),
inference(variable_rename,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U]) ).
cnf(i_0_942,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_584]) ).
fof(i_0_943,plain,
! [X1814,X1815] :
( ~ hBOOL(X1815)
| ~ hBOOL(X1814)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1815),X1814)) ),
inference(variable_rename,[status(thm)],[i_0_585]) ).
fof(i_0_944,plain,
! [X1828,X1829] :
( ~ hBOOL(X1829)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1828),X1829)) ),
inference(variable_rename,[status(thm)],[i_0_586]) ).
fof(i_0_945,plain,
! [X1820,X1821] :
( ~ hBOOL(X1821)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1821),X1820)) ),
inference(variable_rename,[status(thm)],[i_0_587]) ).
fof(i_0_946,plain,
! [X1822,X1823] :
( ~ hBOOL(X1823)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1822),X1823)) ),
inference(variable_rename,[status(thm)],[i_0_588]) ).
fof(i_0_947,plain,
! [X1826,X1827] :
( hBOOL(X1827)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1827),X1826)) ),
inference(variable_rename,[status(thm)],[help_fimplies_1_1_U]) ).
fof(i_0_948,plain,
! [X1937,X1938,X1939] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(X1937,X1938),X1939) = hAPP_b589554111l_bool(X1937,hAPP_f1664156314l_bool(X1938,X1939)),
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_949,plain,
! [X1934,X1935,X1936] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(X1934,X1935),X1936) = hAPP_b589554111l_bool(X1934,hAPP_f54304608l_bool(X1935,X1936)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009]) ).
fof(i_0_950,plain,
! [X1928,X1929,X1930] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(X1928,X1929),X1930) = hAPP_b589554111l_bool(X1928,hAPP_fun_a_bool_bool(X1929,X1930)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008]) ).
fof(i_0_951,plain,
! [X1916,X1917,X1918] : hAPP_p393069232l_bool(cOMBB_675860798_pname(X1916,X1917),X1918) = hAPP_b589554111l_bool(X1916,hAPP_pname_bool(X1917,X1918)),
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_952,plain,
! [X1907,X1908,X1909] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(X1907,X1908),X1909) = hAPP_b589554111l_bool(X1907,hAPP_nat_bool(X1908,X1909)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006]) ).
fof(i_0_953,plain,
! [X1895,X1896,X1897] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(X1895,X1896),X1897) = hAPP_b589554111l_bool(X1895,hAPP_a_bool(X1896,X1897)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo]) ).
fof(i_0_954,plain,
! [X1904,X1905,X1906] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(X1904,X1905),X1906) = hAPP_bool_bool(X1904,hAPP_f54304608l_bool(X1905,X1906)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On]) ).
fof(i_0_955,plain,
! [X1913,X1914,X1915] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(X1913,X1914),X1915) = hAPP_bool_bool(X1913,hAPP_f1664156314l_bool(X1914,X1915)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op]) ).
fof(i_0_956,plain,
! [X1892,X1893,X1894] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(X1892,X1893),X1894) = hAPP_bool_bool(X1892,hAPP_fun_a_bool_bool(X1893,X1894)),
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_957,plain,
! [X1871,X1872,X1873] : hAPP_nat_bool(cOMBB_bool_bool_nat(X1871,X1872),X1873) = hAPP_bool_bool(X1871,hAPP_nat_bool(X1872,X1873)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U]) ).
fof(i_0_958,plain,
! [X1889,X1890,X1891] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(X1889,X1890),X1891) = hAPP_a_fun_a_bool(X1889,hAPP_pname_a(X1890,X1891)),
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_959,plain,
! [X1877,X1878,X1879] : hAPP_pname_bool(cOMBB_647938656_pname(X1877,X1878),X1879) = hAPP_bool_bool(X1877,hAPP_pname_bool(X1878,X1879)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U]) ).
fof(i_0_960,plain,
! [X1851,X1852,X1853] : hAPP_a_bool(cOMBB_bool_bool_a(X1851,X1852),X1853) = hAPP_bool_bool(X1851,hAPP_a_bool(X1852,X1853)),
inference(variable_rename,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U]) ).
fof(i_0_961,plain,
! [X1862,X1863] :
( X1862 != X1863
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1862),X1863)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T]) ).
fof(i_0_962,plain,
! [X1677,X1678] :
( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1677),X1678))
| X1677 != X1678 )
& ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1678),X1677))
| X1677 != X1678 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_589])])]) ).
fof(i_0_963,plain,
! [X1629,X1630] :
( X1629 != X1630
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1629),X1630)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_231_equalityD1])]) ).
fof(i_0_964,plain,
! [X1635,X1636] :
( X1635 != X1636
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1636),X1635)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_234_equalityD2])]) ).
fof(i_0_965,plain,
! [X1866,X1867] :
( X1866 != X1867
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1866),X1867)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T]) ).
fof(i_0_966,plain,
! [X1679,X1680] :
( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1679),X1680))
| X1679 != X1680 )
& ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1680),X1679))
| X1679 != X1680 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_590])])]) ).
fof(i_0_967,plain,
! [X1631,X1632] :
( X1631 != X1632
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1631),X1632)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_232_equalityD1])]) ).
fof(i_0_968,plain,
! [X1637,X1638] :
( X1637 != X1638
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1638),X1637)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_235_equalityD2])]) ).
fof(i_0_969,plain,
! [X1849,X1850] :
( X1849 != X1850
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1849),X1850)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T]) ).
fof(i_0_970,plain,
! [X1681,X1682] :
( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1681),X1682))
| X1681 != X1682 )
& ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1682),X1681))
| X1681 != X1682 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_591])])]) ).
fof(i_0_971,plain,
! [X1633,X1634] :
( X1633 != X1634
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1633),X1634)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_233_equalityD1])]) ).
fof(i_0_972,plain,
! [X1639,X1640] :
( X1639 != X1640
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1640),X1639)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_236_equalityD2])]) ).
fof(i_0_973,plain,
! [X1838,X1839] :
( X1838 != X1839
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1838),X1839)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__Nat__Onat_T]) ).
fof(i_0_974,plain,
! [X1377,X1378] :
( X1377 != X1378
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1377),X1378)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_125_eq__imp__le])]) ).
fof(i_0_975,plain,
! [X1842,X1843] :
( X1842 != X1843
| hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1842),X1843)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000tc__Com__Opname_T]) ).
fof(i_0_976,plain,
! [X1834,X1835] :
( X1834 != X1835
| hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1834),X1835)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_000t__a_T]) ).
fof(i_0_977,plain,
! [X1802] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1802),X1802)),
inference(variable_rename,[status(thm)],[fact_295_order__refl]) ).
fof(i_0_978,plain,
! [X1620] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1620),X1620)),
inference(variable_rename,[status(thm)],[fact_225_subset__refl]) ).
fof(i_0_979,plain,
! [X1803] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1803),X1803)),
inference(variable_rename,[status(thm)],[fact_296_order__refl]) ).
fof(i_0_980,plain,
! [X1621] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1621),X1621)),
inference(variable_rename,[status(thm)],[fact_226_subset__refl]) ).
fof(i_0_981,plain,
! [X1805] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1805),X1805)),
inference(variable_rename,[status(thm)],[fact_298_order__refl]) ).
fof(i_0_982,plain,
! [X1622] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1622),X1622)),
inference(variable_rename,[status(thm)],[fact_227_subset__refl]) ).
fof(i_0_983,plain,
! [X1804] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1804),X1804)),
inference(variable_rename,[status(thm)],[fact_297_order__refl]) ).
fof(i_0_984,plain,
! [X1381] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1381),X1381)),
inference(variable_rename,[status(thm)],[fact_127_le__refl]) ).
cnf(i_0_985,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_592]) ).
fof(i_0_986,plain,
! [X1812] :
( ~ hBOOL(hAPP_bool_bool(fNot,X1812))
| ~ hBOOL(X1812) ),
inference(variable_rename,[status(thm)],[i_0_593]) ).
fof(i_0_987,hypothesis,
! [X1108,X1109] :
( ~ is_fun1661590463l_bool(X1108)
| ~ is_fun_pname_bool(X1109)
| is_bool(hAPP_f1664156314l_bool(X1108,X1109)) ),
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_988,hypothesis,
! [X1102,X1103] :
( ~ is_fun949378684l_bool(X1102)
| ~ is_fun_a_bool(X1103)
| is_bool(hAPP_fun_a_bool_bool(X1102,X1103)) ),
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_989,plain,
! [X1086,X1087] :
( ~ is_fun_pname_bool(X1086)
| ~ is_pname(X1087)
| is_bool(hAPP_pname_bool(X1086,X1087)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool])]) ).
fof(i_0_990,plain,
! [X1076,X1077] :
( ~ is_fun_a_bool(X1076)
| ~ is_a(X1077)
| is_bool(hAPP_a_bool(X1076,X1077)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__HOL__Obool])]) ).
fof(i_0_991,plain,
! [X1368,X1369] :
( ( hAPP_nat_nat(suc,X1368) != hAPP_nat_nat(suc,X1369)
| X1368 = X1369 )
& ( X1368 != X1369
| hAPP_nat_nat(suc,X1368) = hAPP_nat_nat(suc,X1369) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_120_nat_Oinject])]) ).
fof(i_0_992,plain,
! [X1366,X1367] :
( hAPP_nat_nat(suc,X1366) != hAPP_nat_nat(suc,X1367)
| X1366 = X1367 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_119_Suc__inject])]) ).
fof(i_0_993,plain,
! [X1120,X1121] :
( ~ is_fun1661590463l_bool(X1121)
| is_bool(hAPP_f1935102916l_bool(X1120,X1121)) ),
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_994,plain,
! [X1116,X1117] :
( ~ is_fun949378684l_bool(X1117)
| is_bool(hAPP_f621171935l_bool(X1116,X1117)) ),
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_995,plain,
! [X1094,X1095] :
( ~ is_bool(X1095)
| is_bool(hAPP_bool_bool(X1094,X1095)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool])]) ).
fof(i_0_996,hypothesis,
! [X1084,X1085] :
( ~ is_pname(X1085)
| is_a(hAPP_pname_a(X1084,X1085)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000t__a])]) ).
fof(i_0_997,plain,
! [X1122,X1123] :
( ~ is_fun1661590463l_bool(X1123)
| is_fun1661590463l_bool(hAPP_f559147733l_bool(X1122,X1123)) ),
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_005])]) ).
fof(i_0_998,plain,
! [X1112,X1113] :
( ~ is_fun_pname_bool(X1113)
| is_fun1661590463l_bool(hAPP_f434788991l_bool(X1112,X1113)) ),
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_999,hypothesis,
! [X1092,X1093] :
( ~ is_pname(X1093)
| is_fun1661590463l_bool(hAPP_p338031245l_bool(X1092,X1093)) ),
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_1000,plain,
! [X1034,X1035] :
( ~ is_fun_pname_bool(X1035)
| is_fun1661590463l_bool(image_47868345e_bool(X1034,X1035)) ),
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_1001,plain,
! [X1018,X1019] :
( ~ is_fun1661590463l_bool(X1019)
| is_fun1661590463l_bool(cOMBS_350070575l_bool(X1018,X1019)) ),
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_1002,plain,
! [X1010,X1011] :
( ~ is_fun1661590463l_bool(X1011)
| is_fun1661590463l_bool(cOMBB_307249310e_bool(X1010,X1011)) ),
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_1003,plain,
! [X1118,X1119] :
( ~ is_fun949378684l_bool(X1119)
| is_fun949378684l_bool(hAPP_f2117159681l_bool(X1118,X1119)) ),
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___004])]) ).
fof(i_0_1004,hypothesis,
! [X1106,X1107] :
( ~ is_fun_a_bool(X1107)
| is_fun949378684l_bool(hAPP_f1631501043l_bool(X1106,X1107)) ),
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_1005,hypothesis,
! [X1082,X1083] :
( ~ is_a(X1083)
| is_fun949378684l_bool(hAPP_a85458249l_bool(X1082,X1083)) ),
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_1006,plain,
! [X1032,X1033] :
( ~ is_fun_pname_bool(X1033)
| is_fun949378684l_bool(image_112932426a_bool(X1032,X1033)) ),
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_1007,plain,
! [X1016,X1017] :
( ~ is_fun949378684l_bool(X1017)
| is_fun949378684l_bool(cOMBS_1035972772l_bool(X1016,X1017)) ),
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_1008,plain,
! [X1008,X1009] :
( ~ is_fun949378684l_bool(X1009)
| is_fun949378684l_bool(cOMBB_2140588453a_bool(X1008,X1009)) ),
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_1009,plain,
! [X1110,X1111] :
( ~ is_fun_pname_bool(X1111)
| is_fun_pname_bool(hAPP_f759274231e_bool(X1110,X1111)) ),
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_1010,plain,
! [X1090,X1091] :
( ~ is_pname(X1091)
| is_fun_pname_bool(hAPP_p61793385e_bool(X1090,X1091)) ),
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_1011,plain,
! [X1080,X1081] :
( ~ is_a(X1081)
| is_fun_pname_bool(hAPP_a93125764e_bool(X1080,X1081)) ),
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_1012,plain,
! [X1050,X1051] :
( ~ is_fun1661590463l_bool(X1051)
| is_fun_pname_bool(image_1283814551_pname(X1050,X1051)) ),
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_1013,plain,
! [X1046,X1047] :
( ~ is_fun949378684l_bool(X1047)
| is_fun_pname_bool(image_1854862208_pname(X1046,X1047)) ),
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_1014,plain,
! [X1030,X1031] :
( ~ is_fun_pname_bool(X1031)
| is_fun_pname_bool(image_pname_pname(X1030,X1031)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname])]) ).
fof(i_0_1015,plain,
! [X1026,X1027] :
( ~ is_fun_a_bool(X1027)
| is_fun_pname_bool(image_a_pname(X1026,X1027)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000t__a_000tc__Com__Opname])]) ).
fof(i_0_1016,plain,
! [X1014,X1015] :
( ~ is_fun_pname_bool(X1015)
| is_fun_pname_bool(cOMBS_568398431l_bool(X1014,X1015)) ),
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_1017,plain,
! [X1006,X1007] :
( ~ is_fun_pname_bool(X1007)
| is_fun_pname_bool(cOMBB_647938656_pname(X1006,X1007)) ),
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_1018,plain,
! [X1104,X1105] :
( ~ is_fun_a_bool(X1105)
| is_fun_a_bool(hAPP_f2050579477a_bool(X1104,X1105)) ),
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_1019,plain,
! [X1088,X1089] :
( ~ is_pname(X1089)
| is_fun_a_bool(hAPP_p1534023578a_bool(X1088,X1089)) ),
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_1020,plain,
! [X1078,X1079] :
( ~ is_a(X1079)
| is_fun_a_bool(hAPP_a_fun_a_bool(X1078,X1079)) ),
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_1021,plain,
! [X1048,X1049] :
( ~ is_fun1661590463l_bool(X1049)
| is_fun_a_bool(image_876012084bool_a(X1048,X1049)) ),
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_1022,plain,
! [X1044,X1045] :
( ~ is_fun949378684l_bool(X1045)
| is_fun_a_bool(image_fun_a_bool_a(X1044,X1045)) ),
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_1023,hypothesis,
! [X1028,X1029] :
( ~ is_fun_pname_bool(X1029)
| is_fun_a_bool(image_pname_a(X1028,X1029)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000t__a])]) ).
fof(i_0_1024,plain,
! [X1024,X1025] :
( ~ is_fun_a_bool(X1025)
| is_fun_a_bool(image_a_a(X1024,X1025)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000t__a_000t__a])]) ).
fof(i_0_1025,plain,
! [X1012,X1013] :
( ~ is_fun_a_bool(X1013)
| is_fun_a_bool(cOMBS_a_bool_bool(X1012,X1013)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool])]) ).
fof(i_0_1026,plain,
! [X1004,X1005] :
( ~ is_fun_a_bool(X1005)
| is_fun_a_bool(cOMBB_bool_bool_a(X1004,X1005)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a])]) ).
fof(i_0_1027,plain,
! [X1813] :
( hBOOL(X1813)
| hBOOL(hAPP_bool_bool(fNot,X1813)) ),
inference(variable_rename,[status(thm)],[help_fNot_2_1_U]) ).
fof(i_0_1028,plain,
! [X1136,X1137] : is_bool(hAPP_f1295398978l_bool(X1136,X1137)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).
fof(i_0_1029,plain,
! [X1134,X1135] : is_bool(hAPP_f595608956l_bool(X1134,X1135)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo]) ).
fof(i_0_1030,plain,
! [X1132,X1133] : is_bool(hAPP_f1363661463l_bool(X1132,X1133)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HO]) ).
fof(i_0_1031,plain,
! [X1130,X1131] : is_bool(hAPP_f937997336l_bool(X1130,X1131)),
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_1032,plain,
! [X1128,X1129] : is_bool(hAPP_f389811538l_bool(X1128,X1129)),
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_1033,plain,
! [X1126,X1127] : is_bool(hAPP_f292226953l_bool(X1126,X1127)),
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_1034,plain,
! [X1124,X1125] : is_bool(hAPP_f1637334154l_bool(X1124,X1125)),
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_1035,plain,
! [X1114,X1115] : is_bool(hAPP_f54304608l_bool(X1114,X1115)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).
fof(i_0_1036,hypothesis,
! [X1096,X1097] : is_bool(hAPP_nat_bool(X1096,X1097)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool]) ).
fof(i_0_1037,plain,
! [X1042,X1043] : is_fun1661590463l_bool(image_1655916159e_bool(X1042,X1043)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).
fof(i_0_1038,plain,
! [X1040,X1041] : is_fun949378684l_bool(image_nat_fun_a_bool(X1040,X1041)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).
fof(i_0_1039,plain,
! [X1100,X1101] : is_fun_pname_bool(hAPP_n1025906991e_bool(X1100,X1101)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).
fof(i_0_1040,plain,
! [X1066,X1067] : is_fun_pname_bool(image_1604018183_pname(X1066,X1067)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL___003]) ).
fof(i_0_1041,plain,
! [X1062,X1063] : is_fun_pname_bool(image_1705983821_pname(X1062,X1063)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL_002]) ).
fof(i_0_1042,plain,
! [X1058,X1059] : is_fun_pname_bool(image_990671762_pname(X1058,X1059)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0_001]) ).
fof(i_0_1043,plain,
! [X1054,X1055] : is_fun_pname_bool(image_1921560913_pname(X1054,X1055)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname]) ).
fof(i_0_1044,plain,
! [X1038,X1039] : is_fun_pname_bool(image_nat_pname(X1038,X1039)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname]) ).
fof(i_0_1045,plain,
! [X1098,X1099] : is_fun_a_bool(hAPP_nat_fun_a_bool(X1098,X1099)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).
fof(i_0_1046,plain,
! [X1064,X1065] : is_fun_a_bool(image_526090948bool_a(X1064,X1065)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__]) ).
fof(i_0_1047,plain,
! [X1060,X1061] : is_fun_a_bool(image_349102846bool_a(X1060,X1061)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL]) ).
fof(i_0_1048,plain,
! [X1056,X1057] : is_fun_a_bool(image_573985017bool_a(X1056,X1057)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0]) ).
fof(i_0_1049,plain,
! [X1052,X1053] : is_fun_a_bool(image_fun_nat_bool_a(X1052,X1053)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a]) ).
fof(i_0_1050,plain,
! [X1036,X1037] : is_fun_a_bool(image_nat_a(X1036,X1037)),
inference(variable_rename,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a]) ).
fof(i_0_1051,plain,
! [X1370] : hAPP_nat_nat(suc,X1370) != X1370,
inference(variable_rename,[status(thm)],[fact_121_Suc__n__not__n]) ).
fof(i_0_1052,plain,
! [X1371] : X1371 != hAPP_nat_nat(suc,X1371),
inference(variable_rename,[status(thm)],[fact_122_n__not__Suc__n]) ).
fof(i_0_1053,plain,
! [X1023] :
( ~ is_fun1661590463l_bool(X1023)
| is_fun1661590463l_bool(collec1974731493e_bool(X1023)) ),
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_1054,plain,
! [X1138] :
( ~ is_fun_a_bool(X1138)
| is_fun949378684l_bool(p(X1138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_v_P])]) ).
fof(i_0_1055,plain,
! [X1022] :
( ~ is_fun949378684l_bool(X1022)
| is_fun949378684l_bool(collect_fun_a_bool(X1022)) ),
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_1056,plain,
! [X1021] :
( ~ is_fun_pname_bool(X1021)
| is_fun_pname_bool(collect_pname(X1021)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000tc__Com__Opname])]) ).
fof(i_0_1057,plain,
! [X1020] :
( ~ is_fun_a_bool(X1020)
| is_fun_a_bool(collect_a(X1020)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000t__a])]) ).
fof(i_0_1058,plain,
! [X1691] :
( ~ is_fun1661590463l_bool(X1691)
| collec1974731493e_bool(X1691) = X1691 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_257_Collect__def])]) ).
fof(i_0_1059,plain,
! [X1692] :
( ~ is_fun949378684l_bool(X1692)
| collect_fun_a_bool(X1692) = X1692 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_258_Collect__def])]) ).
fof(i_0_1060,plain,
! [X1689] :
( ~ is_fun_pname_bool(X1689)
| collect_pname(X1689) = X1689 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_255_Collect__def])]) ).
cnf(i_0_1061,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_594,c_0_595]),
[final] ).
cnf(i_0_1062,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,esk6_2(X2,X1)))))))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(X2,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_596]),
[final] ).
cnf(i_0_1063,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_597,c_0_598]),c_0_598]),c_0_598]),c_0_598]),
[final] ).
cnf(i_0_1064,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_599,c_0_595]),c_0_595]),c_0_595]),c_0_595]),
[final] ).
cnf(i_0_1065,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_600,c_0_598]),
[final] ).
cnf(i_0_1066,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_601,c_0_598]),
[final] ).
cnf(i_0_1067,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_602,c_0_595]),
[final] ).
cnf(i_0_1068,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_603,c_0_595]),
[final] ).
cnf(i_0_1069,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,esk2_3(X2,X3,X1))),hAPP_n1699378549t_bool(X1,hAPP_nat_nat(suc,esk2_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_604]),
[final] ).
cnf(i_0_1070,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,esk3_3(X2,X3,X1))),hAPP_n1025906991e_bool(X1,hAPP_nat_nat(suc,esk3_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_605]),
[final] ).
cnf(i_0_1071,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,esk5_3(X2,X3,X1))),hAPP_nat_fun_a_bool(X1,hAPP_nat_nat(suc,esk5_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_606]),
[final] ).
cnf(i_0_1072,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,esk4_3(X2,X3,X1))),hAPP_nat_nat(X1,hAPP_nat_nat(suc,esk4_3(X2,X3,X1)))))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_607]),
[final] ).
cnf(i_0_1073,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_608,c_0_598]),c_0_598]),
[final] ).
cnf(i_0_1074,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_609,c_0_595]),c_0_595]),
[final] ).
cnf(i_0_1075,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_610,c_0_598]),c_0_598]),c_0_598]),
[final] ).
cnf(i_0_1076,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_611,c_0_595]),c_0_595]),c_0_595]),
[final] ).
cnf(i_0_1077,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_612,c_0_598]),
[final] ).
cnf(i_0_1078,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_613,c_0_595]),
[final] ).
cnf(i_0_1079,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_614,c_0_615]),
[final] ).
cnf(i_0_1080,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_616,c_0_617]),
[final] ).
cnf(i_0_1081,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_618,c_0_595]),
[final] ).
cnf(i_0_1082,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_619,c_0_598]),
[final] ).
cnf(i_0_1083,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_620,c_0_598]),
[final] ).
cnf(i_0_1084,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_621,c_0_595]),
[final] ).
cnf(i_0_1085,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_622,c_0_598]),
[final] ).
cnf(i_0_1086,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_623,c_0_598]),
[final] ).
cnf(i_0_1087,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_624,c_0_595]),
[final] ).
cnf(i_0_1088,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_625,c_0_595]),
[final] ).
cnf(i_0_1089,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_626,c_0_627]),
[final] ).
cnf(i_0_1090,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_628,c_0_627]),
[final] ).
cnf(i_0_1091,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,esk15_3(X1,X2,X3))),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_629]),
[final] ).
cnf(i_0_1092,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_630,c_0_627]),c_0_627]),
[final] ).
cnf(i_0_1093,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_631,c_0_598]),
[final] ).
cnf(i_0_1094,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_632,c_0_595]),
[final] ).
cnf(i_0_1095,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_633,c_0_617]),
[final] ).
cnf(i_0_1096,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_634,c_0_615]),
[final] ).
cnf(i_0_1097,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_635,c_0_598]),
[final] ).
cnf(i_0_1098,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_636,c_0_595]),
[final] ).
cnf(i_0_1099,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_637,c_0_627]),
[final] ).
cnf(i_0_1100,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_638,c_0_598]),
[final] ).
cnf(i_0_1101,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_639,c_0_595]),
[final] ).
cnf(i_0_1102,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_640,c_0_627]),c_0_627]),c_0_627]),c_0_627]),
[final] ).
cnf(i_0_1103,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_641,c_0_642]),
[final] ).
cnf(i_0_1104,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_643,c_0_627]),
[final] ).
cnf(i_0_1105,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_644,c_0_598]),
[final] ).
cnf(i_0_1106,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_645,c_0_595]),
[final] ).
cnf(i_0_1107,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_646,c_0_598]),
[final] ).
cnf(i_0_1108,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_647,c_0_598]),
[final] ).
cnf(i_0_1109,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_648,c_0_598]),
[final] ).
cnf(i_0_1110,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_649,c_0_595]),
[final] ).
cnf(i_0_1111,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_650,c_0_595]),
[final] ).
cnf(i_0_1112,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_651,c_0_595]),
[final] ).
cnf(i_0_1113,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_652,c_0_598]),
[final] ).
cnf(i_0_1114,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_653,c_0_595]),
[final] ).
cnf(i_0_1115,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_654,c_0_598]),
[final] ).
cnf(i_0_1116,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_655,c_0_595]),
[final] ).
cnf(i_0_1117,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_656,c_0_598]),
[final] ).
cnf(i_0_1118,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_657,c_0_595]),
[final] ).
cnf(i_0_1119,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_658,c_0_598]),
[final] ).
cnf(i_0_1120,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_659,c_0_598]),
[final] ).
cnf(i_0_1121,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_660,c_0_595]),
[final] ).
cnf(i_0_1122,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_661,c_0_595]),
[final] ).
cnf(i_0_1123,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_662,c_0_617]),
[final] ).
cnf(i_0_1124,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_663,c_0_617]),
[final] ).
cnf(i_0_1125,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_664,c_0_615]),
[final] ).
cnf(i_0_1126,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_665,c_0_615]),
[final] ).
cnf(i_0_1127,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_666,c_0_598]),
[final] ).
cnf(i_0_1128,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_667,c_0_598]),
[final] ).
cnf(i_0_1129,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_668,c_0_595]),
[final] ).
cnf(i_0_1130,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_669,c_0_595]),
[final] ).
cnf(i_0_1131,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_670,c_0_595]),c_0_598]),
[final] ).
cnf(i_0_1132,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_671,c_0_598]),
[final] ).
cnf(i_0_1133,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_672,c_0_595]),
[final] ).
cnf(i_0_1134,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_673,c_0_627]),
[final] ).
cnf(i_0_1135,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_674,c_0_627]),
[final] ).
cnf(i_0_1136,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_675,c_0_627]),
[final] ).
cnf(i_0_1137,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_676,c_0_598]),c_0_598]),
[final] ).
cnf(i_0_1138,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_677,c_0_595]),c_0_595]),
[final] ).
cnf(i_0_1139,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_678,c_0_627]),
[final] ).
cnf(i_0_1140,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_679,c_0_642]),
[final] ).
cnf(i_0_1141,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_680,c_0_627]),
[final] ).
cnf(i_0_1142,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_681,c_0_627]),
[final] ).
cnf(i_0_1143,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_682]),
[final] ).
cnf(i_0_1144,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_683,c_0_627]),c_0_627]),c_0_627]),
[final] ).
cnf(i_0_1145,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk1_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_684]),
[final] ).
cnf(i_0_1146,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_685,c_0_627]),
[final] ).
cnf(i_0_1147,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_686,c_0_627]),
[final] ).
cnf(i_0_1148,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_687,c_0_627]),
[final] ).
cnf(i_0_1149,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_688,c_0_627]),
[final] ).
cnf(i_0_1150,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_689,c_0_615]),
[final] ).
cnf(i_0_1151,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_690,c_0_617]),
[final] ).
cnf(i_0_1152,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_691,c_0_595]),
[final] ).
cnf(i_0_1153,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_692,c_0_598]),
[final] ).
cnf(i_0_1154,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_693,c_0_617]),
[final] ).
cnf(i_0_1155,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_694,c_0_615]),
[final] ).
cnf(i_0_1156,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_695,c_0_598]),
[final] ).
cnf(i_0_1157,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_696,c_0_595]),
[final] ).
cnf(i_0_1158,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_697,c_0_595]),
[final] ).
cnf(i_0_1159,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,esk8_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_698]),
[final] ).
cnf(i_0_1160,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk9_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_699]),
[final] ).
cnf(i_0_1161,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk7_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_700]),
[final] ).
cnf(i_0_1162,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_701,c_0_615]),
[final] ).
cnf(i_0_1163,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_702,c_0_615]),
[final] ).
cnf(i_0_1164,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_703,c_0_617]),
[final] ).
cnf(i_0_1165,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_704,c_0_617]),
[final] ).
cnf(i_0_1166,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_705,c_0_595]),
[final] ).
cnf(i_0_1167,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_706,c_0_595]),
[final] ).
cnf(i_0_1168,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_707,c_0_598]),
[final] ).
cnf(i_0_1169,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_708,c_0_598]),
[final] ).
cnf(i_0_1170,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk15_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_629]),
[final] ).
cnf(i_0_1171,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_682]),
[final] ).
cnf(i_0_1172,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(suc,esk13_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_709]),
[final] ).
cnf(i_0_1173,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_710,c_0_627]),
[final] ).
cnf(i_0_1174,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_711,c_0_627]),
[final] ).
cnf(i_0_1175,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_712,c_0_627]),
[final] ).
cnf(i_0_1176,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_713,c_0_627]),
[final] ).
cnf(i_0_1177,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_714,c_0_627]),
[final] ).
cnf(i_0_1178,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_715,c_0_642]),
[final] ).
cnf(i_0_1179,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_716,c_0_642]),
[final] ).
cnf(i_0_1180,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_717,c_0_627]),
[final] ).
cnf(i_0_1181,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_718,c_0_627]),
[final] ).
cnf(i_0_1182,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_719,c_0_627]),c_0_627]),
[final] ).
cnf(i_0_1183,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_720,c_0_627]),
[final] ).
cnf(i_0_1184,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_721,c_0_617]),
[final] ).
cnf(i_0_1185,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_722,c_0_615]),
[final] ).
cnf(i_0_1186,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_723,c_0_598]),
[final] ).
cnf(i_0_1187,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_724,c_0_595]),
[final] ).
cnf(i_0_1188,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_725]),
[final] ).
cnf(i_0_1189,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_725]),
[final] ).
cnf(i_0_1190,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_726]),
[final] ).
cnf(i_0_1191,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_726]),
[final] ).
cnf(i_0_1192,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_727]),
[final] ).
cnf(i_0_1193,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_727]),
[final] ).
cnf(i_0_1194,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_728]),
[final] ).
cnf(i_0_1195,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_728]),
[final] ).
cnf(i_0_1196,plain,
( hBOOL(hAPP_nat_bool(X1,hAPP_nat_nat(minus_minus_nat(X3),X2)))
| ~ hBOOL(hAPP_nat_bool(X1,esk13_3(X2,X1,X3)))
| ~ hBOOL(hAPP_nat_bool(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_709]),
[final] ).
cnf(i_0_1197,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_729]),
[final] ).
cnf(i_0_1198,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_730]),
[final] ).
cnf(i_0_1199,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_731]),
[final] ).
cnf(i_0_1200,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_732]),
[final] ).
cnf(i_0_1201,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_733]),
[final] ).
cnf(i_0_1202,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_734]),
[final] ).
cnf(i_0_1203,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,esk1_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_684]),
[final] ).
cnf(i_0_1204,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(X2,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_735]),
[final] ).
cnf(i_0_1205,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(X2,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_736]),
[final] ).
cnf(i_0_1206,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(X2,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_737]),
[final] ).
cnf(i_0_1207,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(X2,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_738]),
[final] ).
cnf(i_0_1208,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(X2,X1))),hAPP_f921600141ol_nat(finite_card_pname,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_739]),
[final] ).
cnf(i_0_1209,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(X2,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_740]),
[final] ).
cnf(i_0_1210,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(X2,X1))),hAPP_f1690079119ol_nat(finite1352710292l_bool,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_741]),
[final] ).
cnf(i_0_1211,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(X2,X1))),hAPP_f98387925ol_nat(finite269641166l_bool,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_742]),
[final] ).
cnf(i_0_1212,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(X2,X1))),hAPP_f1253658590ol_nat(finite1659325229l_bool,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_743]),
[final] ).
cnf(i_0_1213,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_744]),
[final] ).
cnf(i_0_1214,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_745]),
[final] ).
cnf(i_0_1215,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_746]),
[final] ).
cnf(i_0_1216,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(X2,X1))),hAPP_f22106695ol_nat(finite_card_nat,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_747]),
[final] ).
cnf(i_0_1217,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_748]),
[final] ).
cnf(i_0_1218,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_749]),
[final] ).
cnf(i_0_1219,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(X2,X1))),hAPP_f696928925ol_nat(finite346522414t_bool,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_750]),
[final] ).
cnf(i_0_1220,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(X2,X1))),hAPP_f55526627ol_nat(finite1340463720e_bool,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_751]),
[final] ).
cnf(i_0_1221,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(X2,X1))),hAPP_f2009550088ol_nat(finite1306199131a_bool,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_752]),
[final] ).
cnf(i_0_1222,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_753]),
[final] ).
cnf(i_0_1223,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_754]),
[final] ).
cnf(i_0_1224,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_755]),
[final] ).
cnf(i_0_1225,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_756]),
[final] ).
cnf(i_0_1226,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_757]),
[final] ).
cnf(i_0_1227,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_758]),
[final] ).
cnf(i_0_1228,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_759]),
[final] ).
cnf(i_0_1229,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_760]),
[final] ).
cnf(i_0_1230,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_761,c_0_642]),
[final] ).
cnf(i_0_1231,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_762,c_0_627]),
[final] ).
cnf(i_0_1232,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_725]),
[final] ).
cnf(i_0_1233,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_726]),
[final] ).
cnf(i_0_1234,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_727]),
[final] ).
cnf(i_0_1235,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_728]),
[final] ).
cnf(i_0_1236,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_763,c_0_642]),
[final] ).
cnf(i_0_1237,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_764,c_0_642]),
[final] ).
cnf(i_0_1238,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_765,c_0_627]),
[final] ).
cnf(i_0_1239,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_766,c_0_627]),
[final] ).
cnf(i_0_1240,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_767]),
[final] ).
cnf(i_0_1241,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_768]),
[final] ).
cnf(i_0_1242,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_769]),
[final] ).
cnf(i_0_1243,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_770]),
[final] ).
cnf(i_0_1244,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_771,c_0_598]),
[final] ).
cnf(i_0_1245,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_772,c_0_595]),
[final] ).
cnf(i_0_1246,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_773]),
[final] ).
cnf(i_0_1247,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_774]),
[final] ).
cnf(i_0_1248,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_774]),
[final] ).
cnf(i_0_1249,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_775]),
[final] ).
cnf(i_0_1250,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_775]),
[final] ).
cnf(i_0_1251,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_776]),
[final] ).
cnf(i_0_1252,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_776]),
[final] ).
cnf(i_0_1253,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_777]),
[final] ).
cnf(i_0_1254,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_777]),
[final] ).
cnf(i_0_1255,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_778]),
[final] ).
cnf(i_0_1256,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_779]),
[final] ).
cnf(i_0_1257,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_780]),
[final] ).
cnf(i_0_1258,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_781]),
[final] ).
cnf(i_0_1259,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_782]),
[final] ).
cnf(i_0_1260,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_783]),
[final] ).
cnf(i_0_1261,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_784]),
[final] ).
cnf(i_0_1262,plain,
( X1 = image_pname_a(X2,esk1_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_684]),
[final] ).
cnf(i_0_1263,plain,
( is_fun_pname_bool(esk1_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_684]),
[final] ).
cnf(i_0_1264,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk10_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_785]),
[final] ).
cnf(i_0_1265,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk12_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_786]),
[final] ).
cnf(i_0_1266,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,esk11_2(X1,X2)),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_787]),
[final] ).
cnf(i_0_1267,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_788]),
[final] ).
cnf(i_0_1268,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_789]),
[final] ).
cnf(i_0_1269,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_790,c_0_494]),c_0_494]),c_0_627]),
[final] ).
cnf(i_0_1270,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_791,c_0_505]),c_0_505]),c_0_642]),
[final] ).
cnf(i_0_1271,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_792]),
[final] ).
cnf(i_0_1272,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_769]),
[final] ).
cnf(i_0_1273,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk6_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_596]),
[final] ).
cnf(i_0_1274,plain,
( X1 = hAPP_pname_a(X2,esk9_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_699]),
[final] ).
cnf(i_0_1275,plain,
( X1 = hAPP_pname_a(X2,esk7_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_700]),
[final] ).
cnf(i_0_1276,plain,
( X1 = image_pname_a(X2,esk8_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_698]),
[final] ).
cnf(i_0_1277,plain,
( is_pname(esk9_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_699]),
[final] ).
cnf(i_0_1278,plain,
( is_pname(esk7_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_700]),
[final] ).
cnf(i_0_1279,plain,
( is_fun_pname_bool(esk8_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_698]),
[final] ).
cnf(i_0_1280,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_793]),
[final] ).
cnf(i_0_1281,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_794]),
[final] ).
cnf(i_0_1282,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_795]),
[final] ).
cnf(i_0_1283,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_796]),
[final] ).
cnf(i_0_1284,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_797]),
[final] ).
cnf(i_0_1285,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_798]),
[final] ).
cnf(i_0_1286,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_799]),
[final] ).
cnf(i_0_1287,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_800]),
[final] ).
cnf(i_0_1288,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_801]),
[final] ).
cnf(i_0_1289,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_802]),
[final] ).
cnf(i_0_1290,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_803]),
[final] ).
cnf(i_0_1291,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_804]),
[final] ).
cnf(i_0_1292,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_805]),
[final] ).
cnf(i_0_1293,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_806]),
[final] ).
cnf(i_0_1294,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_807]),
[final] ).
cnf(i_0_1295,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_808]),
[final] ).
cnf(i_0_1296,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,esk17_2(X1,X2)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_809]),
[final] ).
cnf(i_0_1297,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_810]),
[final] ).
cnf(i_0_1298,plain,
( X2 = hAPP_nat_nat(suc,esk14_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_811]),
[final] ).
cnf(i_0_1299,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_812,c_0_505]),c_0_505]),
[final] ).
cnf(i_0_1300,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_813,c_0_505]),c_0_505]),
[final] ).
cnf(i_0_1301,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_814,c_0_494]),c_0_494]),
[final] ).
cnf(i_0_1302,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_815,c_0_494]),c_0_494]),
[final] ).
cnf(i_0_1303,plain,
( is_pname(esk15_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_629]),
[final] ).
cnf(i_0_1304,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_698]),
[final] ).
cnf(i_0_1305,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_700]),
[final] ).
cnf(i_0_1306,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_816]),
[final] ).
cnf(i_0_1307,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_817]),
[final] ).
cnf(i_0_1308,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_1309,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_818]),
[final] ).
cnf(i_0_1310,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_819]),
[final] ).
cnf(i_0_1311,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_820]),
[final] ).
cnf(i_0_1312,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_821]),
[final] ).
cnf(i_0_1313,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_822,c_0_505]),c_0_505]),c_0_505]),
[final] ).
cnf(i_0_1314,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_823,c_0_494]),c_0_494]),c_0_494]),
[final] ).
cnf(i_0_1315,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_824]),
[final] ).
cnf(i_0_1316,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_825]),
[final] ).
cnf(i_0_1317,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_826]),
[final] ).
cnf(i_0_1318,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_827]),
[final] ).
cnf(i_0_1319,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk10_2(X1,X2)),X2))
| hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_785]),
[final] ).
cnf(i_0_1320,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,esk12_2(X1,X2)),X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_786]),
[final] ).
cnf(i_0_1321,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,esk11_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_787]),
[final] ).
cnf(i_0_1322,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_828,c_0_627]),
[final] ).
cnf(i_0_1323,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X2),esk16_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_809]),
[final] ).
cnf(i_0_1324,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_778]),
[final] ).
cnf(i_0_1325,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_829]),
[final] ).
cnf(i_0_1326,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_830]),
[final] ).
cnf(i_0_1327,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_831]),
[final] ).
cnf(i_0_1328,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_816]),
[final] ).
cnf(i_0_1329,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_832]),
[final] ).
cnf(i_0_1330,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_833]),
[final] ).
cnf(i_0_1331,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_834]),
[final] ).
cnf(i_0_1332,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_835]),
[final] ).
cnf(i_0_1333,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_836,c_0_505]),c_0_505]),
[final] ).
cnf(i_0_1334,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_837,c_0_505]),c_0_505]),
[final] ).
cnf(i_0_1335,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_838,c_0_494]),c_0_494]),
[final] ).
cnf(i_0_1336,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_839,c_0_494]),c_0_494]),
[final] ).
cnf(i_0_1337,plain,
( hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),X1))))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_840]),
[final] ).
cnf(i_0_1338,plain,
( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),X1))))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_841]),
[final] ).
cnf(i_0_1339,plain,
( hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),X1))))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_842]),
[final] ).
cnf(i_0_1340,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_843]),
[final] ).
cnf(i_0_1341,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_844]),
[final] ).
cnf(i_0_1342,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_845]),
[final] ).
cnf(i_0_1343,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_846]),
[final] ).
cnf(i_0_1344,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_847]),
[final] ).
cnf(i_0_1345,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,esk17_2(X1,X2)),X1))
| hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_809]),
[final] ).
cnf(i_0_1346,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_848]),
[final] ).
cnf(i_0_1347,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_849]),
[final] ).
cnf(i_0_1348,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_850]),
[final] ).
cnf(i_0_1349,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_851]),
[final] ).
cnf(i_0_1350,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_852]),
[final] ).
cnf(i_0_1351,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_853]),
[final] ).
cnf(i_0_1352,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_854]),
[final] ).
cnf(i_0_1353,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_855]),
[final] ).
cnf(i_0_1354,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_856]),
[final] ).
cnf(i_0_1355,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_857]),
[final] ).
cnf(i_0_1356,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_858]),
[final] ).
cnf(i_0_1357,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_859]),
[final] ).
cnf(i_0_1358,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_860]),
[final] ).
cnf(i_0_1359,plain,
( is_pname(esk6_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_596]),
[final] ).
cnf(i_0_1360,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_861]),
[final] ).
cnf(i_0_1361,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_1362,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_862]),
[final] ).
cnf(i_0_1363,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_863]),
[final] ).
cnf(i_0_1364,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_864]),
[final] ).
cnf(i_0_1365,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_865]),
[final] ).
cnf(i_0_1366,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_866]),
[final] ).
cnf(i_0_1367,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_816]),
[final] ).
cnf(i_0_1368,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_867]),
[final] ).
cnf(i_0_1369,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_868]),
[final] ).
cnf(i_0_1370,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_869]),
[final] ).
cnf(i_0_1371,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_870]),
[final] ).
cnf(i_0_1372,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_1373,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_1374,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_871,c_0_505]),
[final] ).
cnf(i_0_1375,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_872]),
[final] ).
cnf(i_0_1376,plain,
( hBOOL(X1)
| hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_873]),
[final] ).
cnf(i_0_1377,plain,
( hBOOL(X1)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_874]),
[final] ).
cnf(i_0_1378,plain,
( hBOOL(X2)
| ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_875]),
[final] ).
cnf(i_0_1379,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_864]),
[final] ).
cnf(i_0_1380,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_865]),
[final] ).
cnf(i_0_1381,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_866]),
[final] ).
cnf(i_0_1382,plain,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(X2,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_876]),
[final] ).
cnf(i_0_1383,plain,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_877]),
[final] ).
cnf(i_0_1384,plain,
( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_878]),
[final] ).
cnf(i_0_1385,plain,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(X2,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_879]),
[final] ).
cnf(i_0_1386,plain,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_880]),
[final] ).
cnf(i_0_1387,plain,
( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_881]),
[final] ).
cnf(i_0_1388,plain,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(X2,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_882]),
[final] ).
cnf(i_0_1389,plain,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_883]),
[final] ).
cnf(i_0_1390,plain,
( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_884]),
[final] ).
cnf(i_0_1391,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_885]),
[final] ).
cnf(i_0_1392,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_886]),
[final] ).
cnf(i_0_1393,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_887]),
[final] ).
cnf(i_0_1394,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_888]),
[final] ).
cnf(i_0_1395,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_889]),
[final] ).
cnf(i_0_1396,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_890]),
[final] ).
cnf(i_0_1397,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_891]),
[final] ).
cnf(i_0_1398,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_892]),
[final] ).
cnf(i_0_1399,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_893]),
[final] ).
cnf(i_0_1400,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_894]),
[final] ).
cnf(i_0_1401,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_895]),
[final] ).
cnf(i_0_1402,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(X2,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_896]),
[final] ).
cnf(i_0_1403,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(X2,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_897]),
[final] ).
cnf(i_0_1404,plain,
( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(X2,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_898]),
[final] ).
cnf(i_0_1405,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(X2,X1)))
| ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_899]),
[final] ).
cnf(i_0_1406,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(X2,X1)))
| ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_900]),
[final] ).
cnf(i_0_1407,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(X2,X1)))
| ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_901]),
[final] ).
cnf(i_0_1408,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_902]),
[final] ).
cnf(i_0_1409,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_903]),
[final] ).
cnf(i_0_1410,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_904]),
[final] ).
cnf(i_0_1411,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(X2,X1)))
| ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_905]),
[final] ).
cnf(i_0_1412,plain,
( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(X2,X1)))
| ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_906]),
[final] ).
cnf(i_0_1413,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_907]),
[final] ).
cnf(i_0_1414,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(X2,X1)))
| ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_908]),
[final] ).
cnf(i_0_1415,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(X2,X1)))
| ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_909]),
[final] ).
cnf(i_0_1416,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(X2,X1)))
| ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_910]),
[final] ).
cnf(i_0_1417,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_911]),
[final] ).
cnf(i_0_1418,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_912]),
[final] ).
cnf(i_0_1419,plain,
( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(X2,X1)))
| ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_913]),
[final] ).
cnf(i_0_1420,plain,
( X1 = X2
| ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_914]),
[final] ).
cnf(i_0_1421,plain,
( X1 = X2
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_915]),
[final] ).
cnf(i_0_1422,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_1423,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_916]),
[final] ).
cnf(i_0_1424,plain,
( is_pname(esk12_2(X1,X2))
| hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_786]),
[final] ).
cnf(i_0_1425,plain,
( is_a(esk11_2(X1,X2))
| hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_787]),
[final] ).
cnf(i_0_1426,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_917]),
[final] ).
cnf(i_0_1427,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_918]),
[final] ).
cnf(i_0_1428,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_919]),
[final] ).
cnf(i_0_1429,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_920]),
[final] ).
cnf(i_0_1430,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_921]),
[final] ).
cnf(i_0_1431,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_922]),
[final] ).
cnf(i_0_1432,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_824]),
[final] ).
cnf(i_0_1433,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_824]),
[final] ).
cnf(i_0_1434,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_826]),
[final] ).
cnf(i_0_1435,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_826]),
[final] ).
cnf(i_0_1436,plain,
hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(X1),X2),X3) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_923]),
[final] ).
cnf(i_0_1437,plain,
hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(X1),X2),X3) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_924]),
[final] ).
cnf(i_0_1438,plain,
hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(X1),X2),X3) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_925]),
[final] ).
cnf(i_0_1439,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_926]),
[final] ).
cnf(i_0_1440,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_927]),
[final] ).
cnf(i_0_1441,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_928]),
[final] ).
cnf(i_0_1442,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_929]),
[final] ).
cnf(i_0_1443,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_930]),
[final] ).
cnf(i_0_1444,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_931]),
[final] ).
cnf(i_0_1445,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_932]),
[final] ).
cnf(i_0_1446,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_933]),
[final] ).
cnf(i_0_1447,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_934]),
[final] ).
cnf(i_0_1448,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_935]),
[final] ).
cnf(i_0_1449,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_936]),
[final] ).
cnf(i_0_1450,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_937]),
[final] ).
cnf(i_0_1451,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_938]),
[final] ).
cnf(i_0_1452,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_939]),
[final] ).
cnf(i_0_1453,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_940]),
[final] ).
cnf(i_0_1454,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_941]),
[final] ).
cnf(i_0_1455,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_942,c_0_494]),
[final] ).
cnf(i_0_1456,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,X1),X2))
| ~ hBOOL(X1)
| ~ hBOOL(X2) ),
inference(split_conjunct,[status(thm)],[i_0_943]),
[final] ).
cnf(i_0_1457,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_944]),
[final] ).
cnf(i_0_1458,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X1),X2))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_945]),
[final] ).
cnf(i_0_1459,plain,
( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,X2),X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_946]),
[final] ).
cnf(i_0_1460,plain,
( hBOOL(X1)
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_947]),
[final] ).
cnf(i_0_1461,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_948]),
[final] ).
cnf(i_0_1462,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_949]),
[final] ).
cnf(i_0_1463,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_950]),
[final] ).
cnf(i_0_1464,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_951]),
[final] ).
cnf(i_0_1465,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_952]),
[final] ).
cnf(i_0_1466,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_953]),
[final] ).
cnf(i_0_1467,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_954]),
[final] ).
cnf(i_0_1468,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_955]),
[final] ).
cnf(i_0_1469,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_956]),
[final] ).
cnf(i_0_1470,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_957]),
[final] ).
cnf(i_0_1471,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_958]),
[final] ).
cnf(i_0_1472,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_959]),
[final] ).
cnf(i_0_1473,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_960]),
[final] ).
cnf(i_0_1474,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_961]),
[final] ).
cnf(i_0_1475,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_962]),
[final] ).
cnf(i_0_1476,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_962]),
[final] ).
cnf(i_0_1477,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_963]),
[final] ).
cnf(i_0_1478,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_829]),
[final] ).
cnf(i_0_1479,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_829]),
[final] ).
cnf(i_0_1480,plain,
( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_964]),
[final] ).
cnf(i_0_1481,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_965]),
[final] ).
cnf(i_0_1482,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_966]),
[final] ).
cnf(i_0_1483,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_966]),
[final] ).
cnf(i_0_1484,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_967]),
[final] ).
cnf(i_0_1485,plain,
( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_968]),
[final] ).
cnf(i_0_1486,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_969]),
[final] ).
cnf(i_0_1487,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_970]),
[final] ).
cnf(i_0_1488,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_970]),
[final] ).
cnf(i_0_1489,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_971]),
[final] ).
cnf(i_0_1490,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X2),X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_972]),
[final] ).
cnf(i_0_1491,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_973]),
[final] ).
cnf(i_0_1492,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_974]),
[final] ).
cnf(i_0_1493,plain,
( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_975]),
[final] ).
cnf(i_0_1494,plain,
( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_976]),
[final] ).
cnf(i_0_1495,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_977]),
[final] ).
cnf(i_0_1496,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_978]),
[final] ).
cnf(i_0_1497,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_979]),
[final] ).
cnf(i_0_1498,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_980]),
[final] ).
cnf(i_0_1499,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_981]),
[final] ).
cnf(i_0_1500,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_982]),
[final] ).
cnf(i_0_1501,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_983]),
[final] ).
cnf(i_0_1502,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(split_conjunct,[status(thm)],[i_0_984]),
[final] ).
cnf(i_0_1503,hypothesis,
hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
inference(split_conjunct,[status(thm)],[conj_4]),
[final] ).
cnf(i_0_1504,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_985,c_0_494]),
[final] ).
cnf(i_0_1505,plain,
( ~ hBOOL(hAPP_bool_bool(fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[i_0_986]),
[final] ).
cnf(i_0_1506,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_1507,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_1508,hypothesis,
( is_bool(hAPP_f1664156314l_bool(X1,X2))
| ~ is_fun1661590463l_bool(X1)
| ~ is_fun_pname_bool(X2) ),
inference(split_conjunct,[status(thm)],[i_0_987]),
[final] ).
cnf(i_0_1509,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_988]),
[final] ).
cnf(i_0_1510,plain,
( is_bool(hAPP_pname_bool(X1,X2))
| ~ is_fun_pname_bool(X1)
| ~ is_pname(X2) ),
inference(split_conjunct,[status(thm)],[i_0_989]),
[final] ).
cnf(i_0_1511,plain,
( is_bool(hAPP_a_bool(X1,X2))
| ~ is_fun_a_bool(X1)
| ~ is_a(X2) ),
inference(split_conjunct,[status(thm)],[i_0_990]),
[final] ).
cnf(i_0_1512,plain,
( X1 = X2
| hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_991]),
[final] ).
cnf(i_0_1513,plain,
( X1 = X2
| hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2) ),
inference(split_conjunct,[status(thm)],[i_0_992]),
[final] ).
cnf(i_0_1514,plain,
( is_bool(hAPP_f1935102916l_bool(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_993]),
[final] ).
cnf(i_0_1515,plain,
( is_bool(hAPP_f621171935l_bool(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_994]),
[final] ).
cnf(i_0_1516,plain,
( is_bool(hAPP_bool_bool(X2,X1))
| ~ is_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_995]),
[final] ).
cnf(i_0_1517,hypothesis,
( is_a(hAPP_pname_a(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_996]),
[final] ).
cnf(i_0_1518,plain,
( is_fun1661590463l_bool(hAPP_f559147733l_bool(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_997]),
[final] ).
cnf(i_0_1519,plain,
( is_fun1661590463l_bool(hAPP_f434788991l_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_998]),
[final] ).
cnf(i_0_1520,hypothesis,
( is_fun1661590463l_bool(hAPP_p338031245l_bool(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_999]),
[final] ).
cnf(i_0_1521,plain,
( is_fun1661590463l_bool(image_47868345e_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1000]),
[final] ).
cnf(i_0_1522,plain,
( is_fun1661590463l_bool(cOMBS_350070575l_bool(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1001]),
[final] ).
cnf(i_0_1523,plain,
( is_fun1661590463l_bool(cOMBB_307249310e_bool(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1002]),
[final] ).
cnf(i_0_1524,plain,
( is_fun949378684l_bool(hAPP_f2117159681l_bool(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1003]),
[final] ).
cnf(i_0_1525,hypothesis,
( is_fun949378684l_bool(hAPP_f1631501043l_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1004]),
[final] ).
cnf(i_0_1526,hypothesis,
( is_fun949378684l_bool(hAPP_a85458249l_bool(X2,X1))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1005]),
[final] ).
cnf(i_0_1527,plain,
( is_fun949378684l_bool(image_112932426a_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1006]),
[final] ).
cnf(i_0_1528,plain,
( is_fun949378684l_bool(cOMBS_1035972772l_bool(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1007]),
[final] ).
cnf(i_0_1529,plain,
( is_fun949378684l_bool(cOMBB_2140588453a_bool(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1008]),
[final] ).
cnf(i_0_1530,plain,
( is_fun_pname_bool(hAPP_f759274231e_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1009]),
[final] ).
cnf(i_0_1531,plain,
( is_fun_pname_bool(hAPP_p61793385e_bool(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1010]),
[final] ).
cnf(i_0_1532,plain,
( is_fun_pname_bool(hAPP_a93125764e_bool(X2,X1))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1011]),
[final] ).
cnf(i_0_1533,plain,
( is_fun_pname_bool(image_1283814551_pname(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1012]),
[final] ).
cnf(i_0_1534,plain,
( is_fun_pname_bool(image_1854862208_pname(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1013]),
[final] ).
cnf(i_0_1535,plain,
( is_fun_pname_bool(image_pname_pname(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1014]),
[final] ).
cnf(i_0_1536,plain,
( is_fun_pname_bool(image_a_pname(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1015]),
[final] ).
cnf(i_0_1537,plain,
( is_fun_pname_bool(cOMBS_568398431l_bool(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1016]),
[final] ).
cnf(i_0_1538,plain,
( is_fun_pname_bool(cOMBB_647938656_pname(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1017]),
[final] ).
cnf(i_0_1539,plain,
( is_fun_a_bool(hAPP_f2050579477a_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1018]),
[final] ).
cnf(i_0_1540,plain,
( is_fun_a_bool(hAPP_p1534023578a_bool(X2,X1))
| ~ is_pname(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1019]),
[final] ).
cnf(i_0_1541,plain,
( is_fun_a_bool(hAPP_a_fun_a_bool(X2,X1))
| ~ is_a(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1020]),
[final] ).
cnf(i_0_1542,plain,
( is_fun_a_bool(image_876012084bool_a(X2,X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1021]),
[final] ).
cnf(i_0_1543,plain,
( is_fun_a_bool(image_fun_a_bool_a(X2,X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1022]),
[final] ).
cnf(i_0_1544,hypothesis,
( is_fun_a_bool(image_pname_a(X2,X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1023]),
[final] ).
cnf(i_0_1545,plain,
( is_fun_a_bool(image_a_a(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1024]),
[final] ).
cnf(i_0_1546,plain,
( is_fun_a_bool(cOMBS_a_bool_bool(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1025]),
[final] ).
cnf(i_0_1547,plain,
( is_fun_a_bool(cOMBB_bool_bool_a(X2,X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1026]),
[final] ).
cnf(i_0_1548,plain,
( hBOOL(X1)
| hBOOL(hAPP_bool_bool(fNot,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1027]),
[final] ).
cnf(i_0_1549,plain,
is_bool(hAPP_f1295398978l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1028]),
[final] ).
cnf(i_0_1550,plain,
is_bool(hAPP_f595608956l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1029]),
[final] ).
cnf(i_0_1551,plain,
is_bool(hAPP_f1363661463l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1030]),
[final] ).
cnf(i_0_1552,plain,
is_bool(hAPP_f937997336l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1031]),
[final] ).
cnf(i_0_1553,plain,
is_bool(hAPP_f389811538l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1032]),
[final] ).
cnf(i_0_1554,plain,
is_bool(hAPP_f292226953l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1033]),
[final] ).
cnf(i_0_1555,plain,
is_bool(hAPP_f1637334154l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1034]),
[final] ).
cnf(i_0_1556,plain,
is_bool(hAPP_f54304608l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1035]),
[final] ).
cnf(i_0_1557,hypothesis,
is_bool(hAPP_nat_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1036]),
[final] ).
cnf(i_0_1558,plain,
is_fun1661590463l_bool(image_1655916159e_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1037]),
[final] ).
cnf(i_0_1559,plain,
is_fun949378684l_bool(image_nat_fun_a_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1038]),
[final] ).
cnf(i_0_1560,plain,
is_fun_pname_bool(hAPP_n1025906991e_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1039]),
[final] ).
cnf(i_0_1561,plain,
is_fun_pname_bool(image_1604018183_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1040]),
[final] ).
cnf(i_0_1562,plain,
is_fun_pname_bool(image_1705983821_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1041]),
[final] ).
cnf(i_0_1563,plain,
is_fun_pname_bool(image_990671762_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1042]),
[final] ).
cnf(i_0_1564,plain,
is_fun_pname_bool(image_1921560913_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1043]),
[final] ).
cnf(i_0_1565,plain,
is_fun_pname_bool(image_nat_pname(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1044]),
[final] ).
cnf(i_0_1566,plain,
is_fun_a_bool(hAPP_nat_fun_a_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1045]),
[final] ).
cnf(i_0_1567,plain,
is_fun_a_bool(image_526090948bool_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1046]),
[final] ).
cnf(i_0_1568,plain,
is_fun_a_bool(image_349102846bool_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1047]),
[final] ).
cnf(i_0_1569,plain,
is_fun_a_bool(image_573985017bool_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1048]),
[final] ).
cnf(i_0_1570,plain,
is_fun_a_bool(image_fun_nat_bool_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1049]),
[final] ).
cnf(i_0_1571,plain,
is_fun_a_bool(image_nat_a(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1050]),
[final] ).
cnf(i_0_1572,hypothesis,
hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
inference(split_conjunct,[status(thm)],[conj_0]),
[final] ).
cnf(i_0_1573,plain,
hAPP_nat_nat(suc,X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_1051]),
[final] ).
cnf(i_0_1574,plain,
X1 != hAPP_nat_nat(suc,X1),
inference(split_conjunct,[status(thm)],[i_0_1052]),
[final] ).
cnf(i_0_1575,plain,
( is_fun1661590463l_bool(collec1974731493e_bool(X1))
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1053]),
[final] ).
cnf(i_0_1576,plain,
( is_fun949378684l_bool(p(X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1054]),
[final] ).
cnf(i_0_1577,plain,
( is_fun949378684l_bool(collect_fun_a_bool(X1))
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1055]),
[final] ).
cnf(i_0_1578,plain,
( is_fun_pname_bool(collect_pname(X1))
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1056]),
[final] ).
cnf(i_0_1579,plain,
( is_fun_a_bool(collect_a(X1))
| ~ is_fun_a_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1057]),
[final] ).
cnf(i_0_1580,plain,
( collec1974731493e_bool(X1) = X1
| ~ is_fun1661590463l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1058]),
[final] ).
cnf(i_0_1581,plain,
( collect_fun_a_bool(X1) = X1
| ~ is_fun949378684l_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1059]),
[final] ).
cnf(i_0_1582,plain,
( collect_pname(X1) = X1
| ~ is_fun_pname_bool(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1060]),
[final] ).
cnf(i_0_1583,plain,
is_pname(undefined_pname(pname)),
inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Com__Opname]),
[final] ).
cnf(i_0_1584,plain,
is_a(undefined_a(x_a)),
inference(split_conjunct,[status(thm)],[gsy_c_HOL_Oundefined_000t__a]),
[final] ).
cnf(i_0_1585,hypothesis,
is_pname(pn),
inference(split_conjunct,[status(thm)],[gsy_v_pn]),
[final] ).
cnf(i_0_1586,hypothesis,
is_fun1661590463l_bool(finite_finite_pname),
inference(split_conjunct,[status(thm)],[gsy_c_Finite__Set_Ofinite_000tc__Com__Opname]),
[final] ).
cnf(i_0_1587,plain,
is_fun949378684l_bool(finite_finite_a),
inference(split_conjunct,[status(thm)],[gsy_c_Finite__Set_Ofinite_000t__a]),
[final] ).
cnf(i_0_1588,hypothesis,
is_fun_pname_bool(u),
inference(split_conjunct,[status(thm)],[gsy_v_U]),
[final] ).
cnf(i_0_1589,hypothesis,
is_fun_a_bool(g),
inference(split_conjunct,[status(thm)],[gsy_v_G]),
[final] ).
cnf(i_0_1590,axiom,
X1 = X1 ).
cnf(i_0_1591,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1592,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1593,axiom,
( X1 != X2
| hAPP_fun_a_bool_bool(X1,X3) = hAPP_fun_a_bool_bool(X2,X3) ) ).
cnf(i_0_1594,axiom,
( X1 != X2
| hAPP_fun_a_bool_bool(X3,X1) = hAPP_fun_a_bool_bool(X3,X2) ) ).
cnf(i_0_1595,axiom,
( X1 != X2
| hAPP_f292226953l_bool(X1,X3) = hAPP_f292226953l_bool(X2,X3) ) ).
cnf(i_0_1596,axiom,
( X1 != X2
| hAPP_f292226953l_bool(X3,X1) = hAPP_f292226953l_bool(X3,X2) ) ).
cnf(i_0_1597,axiom,
( X1 != X2
| image_pname_a(X1,X3) = image_pname_a(X2,X3) ) ).
cnf(i_0_1598,axiom,
( X1 != X2
| image_pname_a(X3,X1) = image_pname_a(X3,X2) ) ).
cnf(i_0_1599,axiom,
( X1 != X2
| hAPP_f1664156314l_bool(X1,X3) = hAPP_f1664156314l_bool(X2,X3) ) ).
cnf(i_0_1600,axiom,
( X1 != X2
| hAPP_f1664156314l_bool(X3,X1) = hAPP_f1664156314l_bool(X3,X2) ) ).
cnf(i_0_1601,axiom,
( X1 != X2
| collect_pname(X1) = collect_pname(X2) ) ).
cnf(i_0_1602,axiom,
( X1 != X2
| hAPP_bool_bool(X1,X3) = hAPP_bool_bool(X2,X3) ) ).
cnf(i_0_1603,axiom,
( X1 != X2
| hAPP_bool_bool(X3,X1) = hAPP_bool_bool(X3,X2) ) ).
cnf(i_0_1604,axiom,
( X1 != X2
| hAPP_b589554111l_bool(X1,X3) = hAPP_b589554111l_bool(X2,X3) ) ).
cnf(i_0_1605,axiom,
( X1 != X2
| hAPP_b589554111l_bool(X3,X1) = hAPP_b589554111l_bool(X3,X2) ) ).
cnf(i_0_1606,axiom,
( X1 != X2
| hAPP_f1748468828l_bool(X1,X3) = hAPP_f1748468828l_bool(X2,X3) ) ).
cnf(i_0_1607,axiom,
( X1 != X2
| hAPP_f1748468828l_bool(X3,X1) = hAPP_f1748468828l_bool(X3,X2) ) ).
cnf(i_0_1608,axiom,
( X1 != X2
| hAPP_f1476298914l_bool(X1,X3) = hAPP_f1476298914l_bool(X2,X3) ) ).
cnf(i_0_1609,axiom,
( X1 != X2
| hAPP_f1476298914l_bool(X3,X1) = hAPP_f1476298914l_bool(X3,X2) ) ).
cnf(i_0_1610,axiom,
( X1 != X2
| hAPP_f198738859l_bool(X1,X3) = hAPP_f198738859l_bool(X2,X3) ) ).
cnf(i_0_1611,axiom,
( X1 != X2
| hAPP_f198738859l_bool(X3,X1) = hAPP_f198738859l_bool(X3,X2) ) ).
cnf(i_0_1612,axiom,
( X1 != X2
| hAPP_n1006566506l_bool(X1,X3) = hAPP_n1006566506l_bool(X2,X3) ) ).
cnf(i_0_1613,axiom,
( X1 != X2
| hAPP_n1006566506l_bool(X3,X1) = hAPP_n1006566506l_bool(X3,X2) ) ).
cnf(i_0_1614,axiom,
( X1 != X2
| hAPP_p393069232l_bool(X1,X3) = hAPP_p393069232l_bool(X2,X3) ) ).
cnf(i_0_1615,axiom,
( X1 != X2
| hAPP_p393069232l_bool(X3,X1) = hAPP_p393069232l_bool(X3,X2) ) ).
cnf(i_0_1616,axiom,
( X1 != X2
| hAPP_a_fun_bool_bool(X1,X3) = hAPP_a_fun_bool_bool(X2,X3) ) ).
cnf(i_0_1617,axiom,
( X1 != X2
| hAPP_a_fun_bool_bool(X3,X1) = hAPP_a_fun_bool_bool(X3,X2) ) ).
cnf(i_0_1618,axiom,
( X1 != X2
| hAPP_p1534023578a_bool(X1,X3) = hAPP_p1534023578a_bool(X2,X3) ) ).
cnf(i_0_1619,axiom,
( X1 != X2
| hAPP_p1534023578a_bool(X3,X1) = hAPP_p1534023578a_bool(X3,X2) ) ).
cnf(i_0_1620,axiom,
( X1 != X2
| hAPP_f54304608l_bool(X1,X3) = hAPP_f54304608l_bool(X2,X3) ) ).
cnf(i_0_1621,axiom,
( X1 != X2
| hAPP_f54304608l_bool(X3,X1) = hAPP_f54304608l_bool(X3,X2) ) ).
cnf(i_0_1622,axiom,
( X1 != X2
| collect_a(X1) = collect_a(X2) ) ).
cnf(i_0_1623,axiom,
( X1 != X2
| hAPP_nat_nat(X1,X3) = hAPP_nat_nat(X2,X3) ) ).
cnf(i_0_1624,axiom,
( X1 != X2
| hAPP_nat_nat(X3,X1) = hAPP_nat_nat(X3,X2) ) ).
cnf(i_0_1625,axiom,
( X1 != X2
| hAPP_nat_bool(X1,X3) = hAPP_nat_bool(X2,X3) ) ).
cnf(i_0_1626,axiom,
( X1 != X2
| hAPP_nat_bool(X3,X1) = hAPP_nat_bool(X3,X2) ) ).
cnf(i_0_1627,axiom,
( X1 != X2
| hAPP_f2009550088ol_nat(X1,X3) = hAPP_f2009550088ol_nat(X2,X3) ) ).
cnf(i_0_1628,axiom,
( X1 != X2
| hAPP_f2009550088ol_nat(X3,X1) = hAPP_f2009550088ol_nat(X3,X2) ) ).
cnf(i_0_1629,axiom,
( X1 != X2
| collect_fun_a_bool(X1) = collect_fun_a_bool(X2) ) ).
cnf(i_0_1630,axiom,
( X1 != X2
| hAPP_f621171935l_bool(X1,X3) = hAPP_f621171935l_bool(X2,X3) ) ).
cnf(i_0_1631,axiom,
( X1 != X2
| hAPP_f621171935l_bool(X3,X1) = hAPP_f621171935l_bool(X3,X2) ) ).
cnf(i_0_1632,axiom,
( X1 != X2
| hAPP_f55526627ol_nat(X1,X3) = hAPP_f55526627ol_nat(X2,X3) ) ).
cnf(i_0_1633,axiom,
( X1 != X2
| hAPP_f55526627ol_nat(X3,X1) = hAPP_f55526627ol_nat(X3,X2) ) ).
cnf(i_0_1634,axiom,
( X1 != X2
| collec1974731493e_bool(X1) = collec1974731493e_bool(X2) ) ).
cnf(i_0_1635,axiom,
( X1 != X2
| hAPP_f1935102916l_bool(X1,X3) = hAPP_f1935102916l_bool(X2,X3) ) ).
cnf(i_0_1636,axiom,
( X1 != X2
| hAPP_f1935102916l_bool(X3,X1) = hAPP_f1935102916l_bool(X3,X2) ) ).
cnf(i_0_1637,axiom,
( X1 != X2
| hAPP_fun_a_bool_nat(X1,X3) = hAPP_fun_a_bool_nat(X2,X3) ) ).
cnf(i_0_1638,axiom,
( X1 != X2
| hAPP_fun_a_bool_nat(X3,X1) = hAPP_fun_a_bool_nat(X3,X2) ) ).
cnf(i_0_1639,axiom,
( X1 != X2
| hAPP_f921600141ol_nat(X1,X3) = hAPP_f921600141ol_nat(X2,X3) ) ).
cnf(i_0_1640,axiom,
( X1 != X2
| hAPP_f921600141ol_nat(X3,X1) = hAPP_f921600141ol_nat(X3,X2) ) ).
cnf(i_0_1641,axiom,
( X1 != X2
| cOMBS_nat_bool_bool(X1,X3) = cOMBS_nat_bool_bool(X2,X3) ) ).
cnf(i_0_1642,axiom,
( X1 != X2
| cOMBS_nat_bool_bool(X3,X1) = cOMBS_nat_bool_bool(X3,X2) ) ).
cnf(i_0_1643,axiom,
( X1 != X2
| hAPP_a_fun_a_bool(X1,X3) = hAPP_a_fun_a_bool(X2,X3) ) ).
cnf(i_0_1644,axiom,
( X1 != X2
| hAPP_a_fun_a_bool(X3,X1) = hAPP_a_fun_a_bool(X3,X2) ) ).
cnf(i_0_1645,axiom,
( X1 != X2
| hAPP_pname_bool(X1,X3) = hAPP_pname_bool(X2,X3) ) ).
cnf(i_0_1646,axiom,
( X1 != X2
| hAPP_pname_bool(X3,X1) = hAPP_pname_bool(X3,X2) ) ).
cnf(i_0_1647,axiom,
( X1 != X2
| hAPP_a_bool(X1,X3) = hAPP_a_bool(X2,X3) ) ).
cnf(i_0_1648,axiom,
( X1 != X2
| hAPP_a_bool(X3,X1) = hAPP_a_bool(X3,X2) ) ).
cnf(i_0_1649,axiom,
( X1 != X2
| hAPP_f696928925ol_nat(X1,X3) = hAPP_f696928925ol_nat(X2,X3) ) ).
cnf(i_0_1650,axiom,
( X1 != X2
| hAPP_f696928925ol_nat(X3,X1) = hAPP_f696928925ol_nat(X3,X2) ) ).
cnf(i_0_1651,axiom,
( X1 != X2
| cOMBS_1187019125l_bool(X1,X3) = cOMBS_1187019125l_bool(X2,X3) ) ).
cnf(i_0_1652,axiom,
( X1 != X2
| cOMBS_1187019125l_bool(X3,X1) = cOMBS_1187019125l_bool(X3,X2) ) ).
cnf(i_0_1653,axiom,
( X1 != X2
| hAPP_f1637334154l_bool(X1,X3) = hAPP_f1637334154l_bool(X2,X3) ) ).
cnf(i_0_1654,axiom,
( X1 != X2
| hAPP_f1637334154l_bool(X3,X1) = hAPP_f1637334154l_bool(X3,X2) ) ).
cnf(i_0_1655,axiom,
( X1 != X2
| hAPP_f22106695ol_nat(X1,X3) = hAPP_f22106695ol_nat(X2,X3) ) ).
cnf(i_0_1656,axiom,
( X1 != X2
| hAPP_f22106695ol_nat(X3,X1) = hAPP_f22106695ol_nat(X3,X2) ) ).
cnf(i_0_1657,axiom,
( X1 != X2
| hAPP_pname_a(X1,X3) = hAPP_pname_a(X2,X3) ) ).
cnf(i_0_1658,axiom,
( X1 != X2
| hAPP_pname_a(X3,X1) = hAPP_pname_a(X3,X2) ) ).
cnf(i_0_1659,axiom,
( X1 != X2
| hAPP_f937997336l_bool(X1,X3) = hAPP_f937997336l_bool(X2,X3) ) ).
cnf(i_0_1660,axiom,
( X1 != X2
| hAPP_f937997336l_bool(X3,X1) = hAPP_f937997336l_bool(X3,X2) ) ).
cnf(i_0_1661,axiom,
( X1 != X2
| hAPP_f389811538l_bool(X1,X3) = hAPP_f389811538l_bool(X2,X3) ) ).
cnf(i_0_1662,axiom,
( X1 != X2
| hAPP_f389811538l_bool(X3,X1) = hAPP_f389811538l_bool(X3,X2) ) ).
cnf(i_0_1663,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1664,axiom,
( X1 != X2
| ~ is_pname(X1)
| is_pname(X2) ) ).
cnf(i_0_1665,axiom,
( X1 != X2
| ~ is_a(X1)
| is_a(X2) ) ).
cnf(i_0_1666,axiom,
( X1 != X2
| ~ is_fun_pname_bool(X1)
| is_fun_pname_bool(X2) ) ).
cnf(i_0_1667,axiom,
( X1 != X2
| ~ is_fun_a_bool(X1)
| is_fun_a_bool(X2) ) ).
cnf(i_0_1668,axiom,
( X1 != X2
| ~ is_fun1661590463l_bool(X1)
| is_fun1661590463l_bool(X2) ) ).
cnf(i_0_1669,axiom,
( X1 != X2
| ~ is_fun949378684l_bool(X1)
| is_fun949378684l_bool(X2) ) ).
cnf(i_0_1670,axiom,
( X1 != X2
| ~ is_bool(X1)
| is_bool(X2) ) ).
cnf(i_0_1590_001,axiom,
X1 = X1 ).
cnf(i_0_1591_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1592_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1593_004,axiom,
( X1 != X2
| hAPP_fun_a_bool_bool(X1,X3) = hAPP_fun_a_bool_bool(X2,X3) ) ).
cnf(i_0_1594_005,axiom,
( X1 != X2
| hAPP_fun_a_bool_bool(X3,X1) = hAPP_fun_a_bool_bool(X3,X2) ) ).
cnf(i_0_1595_006,axiom,
( X1 != X2
| hAPP_f292226953l_bool(X1,X3) = hAPP_f292226953l_bool(X2,X3) ) ).
cnf(i_0_1596_007,axiom,
( X1 != X2
| hAPP_f292226953l_bool(X3,X1) = hAPP_f292226953l_bool(X3,X2) ) ).
cnf(i_0_1597_008,axiom,
( X1 != X2
| image_pname_a(X1,X3) = image_pname_a(X2,X3) ) ).
cnf(i_0_1598_009,axiom,
( X1 != X2
| image_pname_a(X3,X1) = image_pname_a(X3,X2) ) ).
cnf(i_0_1599_010,axiom,
( X1 != X2
| hAPP_f1664156314l_bool(X1,X3) = hAPP_f1664156314l_bool(X2,X3) ) ).
cnf(i_0_1600_011,axiom,
( X1 != X2
| hAPP_f1664156314l_bool(X3,X1) = hAPP_f1664156314l_bool(X3,X2) ) ).
cnf(i_0_1601_012,axiom,
( X1 != X2
| collect_pname(X1) = collect_pname(X2) ) ).
cnf(i_0_1602_013,axiom,
( X1 != X2
| hAPP_bool_bool(X1,X3) = hAPP_bool_bool(X2,X3) ) ).
cnf(i_0_1603_014,axiom,
( X1 != X2
| hAPP_bool_bool(X3,X1) = hAPP_bool_bool(X3,X2) ) ).
cnf(i_0_1604_015,axiom,
( X1 != X2
| hAPP_b589554111l_bool(X1,X3) = hAPP_b589554111l_bool(X2,X3) ) ).
cnf(i_0_1605_016,axiom,
( X1 != X2
| hAPP_b589554111l_bool(X3,X1) = hAPP_b589554111l_bool(X3,X2) ) ).
cnf(i_0_1606_017,axiom,
( X1 != X2
| hAPP_f1748468828l_bool(X1,X3) = hAPP_f1748468828l_bool(X2,X3) ) ).
cnf(i_0_1607_018,axiom,
( X1 != X2
| hAPP_f1748468828l_bool(X3,X1) = hAPP_f1748468828l_bool(X3,X2) ) ).
cnf(i_0_1608_019,axiom,
( X1 != X2
| hAPP_f1476298914l_bool(X1,X3) = hAPP_f1476298914l_bool(X2,X3) ) ).
cnf(i_0_1609_020,axiom,
( X1 != X2
| hAPP_f1476298914l_bool(X3,X1) = hAPP_f1476298914l_bool(X3,X2) ) ).
cnf(i_0_1610_021,axiom,
( X1 != X2
| hAPP_f198738859l_bool(X1,X3) = hAPP_f198738859l_bool(X2,X3) ) ).
cnf(i_0_1611_022,axiom,
( X1 != X2
| hAPP_f198738859l_bool(X3,X1) = hAPP_f198738859l_bool(X3,X2) ) ).
cnf(i_0_1612_023,axiom,
( X1 != X2
| hAPP_n1006566506l_bool(X1,X3) = hAPP_n1006566506l_bool(X2,X3) ) ).
cnf(i_0_1613_024,axiom,
( X1 != X2
| hAPP_n1006566506l_bool(X3,X1) = hAPP_n1006566506l_bool(X3,X2) ) ).
cnf(i_0_1614_025,axiom,
( X1 != X2
| hAPP_p393069232l_bool(X1,X3) = hAPP_p393069232l_bool(X2,X3) ) ).
cnf(i_0_1615_026,axiom,
( X1 != X2
| hAPP_p393069232l_bool(X3,X1) = hAPP_p393069232l_bool(X3,X2) ) ).
cnf(i_0_1616_027,axiom,
( X1 != X2
| hAPP_a_fun_bool_bool(X1,X3) = hAPP_a_fun_bool_bool(X2,X3) ) ).
cnf(i_0_1617_028,axiom,
( X1 != X2
| hAPP_a_fun_bool_bool(X3,X1) = hAPP_a_fun_bool_bool(X3,X2) ) ).
cnf(i_0_1618_029,axiom,
( X1 != X2
| hAPP_p1534023578a_bool(X1,X3) = hAPP_p1534023578a_bool(X2,X3) ) ).
cnf(i_0_1619_030,axiom,
( X1 != X2
| hAPP_p1534023578a_bool(X3,X1) = hAPP_p1534023578a_bool(X3,X2) ) ).
cnf(i_0_1620_031,axiom,
( X1 != X2
| hAPP_f54304608l_bool(X1,X3) = hAPP_f54304608l_bool(X2,X3) ) ).
cnf(i_0_1621_032,axiom,
( X1 != X2
| hAPP_f54304608l_bool(X3,X1) = hAPP_f54304608l_bool(X3,X2) ) ).
cnf(i_0_1622_033,axiom,
( X1 != X2
| collect_a(X1) = collect_a(X2) ) ).
cnf(i_0_1623_034,axiom,
( X1 != X2
| hAPP_nat_nat(X1,X3) = hAPP_nat_nat(X2,X3) ) ).
cnf(i_0_1624_035,axiom,
( X1 != X2
| hAPP_nat_nat(X3,X1) = hAPP_nat_nat(X3,X2) ) ).
cnf(i_0_1625_036,axiom,
( X1 != X2
| hAPP_nat_bool(X1,X3) = hAPP_nat_bool(X2,X3) ) ).
cnf(i_0_1626_037,axiom,
( X1 != X2
| hAPP_nat_bool(X3,X1) = hAPP_nat_bool(X3,X2) ) ).
cnf(i_0_1627_038,axiom,
( X1 != X2
| hAPP_f2009550088ol_nat(X1,X3) = hAPP_f2009550088ol_nat(X2,X3) ) ).
cnf(i_0_1628_039,axiom,
( X1 != X2
| hAPP_f2009550088ol_nat(X3,X1) = hAPP_f2009550088ol_nat(X3,X2) ) ).
cnf(i_0_1629_040,axiom,
( X1 != X2
| collect_fun_a_bool(X1) = collect_fun_a_bool(X2) ) ).
cnf(i_0_1630_041,axiom,
( X1 != X2
| hAPP_f621171935l_bool(X1,X3) = hAPP_f621171935l_bool(X2,X3) ) ).
cnf(i_0_1631_042,axiom,
( X1 != X2
| hAPP_f621171935l_bool(X3,X1) = hAPP_f621171935l_bool(X3,X2) ) ).
cnf(i_0_1632_043,axiom,
( X1 != X2
| hAPP_f55526627ol_nat(X1,X3) = hAPP_f55526627ol_nat(X2,X3) ) ).
cnf(i_0_1633_044,axiom,
( X1 != X2
| hAPP_f55526627ol_nat(X3,X1) = hAPP_f55526627ol_nat(X3,X2) ) ).
cnf(i_0_1634_045,axiom,
( X1 != X2
| collec1974731493e_bool(X1) = collec1974731493e_bool(X2) ) ).
cnf(i_0_1635_046,axiom,
( X1 != X2
| hAPP_f1935102916l_bool(X1,X3) = hAPP_f1935102916l_bool(X2,X3) ) ).
cnf(i_0_1636_047,axiom,
( X1 != X2
| hAPP_f1935102916l_bool(X3,X1) = hAPP_f1935102916l_bool(X3,X2) ) ).
cnf(i_0_1637_048,axiom,
( X1 != X2
| hAPP_fun_a_bool_nat(X1,X3) = hAPP_fun_a_bool_nat(X2,X3) ) ).
cnf(i_0_1638_049,axiom,
( X1 != X2
| hAPP_fun_a_bool_nat(X3,X1) = hAPP_fun_a_bool_nat(X3,X2) ) ).
cnf(i_0_1639_050,axiom,
( X1 != X2
| hAPP_f921600141ol_nat(X1,X3) = hAPP_f921600141ol_nat(X2,X3) ) ).
cnf(i_0_1640_051,axiom,
( X1 != X2
| hAPP_f921600141ol_nat(X3,X1) = hAPP_f921600141ol_nat(X3,X2) ) ).
cnf(i_0_1641_052,axiom,
( X1 != X2
| cOMBS_nat_bool_bool(X1,X3) = cOMBS_nat_bool_bool(X2,X3) ) ).
cnf(i_0_1642_053,axiom,
( X1 != X2
| cOMBS_nat_bool_bool(X3,X1) = cOMBS_nat_bool_bool(X3,X2) ) ).
cnf(i_0_1643_054,axiom,
( X1 != X2
| hAPP_a_fun_a_bool(X1,X3) = hAPP_a_fun_a_bool(X2,X3) ) ).
cnf(i_0_1644_055,axiom,
( X1 != X2
| hAPP_a_fun_a_bool(X3,X1) = hAPP_a_fun_a_bool(X3,X2) ) ).
cnf(i_0_1645_056,axiom,
( X1 != X2
| hAPP_pname_bool(X1,X3) = hAPP_pname_bool(X2,X3) ) ).
cnf(i_0_1646_057,axiom,
( X1 != X2
| hAPP_pname_bool(X3,X1) = hAPP_pname_bool(X3,X2) ) ).
cnf(i_0_1647_058,axiom,
( X1 != X2
| hAPP_a_bool(X1,X3) = hAPP_a_bool(X2,X3) ) ).
cnf(i_0_1648_059,axiom,
( X1 != X2
| hAPP_a_bool(X3,X1) = hAPP_a_bool(X3,X2) ) ).
cnf(i_0_1649_060,axiom,
( X1 != X2
| hAPP_f696928925ol_nat(X1,X3) = hAPP_f696928925ol_nat(X2,X3) ) ).
cnf(i_0_1650_061,axiom,
( X1 != X2
| hAPP_f696928925ol_nat(X3,X1) = hAPP_f696928925ol_nat(X3,X2) ) ).
cnf(i_0_1651_062,axiom,
( X1 != X2
| cOMBS_1187019125l_bool(X1,X3) = cOMBS_1187019125l_bool(X2,X3) ) ).
cnf(i_0_1652_063,axiom,
( X1 != X2
| cOMBS_1187019125l_bool(X3,X1) = cOMBS_1187019125l_bool(X3,X2) ) ).
cnf(i_0_1653_064,axiom,
( X1 != X2
| hAPP_f1637334154l_bool(X1,X3) = hAPP_f1637334154l_bool(X2,X3) ) ).
cnf(i_0_1654_065,axiom,
( X1 != X2
| hAPP_f1637334154l_bool(X3,X1) = hAPP_f1637334154l_bool(X3,X2) ) ).
cnf(i_0_1655_066,axiom,
( X1 != X2
| hAPP_f22106695ol_nat(X1,X3) = hAPP_f22106695ol_nat(X2,X3) ) ).
cnf(i_0_1656_067,axiom,
( X1 != X2
| hAPP_f22106695ol_nat(X3,X1) = hAPP_f22106695ol_nat(X3,X2) ) ).
cnf(i_0_1657_068,axiom,
( X1 != X2
| hAPP_pname_a(X1,X3) = hAPP_pname_a(X2,X3) ) ).
cnf(i_0_1658_069,axiom,
( X1 != X2
| hAPP_pname_a(X3,X1) = hAPP_pname_a(X3,X2) ) ).
cnf(i_0_1659_070,axiom,
( X1 != X2
| hAPP_f937997336l_bool(X1,X3) = hAPP_f937997336l_bool(X2,X3) ) ).
cnf(i_0_1660_071,axiom,
( X1 != X2
| hAPP_f937997336l_bool(X3,X1) = hAPP_f937997336l_bool(X3,X2) ) ).
cnf(i_0_1661_072,axiom,
( X1 != X2
| hAPP_f389811538l_bool(X1,X3) = hAPP_f389811538l_bool(X2,X3) ) ).
cnf(i_0_1662_073,axiom,
( X1 != X2
| hAPP_f389811538l_bool(X3,X1) = hAPP_f389811538l_bool(X3,X2) ) ).
cnf(i_0_1663_074,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1664_075,axiom,
( X1 != X2
| ~ is_pname(X1)
| is_pname(X2) ) ).
cnf(i_0_1665_076,axiom,
( X1 != X2
| ~ is_a(X1)
| is_a(X2) ) ).
cnf(i_0_1666_077,axiom,
( X1 != X2
| ~ is_fun_pname_bool(X1)
| is_fun_pname_bool(X2) ) ).
cnf(i_0_1667_078,axiom,
( X1 != X2
| ~ is_fun_a_bool(X1)
| is_fun_a_bool(X2) ) ).
cnf(i_0_1668_079,axiom,
( X1 != X2
| ~ is_fun1661590463l_bool(X1)
| is_fun1661590463l_bool(X2) ) ).
cnf(i_0_1669_080,axiom,
( X1 != X2
| ~ is_fun949378684l_bool(X1)
| is_fun949378684l_bool(X2) ) ).
cnf(i_0_1670_081,axiom,
( X1 != X2
| ~ is_bool(X1)
| is_bool(X2) ) ).
cnf(i_0_1671,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,[],[1117]) ).
cnf(i_0_1672,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,[],[1118]) ).
cnf(i_0_1673,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,[],[1132]) ).
cnf(i_0_1674,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,[],[1133]) ).
cnf(i_0_1675,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,[],[1137]) ).
cnf(i_0_1676,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,[],[1138]) ).
cnf(i_0_1677,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,[],[1174]) ).
cnf(i_0_1678,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,[],[1182]) ).
cnf(i_0_1679,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,[],[1183]) ).
cnf(i_0_1680,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,[],[1297]) ).
cnf(i_0_1681,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,[],[1304]) ).
cnf(i_0_1682,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,[],[1311]) ).
cnf(i_0_1683,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X1),X1)),
inference(equality_inference,[],[1474]) ).
cnf(i_0_1684,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(equality_inference,[],[1478]) ).
cnf(i_0_1685,plain,
hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X1),X1)),
inference(equality_inference,[],[1480]) ).
cnf(i_0_1686,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X1),X1)),
inference(equality_inference,[],[1481]) ).
cnf(i_0_1687,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X1)),
inference(equality_inference,[],[1484]) ).
cnf(i_0_1688,plain,
hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X1),X1)),
inference(equality_inference,[],[1485]) ).
cnf(i_0_1689,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X1),X1)),
inference(equality_inference,[],[1486]) ).
cnf(i_0_1690,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(equality_inference,[],[1489]) ).
cnf(i_0_1691,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X1)),
inference(equality_inference,[],[1490]) ).
cnf(i_0_1692,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X1),X1)),
inference(equality_inference,[],[1491]) ).
cnf(i_0_1693,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(equality_inference,[],[1492]) ).
cnf(i_0_1694,plain,
hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X1),X1)),
inference(equality_inference,[],[1493]) ).
cnf(i_0_1695,plain,
hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X1),X1)),
inference(equality_inference,[],[1494]) ).
cnf(i_0_1696,plain,
X1 = X1,
inference(equality_inference,[],[1513]) ).
cnf(i_0_1697,plain,
is_a(esk11_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_1061,i_0_1425]) ).
cnf(i_0_1698,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| is_a(esk11_2(X2,X1)) ),
inference(rename_variables,[],[i_0_1425]) ).
cnf(i_0_1699,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_1061,i_0_1425,i_0_1489]) ).
cnf(i_0_1700,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1489]) ).
cnf(i_0_1701,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_1061,i_0_1425,i_0_1489,i_0_1490]) ).
cnf(i_0_1702,plain,
( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X1),X2))
| X2 != X1 ),
inference(rename_variables,[],[i_0_1490]) ).
cnf(i_0_1703,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_1061,i_0_1503,i_0_1425,i_0_1489,i_0_1490,i_0_1158]) ).
cnf(i_0_1704,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_1158]) ).
cnf(i_0_1705,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),na)),
inference(scs_inference,[],[i_0_1061,i_0_1503,i_0_1308,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255]) ).
cnf(i_0_1706,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_1255]) ).
cnf(i_0_1707,plain,
hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(X1,X2)),image_pname_a(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)))))),
inference(scs_inference,[],[i_0_1061,i_0_1503,i_0_1308,i_0_1119,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267]) ).
cnf(i_0_1708,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_1267]) ).
cnf(i_0_1709,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_1061,i_0_1503,i_0_1308,i_0_1119,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268]) ).
cnf(i_0_1710,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_1268]) ).
cnf(i_0_1711,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),hAPP_nat_nat(suc,X1))),
inference(scs_inference,[],[i_0_1061,i_0_1502,i_0_1503,i_0_1308,i_0_1119,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268,i_0_1271]) ).
cnf(i_0_1712,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(rename_variables,[],[i_0_1502]) ).
cnf(i_0_1713,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_1271]) ).
cnf(i_0_1714,plain,
hAPP_nat_nat(suc,X1) = hAPP_nat_nat(suc,esk14_2(X1,hAPP_nat_nat(suc,X1))),
inference(scs_inference,[],[i_0_1061,i_0_1502,i_0_1712,i_0_1503,i_0_1308,i_0_1119,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268,i_0_1271,i_0_1298]) ).
cnf(i_0_1715,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X1)),
inference(rename_variables,[],[i_0_1502]) ).
cnf(i_0_1716,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X2))
| X2 = hAPP_nat_nat(suc,esk14_2(X1,X2)) ),
inference(rename_variables,[],[i_0_1298]) ).
cnf(i_0_1717,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_1061,i_0_1502,i_0_1712,i_0_1503,i_0_1312,i_0_1308,i_0_1119,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268,i_0_1271,i_0_1298,i_0_1329]) ).
cnf(i_0_1718,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X1)),X1)),
inference(rename_variables,[],[i_0_1312]) ).
cnf(i_0_1719,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_1329]) ).
cnf(i_0_1720,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_1061,i_0_1502,i_0_1712,i_0_1715,i_0_1503,i_0_1312,i_0_1308,i_0_1119,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268,i_0_1271,i_0_1298,i_0_1329,i_0_1331]) ).
cnf(i_0_1721,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_1331]) ).
cnf(i_0_1722,plain,
hAPP_nat_nat(minus_minus_nat(X1),hAPP_nat_nat(minus_minus_nat(X1),X1)) = X1,
inference(scs_inference,[],[i_0_1061,i_0_1502,i_0_1712,i_0_1715,i_0_1503,i_0_1312,i_0_1308,i_0_1119,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268,i_0_1271,i_0_1298,i_0_1329,i_0_1331,i_0_1360]) ).
cnf(i_0_1723,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_1360]) ).
cnf(i_0_1724,plain,
hBOOL(hAPP_fun_a_bool_bool(p(X1),X1)),
inference(scs_inference,[],[i_0_1061,i_0_1500,i_0_1502,i_0_1712,i_0_1715,i_0_1503,i_0_1312,i_0_1308,i_0_1119,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268,i_0_1271,i_0_1298,i_0_1329,i_0_1331,i_0_1360,i_0_1362]) ).
cnf(i_0_1725,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_1362]) ).
cnf(i_0_1726,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,na),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
inference(scs_inference,[],[i_0_1061,i_0_1500,i_0_1502,i_0_1712,i_0_1715,i_0_1503,i_0_1312,i_0_1308,i_0_1119,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268,i_0_1271,i_0_1298,i_0_1329,i_0_1331,i_0_1360,i_0_1362,i_0_1363]) ).
cnf(i_0_1727,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_1363]) ).
cnf(i_0_1728,plain,
hBOOL(hAPP_pname_bool(u,pn)),
inference(scs_inference,[],[i_0_1061,i_0_1500,i_0_1502,i_0_1712,i_0_1715,i_0_1503,i_0_1312,i_0_1308,i_0_1119,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268,i_0_1271,i_0_1298,i_0_1329,i_0_1331,i_0_1360,i_0_1362,i_0_1363,i_0_1365]) ).
cnf(i_0_1729,plain,
( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X1),X2))
| hBOOL(hAPP_pname_bool(X2,X1)) ),
inference(rename_variables,[],[i_0_1365]) ).
cnf(i_0_1730,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_1061,i_0_1500,i_0_1502,i_0_1712,i_0_1715,i_0_1503,i_0_1312,i_0_1308,i_0_1119,i_0_1122,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268,i_0_1271,i_0_1298,i_0_1329,i_0_1331,i_0_1360,i_0_1362,i_0_1363,i_0_1365,i_0_1366]) ).
cnf(i_0_1731,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_1366]) ).
cnf(i_0_1732,plain,
~ hBOOL(hAPP_a_bool(g,hAPP_pname_a(mgt_call,pn))),
inference(scs_inference,[],[i_0_1061,i_0_1500,i_0_1502,i_0_1712,i_0_1715,i_0_1503,i_0_1312,i_0_1308,i_0_1330,i_0_1119,i_0_1122,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268,i_0_1271,i_0_1298,i_0_1329,i_0_1331,i_0_1360,i_0_1362,i_0_1363,i_0_1365,i_0_1366,i_0_1381]) ).
cnf(i_0_1733,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_1381]) ).
cnf(i_0_1734,plain,
hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)) != na,
inference(scs_inference,[],[i_0_1061,i_0_1500,i_0_1502,i_0_1712,i_0_1715,i_0_1503,i_0_1312,i_0_1308,i_0_1330,i_0_1119,i_0_1122,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268,i_0_1271,i_0_1298,i_0_1329,i_0_1331,i_0_1360,i_0_1362,i_0_1363,i_0_1365,i_0_1366,i_0_1381,i_0_1492]) ).
cnf(i_0_1735,plain,
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X1),X2))
| X1 != X2 ),
inference(rename_variables,[],[i_0_1492]) ).
cnf(i_0_1736,plain,
X1 = esk14_2(X1,hAPP_nat_nat(suc,X1)),
inference(scs_inference,[],[i_0_1061,i_0_1500,i_0_1502,i_0_1712,i_0_1715,i_0_1503,i_0_1312,i_0_1308,i_0_1330,i_0_1119,i_0_1122,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268,i_0_1271,i_0_1298,i_0_1329,i_0_1331,i_0_1360,i_0_1362,i_0_1363,i_0_1365,i_0_1366,i_0_1381,i_0_1492,i_0_1513]) ).
cnf(i_0_1737,plain,
( hAPP_nat_nat(suc,X1) != hAPP_nat_nat(suc,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_1513]) ).
cnf(i_0_1738,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_1061,i_0_1426,i_0_1500,i_0_1502,i_0_1712,i_0_1715,i_0_1503,i_0_1312,i_0_1308,i_0_1330,i_0_1119,i_0_1122,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268,i_0_1271,i_0_1298,i_0_1329,i_0_1331,i_0_1360,i_0_1362,i_0_1363,i_0_1365,i_0_1366,i_0_1381,i_0_1492,i_0_1513,i_0_1591]) ).
cnf(i_0_1739,plain,
$false,
inference(scs_inference,[],[i_0_1061,i_0_1426,i_0_1500,i_0_1502,i_0_1712,i_0_1715,i_0_1422,i_0_1503,i_0_1312,i_0_1308,i_0_1330,i_0_1119,i_0_1122,i_0_1425,i_0_1489,i_0_1490,i_0_1158,i_0_1255,i_0_1267,i_0_1268,i_0_1271,i_0_1298,i_0_1329,i_0_1331,i_0_1360,i_0_1362,i_0_1363,i_0_1365,i_0_1366,i_0_1381,i_0_1492,i_0_1513,i_0_1591,i_0_1078]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW473+1 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n002.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 06:55:46 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.88/1.73 % Version : CSE_E---1.7
% 0.88/1.73 % Problem : theBenchmark.p
% 0.88/1.73 % SZS status Theorem for theBenchmark.p
% 0.88/1.73 % SZS output start CNFRefutation
% See solution above
% 1.08/1.95 % Total time : 1.379s
%------------------------------------------------------------------------------